**Module 01, Mathematics.**

**1.1 Arithmetic.**
Question
Number. 1. A car travels 24 miles in 45 minutes. What is its average
speed?

Option
A. 32 mph.

Option
B. 36 mph.

Option
C. 18 mph.

Correct
Answer is. 32 mph.

Explanation. 45
minutes = 3/4 hour. Speed = distance / time = 24/3/4 = 24 * 4/3 =
32.

Question
Number. 2. Evaluate. Yes

Option
A. 4 ½.

Option
B. 3 ½.

Option
C. 4.

Correct
Answer is. 3 ½.

Explanation.

Question
Number. 3. 15.4/2 - 2*(6.2 - 15.6).

Option
A. 11.1.

Option
B. 26.5.

Option
C. -11.1.

Correct
Answer is. 26.5.

Explanation. 7.7-2(-9.4)7.7-(-18.8)7.7
+ 18.8= 26.5.

Question
Number. 4. A cuboid has dimensions of 4 cm, 6 cm and 12 cm. What is
its volume?.

Option
A. 0.028 m

^{3 }.
Option
B. 2.88 m

^{3 }.
Option
C. 0.000288 m

^{3 }.
Correct
Answer is. 2.88 m

^{3 }.
Explanation. 4
* 6 * 12 = 288, then convert the cm to metres (divide 288 by 100, 3
times).

Question
Number. 5. What is a scalene triange?.

Option
A. 2 sides unequal.

Option
B. All 3 sides unequal.

Option
C. 2 sides equal.

Correct
Answer is. All 3 sides unequal.

Explanation.

Question
Number. 6. Work out the following sum: 4 {2 (5-1) -3} + 8.

Option
A. 28

Option
B. 37.

Option
C. 54.

Correct
Answer is. 28

Explanation. Start
at the inner brackets first, and then work outwards.

Question
Number. 7. A rectangle is 11cm x 120cm. What is its area in m

^{2 }?.
Option
A. 0.132.

Option
B. 1320.

Option
C. 13.2.

Correct
Answer is. 0.132.

Explanation. 100cm
in 1m, so divide 1320 by 100 twice (since it is area).

Question
Number. 8. The surface area of a cone whose height is 10 cm and
diameter is 8 cm is.

Option
A. 40π cm

^{2 }.
Option
B. 120π cm

^{2 }.
Option
C. 80π cm2.

Correct
Answer is. 40π cm

^{2 }.
Explanation. Surface
area of a cone = π * r * l = π x 8/2 * 10 = 40π.

Question
Number. 9. 4 3/8 – 2 1/4 + 1/8 =.

Option
A. 2.25

Option
B. 2.5.

Option
C. 2 1/8

Correct
Answer is. 2 1/4

Explanation. Work
out the whole numbers separate to the fractions.Remember that 1/4 is
2/8.

Question
Number. 10. 11/16 + 5/8 =.

Option
A. 55/128.

Option
B. 21/16.

Option
C. 10/11.

Correct
Answer is. 21/16.

Explanation. 5/8
= 10/16. 11/16 + 10/16 = 21/16.

Question
Number. 11. 3/4 multiplied by 0.82 is equal to.

Option
A. 1.23.

Option
B. 0.615.

Option
C. 2.46.

Correct
Answer is. 0.615.

Explanation. 3/4
= 0.75. Approximate, 0.8 * 0.75 must be less than 0.75.

Question
Number. 12. 7/6 can be expressed as.

Option
A. 1.166.

Option
B. 2.6.

Option
C. 1.6.

Correct
Answer is. 1.166.

Explanation. 6/6
would be 1. So 7/6 is just slightly bigger than 1.

Question
Number. 13. The ratio of 6:5 can be expressed as.

Option
A. 24:20.

Option
B. 20:25.

Option
C. 10:16.

Correct
Answer is. 24:20.

Explanation. 6:5,
multiply each by 4.

Question
Number. 14. 14

^{3 }can be expressed as.
Option
A. 14 * 14 * 14.

Option
B. 14 x

^{3 }.
Option
C. 14 + 14 + 14.

Correct
Answer is. 14 * 14 * 14.

Explanation. Power'
means the number 'times' itself.

Question
Number. 15. 0.0000413 can be written as.

Option
A. 0.413 x 10

^{-7. }
Option
B. 413 x 10

^{-7. }
Option
C. 4.13 x 10

^{-7. }
Correct
Answer is. 413 x 10

^{-7. }
Explanation. 10

^{-7 }means move the decimal place 7 places to the left. Try it on each answer and see what comes out.
Question
Number. 16. 5/8 + 3/4 =.

Option
A. 11/4.

Option
B. 8/8.

Option
C. 11/8.

Correct
Answer is. 11/8.

Explanation. 5/8
+ 3/4 = 5/8 + 6/8 (LCD = 8) = 11/8.

Question
Number. 17. The Lowest Common Denominator for the problem below is
1/6 + 1/5 + 1/17 + 1/2.

Option
A. 510.

Option
B. 1020.

Option
C. 17.

Correct
Answer is. 510.

Explanation. The
LCD is the lowest of the answers which all the denominators can be
divided into.

Question
Number. 18. The formula for calculating the area of a right angled
triangle is.

Option
A. ½ height + base.

Option
B. ½ (base * height).

Option
C. ½ base / height.

Correct
Answer is. ½ (base * height).

Explanation. Area
of 'any' triangle is 1/2 base x height. Can also be written 1/2 (base
* height).

Question
Number. 19. The area of a circle whose circumference is given as 12cm
is approximately.

Option
A. 3.8 sq.cm.

Option
B. 11.3 sq.cm.

Option
C. 38 sq cm.

Correct
Answer is. 11.3 sq.cm.

Explanation. Area
= Circumference squared / 4π = 144 / (4 * 3.14) =.

Question
Number. 20. Area of a right circular cone of base radius r, and
height l, is.

Option
A. 2/3 (π * r * l).

Option
B. (π * r * l) + 2π * r * r.

Option
C. π * r * l.

Correct
Answer is. π * r * l.

Explanation. Area
of a cone is π * r * l.

Question
Number. 21. Determine (+ 3)-(-4).

Option
A. -1.

Option
B. -7.

Option
C. +7.

Correct
Answer is. +7.

Explanation. A
minus number, when subtracted, becomes a plus (a minus and a minus
makes a plus).

Question
Number. 22. To convert imperial gallons to litres, multiply by.

Option
A. 4.5.

Option
B. 5.4.

Option
C. 4.7.

Correct
Answer is. 4.5.

Explanation. There
are 4.54 litres in 1 British (Imperial) gallon.

Question
Number. 23. Express 9/20 as a percentage.

Option
A. 45%.

Option
B. 40%.

Option
C. 47%.

Correct
Answer is. 45%.

Explanation. Multiply
the top and bottom to make the denominator into 100 (*5 in this
case). Then the numerator is the percentage.

Question
Number. 24. To find the area of a circle, multiply.

Option
A. twice the radius by π.

Option
B. the square of the circumference by the radius.

Option
C. the square of the radius by π.

Correct
Answer is. the square of the radius by π.

Explanation. Area
= π x radius

^{2. }
Question
Number. 25. How many centimetres is in an inch?.

Option
A. 25.4.

Option
B. 2.54.

Option
C. 0.254.

Correct
Answer is. 2.54.

Explanation. 1
inch = 2.54 cm.

Question
Number. 26. Find the lowest common multiple of 6; 7; 8.

Option
A. 84.

Option
B. 336.

Option
C. 168.

Correct
Answer is. 168.

Explanation. The
LCM is the lowest number that all 3 can be divided into.

Question
Number. 27. What torque loading would you apply to a nut if the force
is 50 lbs, exerted 2 feet from its axis?.

Option
A. 600 lbs.ft.

Option
B. 100 lbs.ft.

Option
C. 251 lbs.ft.

Correct
Answer is. 100 lbs.ft.

Explanation. Torque
= force x distance.

Question
Number. 28. The formula for calculating the torque loading on a nut
or bolt is.

Option
A. Force used x lever length of the spanner.

Option
B. Lever length of the spanner / Threads per inch.

Option
C. Force used x diameter of the bolt.

Correct
Answer is. Force used x lever length of the spanner.

Explanation. Torque
= force x distance.

Question
Number. 29. How is the area of a circle calculated? (r=radius,
d=diameter).

Option
A. 2 x 3.142 x r.

Option
B. d

^{2 }x 3.142.
Option
C. r

^{2 }x 3.142.
Correct
Answer is. r

^{2 }x 3.142.
Explanation. Area
= πr

^{2 }.
Question
Number. 30. Determine the following : 9/4 + 5/12 + 5 1/8.

Option
A. 2 25/24.

Option
B. 4 1/12.

Option
C. 7 19/24.

Correct
Answer is. 4 1/24.

Explanation. 54/24
+ 10/24 + 5 3/24 = 7 19/24

Question
Number. 31. The specific torque loading for a bolt is 50 lbs.ins but
an extension of 2 is needed to reach the bolt in addition to the 8
torque wrench. What will the actual reading?.

Option
A. 60 lb.ins.

Option
B. 54 lb.ins.

Option
C. 40 lb.ins.

Correct
Answer is. 40 lb.ins.

Explanation. New
torque reading = desired torque x L/(x + L). 50 x 8/10 = 40 lb.ins.

Question
Number. 32. Express the fraction 7/8 as a decimal.

Option
A. 0.785.

Option
B. 0.878.

Option
C. 0.875.

Correct
Answer is. 0.875.

Explanation. Use
long division.

Question
Number. 33. Determine 0.75 x 0.003.

Option
A. 0.225.

Option
B. 0.00225.

Option
C. 0.0225.

Correct
Answer is. 0.00225.

Explanation. Easiest
way is to multiply by 0.001 (0.75 x 0.001 = 0.00075) then multiply by
3. (75 x 3 = 225, so 0.00075 x 3 = 0.00225).

Question
Number. 34. Convert 162 knots to MPH.

Option
A. 186 mph.

Option
B. 176 mph.

Option
C. 196 mph.

Correct
Answer is. 186 mph.

Explanation. 1
knots = 1.15 mph, 162 x 1.15 = 186 mph.

Question
Number. 35. To convert inches to millimetres, it is necessary to.

Option
A. divide by 25.4.

Option
B. multiply by 25.4.

Option
C. multiply by 2.54.

Correct
Answer is. multiply by 25.4.

Explanation. There
are 25.4 mm in 1 inch.

Question
Number. 36. 3/4 x 82 =.

Option
A. 123.

Option
B. 61.5.

Option
C. 81.5.

Correct
Answer is. 61.5.

Explanation. Estimate
3/4 of 82.

Question
Number. 37. A circular patch is held together by seven equally spaced
rivets. What is their angular spacing?.

Option
A. 51.50°.

Option
B. 52°.

Option
C. 51.43°.

Correct
Answer is. 51.43°.

Explanation. 360/7
= 51.43 degrees.

Question
Number. 38. Add together; 3/4, 5/16, 7/8 and 0.375.

Option
A. 2 5/16.

Option
B. 2 1/8.

Option
C. 2 1/4.

Correct
Answer is. 2 5/16.

Explanation. 0.375
= 3/8. 3/4 + 5/16 + 7/8 + 3/8 (LCD = 16) 12/16 + 5/16 + 14/16 + 6/16
= 37/16 = 2 5/16.

Question
Number. 39. To convert pounds of fuel into kilograms, it is necessary
to.

Option
A. divide by 0.4536.

Option
B. multiply by 4536.

Option
C. multiply by 0.4536.

Correct
Answer is. multiply by 0.4536.

Explanation. 2.2
lb = 1 kg. 1lb = 0.4536 kg.

Question
Number. 40. If resin to hardener is used in the ratio of 1000:45, how
much hardener is used with 60 grams of resin?.

Option
A. 145 grams.

Option
B. 47 grams.

Option
C. 2.7 grams.

Correct
Answer is. 2.7 grams.

Explanation. Ratio
of hardener to resin is 45:1000, or 0.45:10. For 60 gms of resin, use
0.45 * 6 hardener = 2.7 gms.

Question
Number. 41. Determine the following 11/16 + 5/8.

Option
A. 11/10.

Option
B. 1 55/128.

Option
C. 1 5/16.

Correct
Answer is. 1 5/16.

Explanation. 11/16
+ 5/8 (LCD = 16) 11/16 + 10/16 = 21/16 = 1 5/16.

Question
Number. 42. 6 mm is equal to.

Option
A. 0.625 inches.

Option
B. 0.236 inches.

Option
C. 0.375 inches.

Correct
Answer is. 0.236 inches.

Explanation. 6mm
= 0.6cm. So, 0.6/2.54 = 0.236

Question
Number. 43. Weight is equal to.

Option
A. volume x gravity.

Option
B. mass x acceleration.

Option
C. mass x gravity.

Correct
Answer is. mass x gravity.

Explanation. Weight
= mass x gravity.

Question
Number. 44. 8 + 4[5 x 2 (5-9/3)] =.

Option
A. 88.

Option
B. 12.

Option
C. 48.

Correct
Answer is. 88.

Explanation. Work
from the inner brackets - outwards.

Question
Number. 45. To convert gallons to litres.

Option
A. multiply by 4.55.

Option
B. multiply by 0.00455.

Option
C. multiply by 0.568.

Correct
Answer is. multiply by 4.55.

Explanation. 1
gallon = 4.55 litres.

Question
Number. 46. A cylinder has a diameter of 20 cm and a length of 20 cm,
what is its volume?.

Option
A. 1240 cm

^{3 }.
Option
B. 6200 cm

^{3 }
Option
C. 400 cm

^{3 }.
Correct
Answer is. 6200 cm

^{3 }.
Explanation. Volume
of a cylinder = π x r2 x length of cylinder = π x 100 x 20 = 3.1 x
100 x 20 = 6200.

Question
Number. 47. 31/8 – 11/5 =.

Option
A. 23/40.

Option
B. 13/40.

Option
C. 67/40.

Correct
Answer is. 67/40.

Explanation. 155/40
- 88/40 = 67/40

Question
Number. 48. What is the formula for calculating the curved area of a
cone?.

Option
A. π x radius2 x height.

Option
B. π x radius x height.

Option
C. 2/3 x π x radius x height.

Correct
Answer is. π x radius x height.

Explanation. π
x radius x height.

Question
Number. 49. Determine 10 ( 23) + 10 ( 25).

Option
A. 520.

Option
B. 320

Option
C. 480.

Correct
Answer is. 480.

Explanation. Work
out the contents of the brackets in this:- (10 x 23) + (10 x 25).

Question
Number. 50. One radian is equal to.

Option
A. 90°.

Option
B. 75°.

Option
C. 57.5°.

Correct
Answer is. 57.5°.

Explanation. There
are 2π radians in one complete circle (360°). So one radian is
360/6.28 = 57.5°.

Question
Number. 51. The surface area of a cylinder of diameter 10 cm and
height 10 cm, is.

Option
A. 80π.

Option
B. 50π.

Option
C. 100π.

Correct
Answer is. 100π.

Explanation. Area
= circumference x height = π x d x h = 10 x 10 x π.

Question
Number. 52. A parallelogram has a base 120cm and height 11 cm. What
is the area?.

Option
A. 0.0132 m

^{2 }.
Option
B. 1.32 m

^{2 }.
Option
C. 1.32 m

^{2 }.
Correct
Answer is. 0.132 m2.

Explanation. Area
of a parallelogram = base x height = 1.2 m * 0.11 m = 0.1322.

Question
Number. 53. The area of this shape is calculated by.

Option
A. Perimeter squared.

Option
B. ½ Base * Height.

Option
C. Base * Height.

Correct
Answer is. Base * Height.

Explanation. It
does not matter which way around the base and the height go when they
are multiplied together.

Question
Number. 54. The area of the shape is calculated by.

Option
A. ½ height * base.

Option
B. ½ base * ½ height.

Option
C. ½ base * ½ height.

Correct
Answer is. ½ height * base.

Explanation. Nil

Question
Number. 55. The area of the curved surface area of a cone is (where r
= radius; h = vertical height and l = slant height).

Option
A. πrh.

Option
B. πr

^{2 }h.
Option
C. 1/3πr

^{2 }h.
Correct
Answer is. πrh.

Explanation.

Question
Number. 56. What is the volume of a cuboid?.

Option
A. height * length * width.

Option
B. height * ½ base * height.

Option
C. height * ½ base * length.

Correct
Answer is. height * length * width.

Explanation.

Question
Number. 57. (4-6)-(9/-3) + (-3) =.

Option
A. -2.

Option
B. 4.5.

Option
C. 4.

Correct
Answer is. -2.

Explanation. 4-6-(-3)-3
4-6 + 3-3 = -2.

Question
Number. 58. An aircraft travels 2150 nautical miles in 2 hours 30
minutes. What is the average speed of the aircraft?.

Option
A. 550 knots.

Option
B. 600 knots.

Option
C. 860 knots.

Correct
Answer is. 860 knots.

Explanation. Knots
= nautical miles per hour. 2150 / 2.5 = 860 knots.

Question
Number. 59. What is the surface area of a cylinder whose diameter is
20cm and height of 15 cm?.

Option
A. 300π.

Option
B. 942π.

Option
C. 350π.

Correct
Answer is. 300π.

Explanation. Surface
area = π * diameter * height = π * 20 * 15 = 300π.

Question
Number. 60. Four percent of 0.01 is.

Option
A. 0.0004.

Option
B. 0.004.

Option
C. 0.04.

Correct
Answer is. 0.0004.

Explanation. 4%
means 4/100. So 4/100 of 0.01 = 0.04/100 = 0.0004.

Question
Number. 61. (6 + 2)2 * 2 (2 * 45) =.

Option
A. 218.

Option
B. 38.

Option
C. 128.

Correct
Answer is. 38.

Explanation. (6
+ 2)2 = 64. *2 = 128. 2*45 = 90. 128-90 = 38.

Question
Number. 62. 17 degrees 49 minutes and 10 seconds added to 22 degrees
22 minutes and 59 seconds, equals.

Option
A. 40 degrees 11 minutes and 69 seconds.

Option
B. 40 degrees 12 minutes and 9 seconds.

Option
C. 39 degrees 11 minutes and 9 seconds.

Correct
Answer is. 40 degrees 12 minutes and 9 seconds.

Explanation. Add
them both together in 3 columns (degrees, minutes, seconds). When
each addition goes over 59, add 1 to the next column.

Question
Number. 63. The diameter of a cylinder is 200 cm and the height is 20
cm, what is the volume?.

Option
A. 628000 cm

^{3 }.
Option
B. 62800 cm

^{3 }.
Option
C. 8000 cm

^{3 }.
Correct
Answer is. 628000 cm

^{3 }.
Explanation. Volume
= π * radius-squared (base area) * height. 3.14 * 100 * 100 * 20 =
628,000.

Question
Number. 64. The comparison of the power input to the power output of
an inverter is expressed as a.

Option
A. ratio.

Option
B. gain.

Option
C. loss.

Correct
Answer is. ratio.

Explanation. A
'ratio' is a comparison of any two values.

Question
Number. 65. The ratio of 6:4 can also be expressed as.

Option
A. 64%.

Option
B. 66%.

Option
C. 150%.

Correct
Answer is. 150%.

Explanation. 6:4
means 6/4 = 3/2 = 150%.

Question
Number. 66. 200 kilovolts can be expressed as.

Option
A. 2 * 103 volts.

Option
B. 2 * 105 volts.

Option
C. 2 * 10-4 volts.

Correct
Answer is. 2 * 105 volts.

Explanation. 200
kV = 200 * 1000 = 200,000 = 2 * 10 to the power of 5 (i.e. 2 with 5
zeros).

Question
Number. 67. What is the surface area of a cone if the base is 8cm
diameter and the height is 10cm?.

Option
A. 40π.

Option
B. 80π.

Option
C. 120π.

Correct
Answer is. 40π.

Explanation. Surface
area of a cone = π * r * l = π * 8/2 * 10 = 40π.

Question
Number. 68. What is the area of a rectangle when its height is 11cm
and the width 120cm?.

Option
A. 0.132 m

^{2 }.
Option
B. 1.32 m

^{2 }.
Option
C. 1320 m

^{2 }.
Correct
Answer is. 0.132 m

^{2 }.
Explanation. Area
of a rectangle = 11 * 120 cm = 1320 square cm. To convert to square
metres divide by 10,000 (since there are 100 cm in each of the sides
i.e. 100 * 100).

Question
Number. 69. 4 3/8 – 2 ¼ + 1/5 =.

Option
A. 2 1/4.

Option
B. 2 13/40.

Option
C. 3 3/10.

Correct
Answer is. 2 13/40.

Explanation. Work
out the whole numbers and the fractions separately. 4-2 = 2. 3/8-1/4
+ 1/5 = 15/40-10/40 + 8/40 (LCD = 40) = 13/40. Now recombine the
wholw numbers and the fractions, so 2 + 13/40 = 2 13/40.

Question
Number. 70. 4*(4 *(4 – 1) –1) –1 =.

Option
A. 31.

Option
B. 15.

Option
C. 43.

Correct
Answer is. 43.

Explanation. Rule
1: Work the innermost brackets first. Rule 2: After calculating the
contents of a bracket, use the multiplier (or divider) before the
adder or subtractor.

Question
Number. 71. Which number is the lowest common factor of 36, 66 and
126?.

Option
A. 23.

Option
B. 12.

Option
C. 6.

Correct
Answer is. 6.

Explanation. The
common factor is the number which can be divided into all 3 without
the answer being a fraction.

Question
Number. 72. What is 3% of 0.001?.

Option
A. 0.00003.

Option
B. 0.003.

Option
C. 0.3.

Correct
Answer is. 0.00003.

Explanation. 3%
of 0.001 means 3/100 * 0.001 = 0.003/100 = 0.00003.

Question
Number. 73. 11/16 divided by 5/8 is.

Option
A. 55/128.

Option
B. 11/10.

Option
C. 10/11.

Correct
Answer is. 11/10.

Explanation. 11/16
divided by 5/8 is the same as 11/16 * 8/5 = 11/2 * 1/5 (after cross
cancelling) = 11/10.

Question
Number. 74. An aircraft uses 1680 gallons of fuel, the left tank uses
45%, the right tank uses 32.5%, how much was used by the centre
tank?.

Option
A. 210 gallons.

Option
B. 21 gallons.

Option
C. 378 gallons.

Correct
Answer is. 378 gallons.

Explanation. 100%-(45%
+ 32.5%) = 22.5%. 22.5% is just less than 1/4. Now estimate 1/4 of
1680 - do not calculate.

Question
Number. 75. What is the fraction 1/7 in decimal?.

Option
A. 0.14295.

Option
B. 0.14286.

Option
C. 1.429.

Correct
Answer is. 0.14286.

Explanation. Use
the long division technique.

Question
Number. 76. The supplement of 13 degrees is.

Option
A. 243.

Option
B. 76.

Option
C. 167.

Correct
Answer is. 167.

Explanation. Supplementary
angles add up to 180 degrees. Complementary angles add up to 90
degrees.

Question
Number. 77. What is the area of a ring with an outer diameter of 90
inches and an inner diameter of 80 inches?.

Option
A. 325π.

Option
B. 435π.

Option
C. 425π.

Correct
Answer is. 425π.

Explanation. Radii
are 45 and 40. (452-402) = 2025-1600 = 425. Area = πr

^{2 }.
Question
Number. 78. What is the area of the shape shown, in centimeters?.

Option
A. 1000.

Option
B. 1225.

Option
C. 1130.

Correct
Answer is. 1225.

Explanation. 12
* 3 = 36, 20 * 5 = 100, (28-8) * 3 = 60. 36 + 100 + 60 = 196. There
are approx. 2.5 cm in 1 inch, so multiply 196 by 2.5 twice (because
it is area).

Question
Number. 79. What is the area of a rectangle with base 160cm and
height 12cm?.

Option
A. 0.0192 m

^{2 }.
Option
B. 0.192 m

^{2 }.
Option
C. 0.00192 m

^{2 }.
Correct
Answer is. 0.192 m

^{2 }.
Explanation. Area
= base * height. To convert to metres divide by 100 twice (because it
is area).

Question
Number. 80. Calculate the area of the shape shown:.

Option
A. 6.75π.

Option
B. 6.75π.

Option
C. 17.5π.

Correct
Answer is. 6.75π.

Explanation. R1
= 1.5, R2 = 3. Area = π *(R22-R12) = π * (9-2.25) = π * 6.75.

Question
Number. 81. An aircraft flies 1350nm in 2 hrs 15 minutes. What is the
average speed?.

Option
A. 850kts.

Option
B. 600kts.

Option
C. 650kts.

Correct
Answer is. 600kts.

Explanation. 1
knot = 1 nm/hour. 1350/2.25 = 600 kts.

Question
Number. 82. What is the supplement of 13 degrees 13 minutes 13
seconds?.

Option
A. 167 degrees 46 minutes 47 seconds.

Option
B. 266 degrees 87 minutes 87 seconds.

Option
C. 166 degree 46 minutes 47 seconds.

Correct
Answer is. 166 degree 46 minutes 47 seconds.

Explanation. Supplementary
angles add up to 180 degrees. Subtract 13 degrees from 180 degrees
you get 167 degrees. But it is slightly more han 13 degrees, so
answer must be slightly less than 167 degrees - hardly any
calculation required!.

Question
Number. 83. Determine 15.4/2-2(6.2-15.6).

Option
A. 11.1.

Option
B. 4.5.

Option
C. 26.5.

Correct
Answer is. 26.5.

Explanation. Start
with brackets. Write down step by step. Remember that a minus number
subtracted becomes a plus.

Question
Number. 84. Calculate the area of the shape shown.

Option
A. 12 sq.ins.

Option
B. 16 sq.ins.

Option
C. 14 sq.ins.

Correct
Answer is. 14 sq.ins.

Explanation. 4
* 1 = 4 for top bit, 4 * 1 = 4 for bottom bit, 3 * 2 for centre bit.
Add all 3 areas together =.

Question
Number. 85. A mound of soil is piled up into a cone of base diameter
1.8m and height 0.6 m. What is the volume of soil?.

Option
A. 0.5 m

^{3 }.
Option
B. 1.0 m

^{3 }.
Option
C. 1.5 m

^{3 }.
Correct
Answer is. 0.5 m

^{3 }.
Explanation. Volume
of a cone = 1/3 * base area * height. Base are = πr

^{2 }= 3 * 0.9 * 0.9 = 2.4. 1/3 * 2.4 * 0.6 = 0.5.
Question
Number. 86. What is the area of the shape below?.

Option
A. 220 square inches.

Option
B. 196 square inches.

Option
C. 200 square inches.

Correct
Answer is. 196 square inches.

Explanation. (12
* 3) + (20 * 5) + ((28-3-5) * 3) = 196.

Question
Number. 87. What is 1 radian in degrees?.

Option
A. 57°.

Option
B. 270°.

Option
C. 66°.

Correct
Answer is. 57°.

Explanation. 2π
radians is 360°. So 1 radian = 360/6.3 = 57°.

Question
Number. 88. (5

^{2 }x 5^{3 })^{2 }is.
Option
A. 5

^{7 }.
Option
B. 5

^{12. }
Option
C. 5

^{10. }
Correct
Answer is. 5

^{10. }
Explanation. Add
the powers when the bases are multiplied. Multiply the powers when a
power is raised a further power. So 2 + 3 = 5. 5 * 2 = 10.

Question
Number. 89. What is 30% of 0.01?.

Option
A. 0.03.

Option
B. 0.003.

Option
C. 0.0003.

Correct
Answer is. 0.003.

Explanation. 30/100
* 0.01 = 3/10 * 0.01.

Question
Number. 90. Evaluate 15.4/2-2(4.6-15.7).

Option
A. 26.5.

Option
B. 29.9.

Option
C. -14.5.

Correct
Answer is. 29.9.

Explanation. 7.7-2(-11.1),
7.7 + 22.2, 29.9.

Question
Number. 91. How many radians are in 360°?.

Option
A. 2π.

Option
B. 6π.

Option
C. 4π.

Correct
Answer is. 2π.

Explanation. 360°
= 2π radians.

Question
Number. 92. What is the area (including the ends) of a cylinder
diameter 10 cm and 10 cm in height?.

Option
A. 50π.

Option
B. 150π.

Option
C. 100π.

Correct
Answer is. 150π.

Explanation. π
* dia. x height + 2 * π * radius-squared. 100π + 50π = 150π
(assuming they want the areas of the ends included).

Question
Number. 93. What is the highest factor of 153?.

Option
A. 6.

Option
B. 3.

Option
C. 9.

Correct
Answer is. 9.

Explanation. The
'factor' is the number which will divide into it (without making a
fraction).

Question
Number. 94. Convert into decimal the fraction 5/8 of 60.

Option
A. 40.

Option
B. 37.5.

Option
C. 37.

Correct
Answer is. 37.5.

Explanation. 5/8
* 60 = 5/2 * 15 = 75/2 = 37.5.

Question
Number. 95. An aeroplane has 1800 gallons of fuel on board. 35% in
the left wing 42.5% in the right wing how much fuel is in the centre
tank?.

Option
A. 405 gallons.

Option
B. 545 gallons.

Option
C. 183 gallons.

Correct
Answer is. 405 gallons.

Explanation. 100-77.5
= 22.5. 22.5/100 * 1800 = 22.5 * 18 = 405.

Question
Number. 96. In the common fraction 2/5, the number 5 is known as.

Option
A. the quotient.

Option
B. the numerator.

Option
C. the denominator.

Correct
Answer is. the denominator.

Explanation. The
number underneath is the denominator. The number on top is the
numerator.

Question
Number. 97. If 42% = 15,000, what is 100%?.

Option
A. 21,300.

Option
B. 35,714.

Option
C. 6,300.

Correct
Answer is. 35,714.

Explanation. Must
be just over double 15000.

Question
Number. 98. What is 12.75 * 26.1 to two significant figures?.

Option
A. 332.775.

Option
B. 332.78.

Option
C. 330.

Correct
Answer is. 330.

Explanation. No
calculation required. Just pick the answer with the 2 most
significant bits, all the rest are zeros.

Question
Number. 99. The fraction 17/11 is classed as.

Option
A. a mixed fraction.

Option
B. an improper fraction.

Option
C. a proper fraction.

Correct
Answer is. an improper fraction.

Explanation. Improper
fraction is one where the numerator is bigger than the denominator.

Question
Number. 100. To convert 1 inch to centimetres.

Option
A. divide by 2.54.

Option
B. multiply by 2.54.

Option
C. divide by 25.4.

Correct
Answer is. multiply by 2.54.

Explanation. There
are 2.54 cm in one inch.

Question
Number. 101. 0.000006 volts can be written as.

Option
A. 60 nanovolts.

Option
B. 6 microvolts.

Option
C. 6 millivolts.

Correct
Answer is. 6 microvolts.

Explanation. Move
decimal place 6 places to right to get it to 6.0. 6 decimal places is
'micro'.

Question
Number. 102. The median of the values 20, 28, 17, 34, 40, 11, 34, 26
is.

Option
A. 34.0.

Option
B. 27.0.

Option
C. 26.25.

Correct
Answer is. 27.0.

Explanation. Median
means 'in the middle'. Put them in order lowest to highest. Find the
middle number, or middle two numbers. 26 and 28 in this case. The
median is half way between these to numbers.

Question
Number. 103. The mode of the following 28, 17, 34, 28, 34, 35, 28, 40
is.

Option
A. 28.0.

Option
B. 30.5.

Option
C. 31.0.

Correct
Answer is. 28.0.

Explanation. Mode
means 'the one which occurs most often'. In this case = 28.

Question
Number. 104. 0.004 amperes can be written as.

Option
A. 0.4mA.

Option
B. 4kA.

Option
C. 4mA.

Correct
Answer is. 4mA.

Explanation. Move
the decimal places 3 places to make it 4.0 Three decimal places is
'milliAmps' (mA).

Question
Number. 105. A sphere with a radius of 2 cm has a surface area of.

Option
A. 16π cm

^{2 }.
Option
B. 64π cm

^{2 }.
Option
C. 8π cm

^{2 }.
Correct
Answer is. 16π cm

^{2 }.
Explanation. Area
of a sphere is 4 π r

^{2 }4*π*2*2 = 16π.
Question
Number. 106. The sum of an odd and an even number is.

Option
A. sometimes odd, sometimes even.

Option
B. always odd.

Option
C. always even.

Correct
Answer is. always odd.

Explanation. Odd
+ odd = even. Even + even = even. Odd + even = odd.

Question
Number. 107. A copper pipe has a radius of 7/32 inch. What is this in
decimal?.

Option
A. 0.28125.

Option
B. 0.15625.

Option
C. 0.21875.

Correct
Answer is. 0.21875.

Explanation. Quickest
way is to remember that 1/32 = 0.03125, and multiply it by 7.

Question
Number. 108. Millibar is the unit of.

Option
A. temperature.

Option
B. pressure.

Option
C. density.

Correct
Answer is. pressure.

Explanation. Millibars
is pressure.

Question
Number. 109. A ball rolls down a hill initially at 60 ft/s. It slows
down at a rate of 5 ft/s

^{2 }for 7 seconds. What will its final speed be?.
Option
A. 15 ft/s.

Option
B. 35 ft/s.

Option
C. 25 ft/s.

Correct
Answer is. 25 ft/s.

Explanation. 5
ft/s2 for 7 seconds = 35 ft/s deceleration. 60-35 = 25 ft/s final
velocity.

Question
Number. 110. A dial gauge is calibrated to an accuracy of 0.001 inch,
when using the dial gauge, you should.

Option
A. round off the answer to calibrated value.

Option
B. read the true value to 4 decimal places.

Option
C. read five significant figures.

Correct
Answer is. round off the answer to calibrated value.

Explanation. Round
the reading to the accuracy it can read (3 decimals in this case).

Question
Number. 111. In a flight control system, the control cable is allowed
an elongation of 3% due to wear. The length from the manufacturer is
78cm, what is its maximum used length?.

Option
A. 80.34 cm.

Option
B. 78.34 cm.

Option
C. 2.34 cm.

Correct
Answer is. 80.34 cm.

Explanation. 3/100
* 78 = 2.34 78 + 2.34 = 80.34.

Question
Number. 112. You have made 20% profit. Your balance is now £900.
What was your pre-profit balance?.

Option
A. £700.

Option
B. £800.

Option
C. £750.

Correct
Answer is. £750.

Explanation. +
20/100 = 900, 100/100 + 20/100 = 900, 120/100 = 900, transpose for.

Question
Number. 113. One of the square roots of a positive number is
positive. What is the other one?.

Option
A. positive or negative.

Option
B. negative.

Option
C. positive.

Correct
Answer is. negative.

Explanation. Example
- Square root of 4 is either 2 (since 2*2=+4), or -2
(since-2*-2=+4).

Question
Number. 114. A cylinder has a radius of 20cm and a length of 40cm.
What is its volume? (Take π as 3.1).

Option
A. 49600cm

^{3 }.
Option
B. 50270cm

^{3 }.
Option
C. 800cm

^{3 }.
Correct
Answer is. 49600cm

^{3 }.
Explanation. Base
Area = π * r

^{2 }= 3.1 * 20 * 20 = 49600.
Question
Number. 115. Can you take the cube root of a negative number?.

Option
A. No.

Option
B. Yes.

Option
C. Only certain numbers.

Correct
Answer is. Yes.

Explanation. You
can take the cube root, but not the square root.

Question
Number. 116. The process of removing roots from the denominator of
fractions is called what?.

Option
A. Rationalizing the denominator.

Option
B. Squaring the denominator.

Option
C. Derooting the denominator.

Correct
Answer is. Rationalizing the denominator.

Explanation. Nil http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm.

Question
Number. 117. Find the curved surface area of a cylinder diameter 20cm
and length 10cm.

Option
A. 1256 cm

^{2 }.
Option
B. 2512 cm

^{2 }.
Option
C. 400 cm

^{2 }.
Correct
Answer is. 1256 cm

^{2 }.
Explanation. Area
= π * d * h = 3.14 * 20 * 10 = 628. Multiply by 2 (because there is
inside and outside) = 1256.

Question
Number. 118. The conversion factor of litres to pints is.

Option
A. 2.2.

Option
B. 1.76.

Option
C. 0.57.

Correct
Answer is. 1.76.

Explanation. Nil http://www.thetipsbank.com/convert.htm.

Question
Number. 119. The volume of a pyramid is ____ times b times h.

Option
A. 1/4.

Option
B. 1/3.

Option
C. 1/2.

Correct
Answer is. 1/3.

Explanation. Nil http://www.aaaknow.com/geo79_x6.htm.

Question
Number. 120. What is the square root of 0.0289?.

Option
A. 0.17.

Option
B. 1.017.

Option
C. 1.7.

Correct
Answer is. 0.17.

Explanation. Only
a number less than 1 can give an even smaller number when squared.

Question
Number. 121. A car travelling at 72 km/hour is travelling at what
speed?.

Option
A. 30m/s.

Option
B. 20m/s.

Option
C. 10m/s.

Correct
Answer is. 20m/s.

Explanation. 72
* 1000/3600 = 20.

Question
Number. 122. If you bought a TV set worth £30 after getting 15%
discount. How much discount did you get?.

Option
A. £15.

Option
B. £5.

Option
C. £35.

Correct
Answer is. £5.

Explanation. Approximate
(10% of 30 + add half again) - Not strictly the correct method (as
this finds 15% of final price, not the original price) but answers
are far apart enough to permit.

Question
Number. 123. If you bought a second hand car worth £4500 after
getting 15% discount. How much did the car cost originally?.

Option
A. £3800.

Option
B. £5300.

Option
C. £6000.

Correct
Answer is. £5300.

Explanation. x-(x
15/100) = 4500 x-0.15x = 4500 0.85x = 4500 x = 4500/0.85 = 5300
(approx).

Question
Number. 124. 31 * 91 * 23 * 52 =.

Option
A. 3,373.

Option
B. 33,739.

Option
C. 3,373,916.

Correct
Answer is. 3,373,916.

Explanation. Round
off to 30, 90, 20 and 50, 3 * 9 * 2 * 5 = 270, 10 * 10 * 10 * 10 =
10,000, 270 * 10,000 = 2,700,000 Now choose the answer based on
order of magnitude.

Question
Number. 125. 1/5 + 2.5-6 =.

Option
A. 3.3.

Option
B. 2.0.

Option
C. -3.3.

Correct
Answer is. -3.3.

Explanation. 1/5
= 0.2 0.2+2.5 = 2.7, 2.7-6 = -3.3.

Question
Number. 126. Express 173942 in standard form.

Option
A. 17.3942 * 104.

Option
B. 173.942 * 103.

Option
C. 1.73942 * 105.

Correct
Answer is. 1.73942 * 105.

Explanation. Standard
form has the mantissa between 1 and 10.

Question
Number. 127. The sum of an odd number + an odd number is a.

Option
A. either odd or even.

Option
B. odd number.

Option
C. even number.

Correct
Answer is. even number.

Explanation. NIL.

Question
Number. 128. Express 750 milligrams in grams.

Option
A. 0.0000075.

Option
B. 0.075.

Option
C. 0.75.

Correct
Answer is. 0.75.

Explanation. 'milli'
is divide by 1000.

Question
Number. 129. There is 1800 pounds of fuel in an aircraft, 25% in the
left tank and 45% in the right. How much fuel is in the centre
tank?.

Option
A. 810 pounds.

Option
B. 450 pounds.

Option
C. 540 pounds.

Correct
Answer is. 540 pounds.

Explanation. 30%
* 1800 = 540.

Question
Number. 130. What is the supplement of an angle of 37°?.

Option
A. 8°.

Option
B. 53°.

Option
C. 143°.

Correct
Answer is. 143°.

Explanation. 180-37
= 143°.

Question
Number. 131. To what power must 10 be raised to equal 100,000?.

Option
A. 6.

Option
B. 4.

Option
C. 5.

Correct
Answer is. 5.

Explanation. An
easy way to tell the power of 10 to which a number has been raised is
to count the number of places the decimal point would have to be
moved to leave a number between 1 and 10. Remember the decimal point
though not written will be after the unit, in this case the last 0.

Question
Number. 132. Find the square root of 1600.

Option
A. 80.

Option
B. 40.

Option
C. 800.

Correct
Answer is. 40.

Explanation. 1600
= 16 * 100 √1600 = √16x√100 = 4x10 = 40.

Question
Number. 133. What is the ratio of 5 feet to 30 inches?.

Option
A. 2 : 1.

Option
B. 5 : 3.

Option
C. 1 : 6.

Correct
Answer is. 2 : 1.

Explanation. In
any ratio caculation the units must be the same. 5 feet is equal to
60 inches. Ratio of 60 : 30 or 60/30 is 2 : 1.

Question
Number. 134. Evaluate 5[ 3 + 6(7-4)-2].

Option
A. 31.

Option
B. 395.

Option
C. 95.

Correct
Answer is. 95.

Explanation. First
work out the inner brackets: 7-4=3, then multiply by 6: 6*3=18, Next
the outer brackets : 3+18-2=19, Finally multiply by 5: 5*19=95.

Question
Number. 135. Find the value of 3[ 5-2( 4-7)].

Option
A. 9.

Option
B. -3.

Option
C. 33.

Correct
Answer is. 33.

Explanation. First
work out the inner brackets: 4-7=-3, then multiply by -2: -2x-3 = 6,
Remember that -x-=+, Next the outer brackets: 5+6=11, finally
multiply by the 3: 3*11=33.

Question
Number. 136. What is the cube root of -64?.

Option
A. 4.

Option
B. -8.

Option
C. -4.

Correct
Answer is. -4.

Explanation. The
cube root of a number is the number which when multiplied by itself 3
times gives the number. In this example -4x-4x-4=-64 hence the
answer is -4.

Question
Number. 137. What is the cube root of 8

^{2 }.
Option
A. 2.

Option
B. 4.

Option
C. 8.

Correct
Answer is. 4.

Explanation. 8

^{2 }= 64, cube root of 64 is 4 as 4x4x4=64.
Question
Number. 138. An engine of 96 horsepower is running at 75% power. What
horsepower is being developed?.

Option
A. 72.

Option
B. 168.

Option
C. 62.

Correct
Answer is. 72.

Explanation. 75%
= 75/100 =3/4, 3/4x96=3x24=72.

Question
Number. 139. A blueprint shows a hole of 0.3751 to be drilled. What
fraction size drill bit is most nearly equal?.

Option
A. 5/16.

Option
B. 3/8.

Option
C. 3/16.

Correct
Answer is. 3/8.

Explanation. 3/16
= 0.1875, 5/16 = 0.3125, 3/8 = 0.375, 3/8 drill is the nearest.

Question
Number. 140. 120 out of 125 bolts produced are of an acceptable
tolerance. What percentage of the bolts are not acceptable?.

Option
A. 5%.

Option
B. 4%.

Option
C. 25%.

Correct
Answer is. 4%.

Explanation. Acceptable
bolts 120/125 = 24/25, as a percentage this is 24/25 * 100 = 96%,
Unacceptable bolts are 100%-96% = 4%.

Question
Number. 141. Evaluate 1/4 + 3/8-1/2.

Option
A. 1/8.

Option
B. 1/14.

Option
C. 1/2.

Correct
Answer is. 1/8.

Explanation. Change
all the fractions to a common denominator ¼ becomes 2/8, 3/8
remains same, ½ becomes 4/8. Now solve them by adding top Numerators
SO answer is 1/8.

Question
Number. 142. 3 3/4 + 4 2/3 =.

Option
A. 8 5/12.

Option
B. 7 5/12.

Option
C. 7 5/7.

Correct
Answer is. 8 5/12.

Explanation. add
the whole numbers: 3+4 = 7, add the fraction 3/4 + 2/3 = 9/12 + 8/12
= 17/12 = 1 5/12, add on the 7: 8 5/12.

Question
Number. 143. An aircraft travels 1400 nautical miles in 1 hour 45
minutes. What is the average speed of the aircraft?.

Option
A. 750 knots.

Option
B. 2450 knots.

Option
C. 800 knots.

Correct
Answer is. 800 knots.

Explanation. Average
speed is found by dividing total distance by total time. 1400 / 1
3/4. This is done by dividing 1400 by 7/4 = 1400 * 4/7 = 200 * 4 =
800.

Question
Number. 144. Evaluate 0.8 * 0.004.

Option
A. 0.32.

Option
B. 0.0032.

Option
C. 0.032.

Correct
Answer is. 0.0032.

Explanation. Count
the digits to the right of the decimal points in both numbers (4),
multiply the numbers without the points 8x4 = 32, put the decimal
point so there are the same number (4) as in the question adding 0's
as appropriate (0.0032).

Question
Number. 145. Convert 10 inches to millimetres.

Option
A. 2540 mm.

Option
B. 254 mm.

Option
C. 25.4 mm.

Correct
Answer is. 254 mm.

Explanation. 1
inch = 2.54 cm =25.4 mm, 10 inches = 10 x 25.4 =254 mm.

Question
Number. 146. What number is the highest common factor of 24, 84,
120?.

Option
A. 8.

Option
B. 12.

Option
C. 24.

Correct
Answer is. 12.

Explanation. 24=2*2*2*3,
84=2*2*3*7 HCF will be 2*2*3=12, 120=2*2*2*3*5.

Question
Number. 147. 0.0000314 can be written as.

Option
A. 3.14 x 10-5.

Option
B. 3.14 x 105.

Option
C. 3.14 x 10-4.

Correct
Answer is. 3.14 x 10-5.

Explanation. The
negative power indicates a reciprocal. 10-5 = 1/10,000, The easy way
to do this problem is to count the number of places you need to move
the decimal point to leave you with a number between 1 and 10. In
this case it is 5.

Question
Number. 148. What is the Lowest Common Multiple of 5; 12; 20.

Option
A. 60.

Option
B. 120.

Option
C. 5.

Correct
Answer is. 60.

Explanation. The
lowest common multiple is the lowest number each number will divide
into exactly. In this case the required number is 60.

Question
Number. 149. Evaluate 1/4{(4-6)-(2-8)}.

Option
A. 3/4.

Option
B. -2.

Option
C. 1.

Correct
Answer is. 1.

Explanation. First
work out the the two inner brackets: (4-6)=-2 and (2-8)=-6, then
-(-6) = +6 followed by -2 +6 = 4 and finally 1/4 x 4 = 1.

Question
Number. 150. What is the average of the following numbers? 5, 13,
23, 12, 17.

Option
A. 14.

Option
B. 15.

Option
C. 23.

Correct
Answer is. 14.

Explanation. The
average(mean) of a set of numbers is the sum divided by the number of
numbers. 5+13+23+12+17 = 70; 70 divided by 5 = 14.

Question
Number. 151. What is the volume of a rectangular tank 5m by 4 m by
150cm?.

Option
A. 3000 cu.m.

Option
B. 30 sq.m.

Option
C. 30 cu.m.

Correct
Answer is. 30 cu.m.

Explanation. Volume
of a cuboid is Length * Width * Height For this problem the
dimensions are 5m * 4m * 1.5m = 30cu. m.

Question
Number. 152. What is the depth of a rectangular tank whose volume is
40 cu. m. and has a base 5m by 10m?.

Option
A. 8m.

Option
B. 80cm.

Option
C. 0.08m.

Correct
Answer is. 80cm.

Explanation. V
= L * W * H , The height will be found by dividing volume by length x
width This will give an answer of 0.8m or 80cm.

Question
Number. 153. Convert 20 imperial gallons to litres.

Option
A. 909.2 litres.

Option
B. 9.092 litres.

Option
C. 90.92 litres.

Correct
Answer is. 90.92 litres.

Explanation. 1
gallon = 4.546 litres, 20 gallons = 20 x 4.546 = 90.92 litres.

Question
Number. 154. To find the area of a circle use the formula.

Option
A. 2πd.

Option
B. πr

^{2 }.
Option
C. 2πr.

Correct
Answer is. πr

^{2 }.
Explanation. 2πr
or πd is the formula to find the area of a circle.

Question
Number. 155. What is the circumference of the top of a cylindrical
tank whose radius is 3 metres?.

Option
A. 3π metres.

Option
B. 6π metres.

Option
C. 9π metres.

Correct
Answer is. 6π metres.

Explanation. Circumference
= 2πR.

Question
Number. 156. 67.5 cu.m.

Option
A. 67.5 cu.m.

Option
B. 675,000 cu.cm.

Option
C. 6.75 cu.m.

Correct
Answer is. 6.75 cu.m.

Explanation. volume
of a cylinder = π*r

^{2 }* h = 3 x (0.75)^{2 }xh, vol = 1.7x^{4 }= 6.75 cu.m., Remember all units must be the same so 150cm is changed to 1.5 m.
Question
Number. 157. What is the surface area of a cylindrical pipe of length
150 cm and diameter 5cm?.

Option
A. 1500π sq.cm.

Option
B. 750π sq.cm.

Option
C. 3750π sq.cm.

Correct
Answer is. 750π sq.cm.

Explanation. Surface
Area of a cylinder = πd x L= π x 5 x 150 = 750π sq.cm.

Question
Number. 158. Find the value of 5/8 of 4/5.

Option
A. 1/2.

Option
B. 3/4.

Option
C. 25/32.

Correct
Answer is. 1/2.

Explanation. 5/8
of 4/5 is the same as 5/8 x 4/5 by cancelling top and bottom of the
fractions, 5's cancel leaving 4/8 =1/2.

Question
Number. 159. What is the square root of 4 raised to the fifth
power?.

Option
A. 32.

Option
B. 128.

Option
C. 64.

Correct
Answer is. 32.

Explanation. The
square root of 4 is 2 two raised to the 5th power is 2*2*2*2*2 = 32.

Question
Number. 160. -3[8-3(5+√9)-( 7-9)].

Option
A. 60.

Option
B. -42.

Option
C. 42.

Correct
Answer is. 42.

Explanation. Work
out the inside brackets first: 5 + √9 = 5 + 3 = 8, then -3 * 8 =
-24, next 7-9 = -2, then 8-24 -(-2) = -14, finally -3 * -14 = 42.

Question
Number. 161. Which of the fractions is equivalent to 0.075?.

Option
A. 1/40.

Option
B. 3/4.

Option
C. 3/40.

Correct
Answer is. 3/40.

Explanation. 3/4
= 0.75, 1/40 = 0.025, 3/40 = 0.075.

Question
Number. 162. Express 3/8 as a percentage.

Option
A. 3.75%.

Option
B. 0.375%.

Option
C. 37.5%.

Correct
Answer is. 37.5%.

Explanation. T
change a fraction to a percentage first find the equivalent decimal
in this case it is 0.375., Then multiply by 100 to give 37.5%.

Question
Number. 163. An aeroplane flies 1000 miles and uses 80 gallons of
fuel. How much fuel will it use on a 2500 mile flight?.

Option
A. 240 gallons.

Option
B. 250 gallons.

Option
C. 200 gallons.

Correct
Answer is. 200 gallons.

Explanation. If
an airplane uses 80 gallons to fly 1000 miles the fuel consumption is
1000 divided by 80 = 12.5 miles per gallon., The fuel used for a 2500
mile flight will be 2500 / 12.5 = 200 gallons.

Question
Number. 164. A pinion gear with 16 teeth is driving a spur gear with
48 teeth at 120 RPM. Find the speed of the pinion gear.

Option
A. 40 RPM.

Option
B. 360 RPM.

Option
C. 144 RPM.

Correct
Answer is. 360 RPM.

Explanation. The
speed ratio is the reciprocal of the gear ratio.The spur gear with 48
teeth is driven by a pinion gear of of 16 teeth. This gives a gear
ratio of 48:16 = 3:1. This means the spur gear will turn at 1/3 of
the speed of the pinion gear, and the pinion gear will turn at 3
times the speed of the spur gear. If the spur gear turns at a speed
of 120 RPM the pinion turns at a speed of 360 RPM.

Question
Number. 165. What is the piston displacement of a master cylinder
with a 4cm diameter bore and a piston stroke of 10 cm?.

Option
A. 8π cu.cm.

Option
B. 40π cu.cm.

Option
C. 160π cu.cm.

Correct
Answer is. 40π cu.cm.

Explanation. The
piston displacement of a master cylinder is found by multiplying the
area of the piston head by its stroke. The area of the piston is πR2
= πx22 = 4π, Therefore the piston displacement will be 40π cu.cm.

Question
Number. 166. The curved surface area of a right cone is.

Option
A. 11/3 πRL.

Option
B. πRL.

Option
C. πR2 H.

Correct
Answer is. πRL.

Explanation. Nil http://www.tpub.com/content/doe/h1014v2/css/h1014v2_33.htm.

Question
Number. 167. How many millimetres in an inch?.

Option
A. 2.54.

Option
B. 25.4.

Option
C. 2540.

Correct
Answer is. 25.4.

Explanation. Nil

Question
Number. 168. Find the the area of a circular ring Whose outer
diameter is 10 cm and inner diameter is 6 diameter?.

Option
A. 64π sq. cm.

Option
B. 16π sq. cm.

Option
C. 4Π sq. cm.

Correct
Answer is. 16π sq. cm.

Explanation. Area
of a ring is π (R2-r2) A = π(52-32).

Question
Number. 169. Find the area of the triangle shown.

Option
A. 9 cm

^{2 }.
Option
B. 12 cm

^{2 }.
Option
C. 6 cm

^{2 }.
Correct
Answer is. 6 cm

^{2 }.
Explanation. A
= 1/2bh where b = base, and h = height. In this case A = 1/2 * 3 4 =
6 cm

^{2 }.
Question
Number. 170. What is the area of the shape shown, in square cm?.

Option
A. 5900.

Option
B. 590.

Option
C. 5.9.

Correct
Answer is. 5.9.

Explanation. Divide
the shape into three rectangles. , (10 * 30) + (20 * 7) + (10 * 15) =
300+140+150 = 590 mm

^{2 }, 1 cm^{2 }= 10x10 = 100mm^{2 }, so the answer is 590/100 = 5.9 cm^{2 }.
Question
Number. 171. What is the area of the trapezium shown?.

Option
A. Area cannot be calculated from information given.

Option
B. 27 cm

^{2 }.
Option
C. 24 cm

^{2 }.
Correct
Answer is. 24 cm

^{2 }.
Explanation. Area
of a trapezium (called trapezoid in US) is A = 1/2(a+b)h. a and b are
the two parallel sides., h is the perpendicular distance between
them. A = 1/2(5+7)4 = 6*4 = 24 cm2.

Question
Number. 172. What is the depth of water in the tank shown if the
volume of water is 4000 litres?.

Option
A. 80 cm.

Option
B. 5 m.

Option
C. 50 cm.

Correct
Answer is. 50 cm.

Explanation. 1
litre = 1000 cm

^{3 }, 4000 litres = 4,000,000 cm^{3 }, Volume of water is 4m x 2m x depth, Change to cm 400 * 200 * depth = 4,000,000, Therefore, depth = 4,000,000/(400*200) = 400/8 = 50 cm.
Question
Number. 173. What is the area of the sector shown? Take π=3.14.

Option
A. 50 cm.

Option
B. 52 ⅓ cm.

Option
C. 10.5 cm.

Correct
Answer is. 52 ⅓ cm.

Explanation. Area
of a circle = πr

^{2 }, = 3.14 * 102 , = 314cm^{2 }, Area of sector = 60/360 * 314 = 314/6 = 52 ⅓ cm^{2 }.
Question
Number. 174. What is the volume of metal used in the pipe shown?.

Option
A. 4500π cm

^{2 }.
Option
B. 45π cm

^{2 }.
Option
C. 18000π cm

^{2 }.
Correct
Answer is. 4500π cm

^{2 }.
Explanation. Work
out the volume of the metal by subtracting the volume of the hole
from the outside volume of the pipe., πR

^{2 }h-πr^{2 }h = πh(R^{2 }-r^{2 }), = πx500x(5^{2 }-4^{2 }).
Question
Number. 175. 24/0 (twenty four divided by nothing) is.

Option
A. nothing.

Option
B. infinity.

Option
C. twenty four.

Correct
Answer is. infinity.

Explanation. 24/0
= infinity.

Question
Number. 176. If 20% of 120 is 24, what is 24% of 20?.

Option
A. 4.8.

Option
B. 28.

Option
C. 18.

Correct
Answer is. 4.8.

Explanation. 10%
of 20 = 2, therefore 20% of 20 = 4, 4% of 10 = 0.4, therefore 4% of
20 = 0.8., 4 + 0.8 = 4.8.

Question
Number. 177. A shop keeper sold his car for £120. If this is 80% of
the buying price, how much loss did he make?.

Option
A. £50.

Option
B. £150.

Option
C. £30.

Correct
Answer is. £30.

Explanation. Buying
price * 80/100 = 120, Buying price * 80 = 120 * 100, Buying price =
12000/80 = 150, 150-120 = £30.

Question
Number. 178. 3 + 4-5(4-2) =.

Option
A. 13.

Option
B. 4.

Option
C. -3.

Correct
Answer is. -3.

Explanation. 3
+ 4-5(4-2) = 7-5(2), 7–10 = -3.

**1.2a Algebra.**
Question
Number. 1. Solve the following equation: 5x = 3x + 2.

Option
A. 3.

Option
B. 5.

Option
C. 1.

Correct
Answer is. 1.

Explanation. 5x-3x
= 2, 2x = 2, x = 1.

Question
Number. 2. Simplify the following (w + z)(x - y)(y - w) / (y - x)(w -
y)(w + z).

Option
A. -1.

Option
B. 0.

Option
C. +1.

Correct
Answer is. +1.

Explanation. First
cancel the (w+z) because they are the same. Then multiply out the top
and bottom lines (remember the smiley face) and cancel what you can
(everything cancels - leaving you with just 1/1=1).

Question
Number. 3. Given 43-x = 21, find the value of x.

Option
A. 43-21.

Option
B. 43/21.

Option
C. 43+21.

Correct
Answer is. 43-21.

Explanation. 43
= 21 + x 43-21 = x.

Question
Number. 4. Make L the subject of the formula 2pfL = x.

Option
A. L = 2pf.

Option
B. L = 2pf / x.

Option
C. L = x / 2pf.

Correct
Answer is. L = x / 2pf.

Explanation. Divide
the x by 2pf.

Question
Number. 5. Given that A = X+BY, what is Y equal to?.

Option
A. A-X add B.

Option
B. A-X divided by B.

Option
C. A-X minus B.

Correct
Answer is. A-X divided by B.

Explanation. Basic
transposition.

Question
Number. 6. If y/x = 4 and y = 5 then x =.

Option
A. 20.

Option
B. 4/5.

Option
C. 1 ¼.

Correct
Answer is. 1¼.

Explanation. 5/x
= 4, x = 5/4 = 1 1/4.

Question
Number. 7. (x - 3)(x + 5)=.

Option
A. x

^{2 }+2x.
Option
B. x

^{2 }+2x-15.
Option
C. x

^{2 }-15.
Correct
Answer is. x

^{2 }+2x-15.
Explanation. Multiply
x by x and +5, then multiply -3 by x and +5. Then gather together all
like terms.

Question
Number. 8. 21=43- , is equal to.

Option
A. 21-43.

Option
B. 43+21.

Option
C. 43-21.

Correct
Answer is. 43-21.

Explanation. 21=43-
, 21+ = 43, = 43-21.

Question
Number. 9. Evaluate. 2X

^{2 }Z^{2 }(3X-Z^{2 }) =.
Option
A. 6X

^{2 }z^{2 }+3x-z^{2 }.
Option
B. 6x

^{2 }z^{2 }-2x^{2 }z^{2 }.
Option
C. 6x

^{3 }z^{2 }-2x^{2 }z^{4 }.
Correct
Answer is. 6x

^{3 }z^{2 }-2x^{2 }z^{4 }.
Explanation. Multiply
out the brackets and add the indices where necessary.

Question
Number. 10. (a * b)(a * b) =.

Option
A. a

^{2 }+ 2ab + b^{2 }.
Option
B. a

^{2 }b2.
Option
C. a

^{2 }+ b2.
Correct
Answer is. a

^{2 }b^{2 }.
Explanation. Do
a x (a-b) (i.e. expand that bracket), then do b x (a-b) (i.e. expand
that bracket too). Then gather together like terms. You will find
that ab and -ab cancel.

Question
Number. 11. If y/x = 4 and x = 5 then y =.

Option
A. 1 ¼.

Option
B. 20.

Option
C. 4/5.

Correct
Answer is. 20.

Explanation. y/5
= 4. y = 5x

^{4 }= 20.
Question
Number. 12. Determine x.

Option
A. 9.029.

Option
B. 9.570.

Option
C. 8.971.

Correct
Answer is. 9.029.

Explanation. Root
of 81 is 9, so it must be 9.xxx (which rules out b). (Since the
content of the brackets comes to a negative number, it is positive
when it is squared).

Question
Number. 13. Find L in the following expression.

Option
A. Q

^{2 }C / R^{2 }.
Option
B. Q

^{2 }C^{2 }/ R.
Option
C. Q

^{2 }R^{2 }C.
Correct
Answer is. Q

^{2 }R^{2 }C.
Explanation. QxR
to remove the R from RHS. Square both sides to remove the root from
RHS. Multiply LHS by C to remove the C from RHS and you are left with
L.

Question
Number. 14. The heat of a resistor is given by the equation h = I

^{2 }RT. Find the current I.
Option
A. .

Option
B. .

Option
C. .

Correct
Answer is. .

Explanation. h/RT
Square root ALL.

Question
Number. 15. Factorise the following : x

^{2 }-x-6=0.
Option
A. (x-2)(x+3).

Option
B. (x-2)(x-3).

Option
C. (x+2)(x-3).

Correct
Answer is. (x+2)(x-3).

Explanation. Choose
2 numbers where the sum = -1 (the coefficient of x) and the product
(multiple) is -6 (the constant). Alternatively, multiply out the
answers a, b, c until you get the question.

Question
Number. 16. Factorise the following : 4x

^{2 }-6x-28 = 0.
Option
A. (4x-14) (x+2).

Option
B. (2x+7) (x-2).

Option
C. (2x

^{2 }+7) (x + 2).
Correct
Answer is. (4x-14) (x + 2).

Explanation. Expand
each answer in turn until you get the question. Remember the smiley
face.

Question
Number. 17. Solve for x in the equation: 3(x + 2) = 30 + 2(x-4).

Option
A. 8.

Option
B. 16.

Option
C. 15.

Correct
Answer is. 16.

Explanation. Multiply
out the bracket first. 3x + 6 = 30 + 2x-8. Then take all 'x' terms to
left, and all 'non-x' terms to right. 3x-2x = 30-8-6 etc.

Question
Number. 18. 2x = 4(x-3), Evaluate x.

Option
A. 6.

Option
B. 0.5.

Option
C. 2.

Correct
Answer is. 6.

Explanation. Expand
the bracket 2x = 4x-12, Take 4x to LHS 2x-4x = -12, -2x = -12, x =
-12/-2 = 6.

Question
Number. 19. 12x/2y + 14 = 50, When y = 2, solve for x.

Option
A. 11.6.

Option
B. 14.

Option
C. 12.

Correct
Answer is. 12.

Explanation. 12x/(2x2)
= 50-14. 12x = 36 x 4. 12x = 144. x = 144/12 = 12.

Question
Number. 20. 27y = 3 so y is equal to:.

Option
A. 1/9.

Option
B. 1/3.

Option
C. 9/1.

Correct
Answer is. 1/9.

Explanation. 3/27
= 1/9.

Question
Number. 21. Determine x in the following: (2x-1)(3x+2) = 0.

Option
A. 1.5, 1.

Option
B. 0.5, 3.

Option
C. -0.67, 0.5.

Correct
Answer is. -0.67, 0.5.

Explanation. Two
values of x, either 2x-1 = 0 (2x = 1, x = 1/2) or 3x + 2 = 0 (3x =
-2, x=-2/3).

Question
Number. 22. (x + y + z)(x + y + z) =.

Option
A. 2(x + y + z).

Option
B. 2x + 2y +2z.

Option
C. (x + y + z)

^{2 }.
Correct
Answer is. (x + y + z)

^{2 }.
Explanation. NIL.

Question
Number. 23. If x in an equation equals Ly + 7cb, define the formula
for finding the subject y.

Option
A. x-7cb/L.

Option
B. x-7cb/L.

Option
C. x-L/7cb.

Correct
Answer is. x-7cb/L.

Explanation. Subtract
the 7cb (x-7cb) then divide all by L.

Question
Number. 24. 64y = 64 what does y =.

Option
A. 1.

Option
B. 0.

Option
C. 0.5.

Correct
Answer is. 1.

Explanation. Anything
to the power of 1 is itself.

Question
Number. 25. Simplify 3a-2b +6a-3b-2a.

Option
A. 7a-5b.

Option
B. 7a +5b.

Option
C. 7a +b.

Correct
Answer is. 7a-5b.

Explanation. Collect
together like terms: 3a +6a-2a-2b-3b = 7a-5b.

Question
Number. 26. Simplify 3x-2xy-3y +5xy-2x +2y.

Option
A. x + 3xy-y.

Option
B. 5x + 3xy-y.

Option
C. x-3xy + y.

Correct
Answer is. x + 3xy-y.

Explanation. Collect
together like terms: 3x-2x +5xy-2xy +2y-3y = x +3xy-y.

Question
Number. 27. Simplify 5(x-2y) + 3(2y-x).

Option
A. 4x +4y.

Option
B. 2x +4y.

Option
C. 2x-4y.

Correct
Answer is. 2x-4y.

Explanation. Remove
the brackets first: 5x-10y +6y-3x Collect like terms: 5x-3x +6y-10y =
2x-4y.

Question
Number. 28. simplify (a+b)(a-c)(b-c) divided by (b+a)(c-a)(c-b).

Option
A. -1.

Option
B. (a+b)(a-c)(b-c).

Option
C. 1.

Correct
Answer is. 1.

Explanation. Because
this is a series of multiplications on both top and bottom we can do
the following: (a+b)/(b+a) = 1 (a-c)/(c-a) =(a-c)/-(a-c) = -1
(b-c)/-(b-c) = -1 hence the result is 1x-1x-1 =1.

Question
Number. 29. Make P the subject of the formula I =PRT/100.

Option
A. P = IRT/100.

Option
B. P = 100I/RT.

Option
C. P = 100RT/I.

Correct
Answer is. P = 100I/RT.

Explanation. Multiply
both sides by 100 then divide both sides by RT to get P =100I/RT.

Question
Number. 30. Make u the subject of the formula v

^{2 }= u^{2 }+ 2as.
Option
A. u = v-2as.

Option
B. u = √(v

^{2 }-2as).
Option
C. u = √(v

^{2 }+2as).
Correct
Answer is. u = √(v

^{2 }-2as).
Explanation. u
= √(v

^{2 }-2as).
Question
Number. 31. Remove the brackets and simplify: (x-y)(x-y).

Option
A. x

^{2 }-2xy-y^{2 }.
Option
B. x

^{2 }+y^{2 }.
Option
C. x

^{2 }-2xy+y^{2 }.
Correct
Answer is. x

^{2 }-2xy+y^{2 }.
Explanation. Multiply
both the x and the -y in the first bracket by both the x and -y in
the second bracket. X

^{2 }-xy-yx + y^{2 }x^{2 }-2xy + y^{2 }( remember -x- = + and yx is the same as xy).
Question
Number. 32. Evaluate (3X

^{2 }-6xy) / (x-2y).
Option
A. cannot be simplified further.

Option
B. 3x-3y.

Option
C. 3x.

Correct
Answer is. 3x.

Explanation. 3x

^{2 }-6xy=3x(x-2y) Dividing by x-2y leaves 3x.
Question
Number. 33. Evaluate (3a + 2b)(2a-3b).

Option
A. 6a

^{2 }-5ab-6b^{2 }.
Option
B. 6a-5ab-6b.

Option
C. 6a

^{2 }+ 5ab-6b^{2 }.
Correct
Answer is. 6a

^{2 }-5ab-6b^{2 }.
Explanation. Multiply
3a(2a-3b) =6a

^{2 }-9ab then multiply 2b(2a-3b) = 4ab-6b^{2 }collect like terms to give 6a^{2 }-5ab-6b^{2 }.

**1.2b Algebra.**
Question
Number. 1. Solve the following equations for x: 4x+8y=64 2x-8y=86.

Option
A. 125.

Option
B. 25.

Option
C. 5.

Correct
Answer is. 25.

Explanation. Add
like terms to eliminate y term. Thus 6x = 150, x = 25.

Question
Number. 2. 11001+11001 =.

Option
A. 502.

Option
B. 5010.

Option
C. 508.

Correct
Answer is. 5010.

Explanation. NIL.

Question
Number. 3. 100000 in binary is what number in decimal?.

Option
A. 32.

Option
B. 16.

Option
C. 64.

Correct
Answer is. 32.

Explanation. From
the right (lsb) binary goes - ones, twos, fours, eights, sixteens,
thirtytwos, sixtyfours etc.

Question
Number. 4. D in hexidecimal is what number in decimal?.

Option
A. 17.

Option
B. 13.

Option
C. 8.

Correct
Answer is. 13.

Explanation. In
hexidecimal, 10 is A, 11 is B, 12 is C, 13 is D, 14 is E and 15 is F.

Question
Number. 5. 10101

_{2 }+11001_{2 }=.
Option
A. 46

_{10. }
Option
B. 46

_{8 }.
Option
C. 46

_{2 . }
Correct
Answer is. 46

_{10. }
Explanation. Add
the two binary numbers then convert the result to decimal. Note:
answer 'a' cannot be a binary number so is wrong by default.

Question
Number. 6. What is 738 in binary coded decimal?.

Option
A. 1011110010.

Option
B. 111100010.

Option
C. 11100111000.

Correct
Answer is. 11100111000.

Explanation. Binary
Coded Decimal is not the same as binary.

Question
Number. 7. (A+B)

^{4 }is (A+B)^{2 }.
Option
A. (A+B)

^{6 }.
Option
B. (A+B)

^{2 }.
Option
C. A+B.

Correct
Answer is. (A+B)

^{2 }.
Explanation. Subtract
the indices.

Question
Number. 8. log 9-log 3=.

Option
A. log 6.

Option
B. log 3.

Option
C. log 9.

Correct
Answer is. log 3.

Explanation. log
9 = log (3x3) = 2 log 3. 2 log 3-log 3 = log 3.

Question
Number. 9. What is y in the formula shown? a=(X+B)/y.

Option
A. (a + X) / B.

Option
B. (X - B) /a.

Option
C. (X +B)/ a.

Correct
Answer is. (X +B)/ a.

Explanation. The
A and y can be swapped in this situation.

Question
Number. 10. 6

^{7 }divided by 12^{7 }is equal to.
Option
A. 1/2.

Option
B. 1/20.

Option
C. 1/128.

Correct
Answer is. 1/128.

Explanation. Cannot
subtract the indices when the base is different. 12

^{7 }=2^{7 }x6^{7 }. Now cancel the 6^{7 }top and bottom. 1/2^{7 }= 1/(2x2x2x2x2x2x2) = 1/128.
Question
Number. 11. If 2x-8y=14 and 4x+8y=16; then x=.

Option
A. -1/2.

Option
B. 5.

Option
C. 3.

Correct
Answer is. 5.

Explanation. Add
the x terms, add the y terms and add the numbers on the right of the
equal sign. The y terms cancel so you are then left with a formula
that can be solved for x.

Question
Number. 12. 2x-3 = 4; x =.

Option
A. 7.

Option
B. -3.

Option
C. 3.50.

Correct
Answer is. 3.50.

Explanation. 2x-3=4,
2x=4+3, 2x=7, x=7/2=3.5.

Question
Number. 13. V = (a+b) r

^{2 }Find a.
Option
A. V – r

^{2 }– b.
Option
B. (V – b)/ r

^{2 }
Option
C. V / r

^{2 }– b.
Correct
Answer is. V / r

^{2 }– b.
Explanation. Basic
transposition.

Question
Number. 14. Make m the subject of the formula in y=mx+c.

Option
A. y-x/c.

Option
B. y-c/x.

Option
C. y+c/x.

Correct
Answer is. y-c/x.

Explanation. Basic
transposition.

Question
Number. 15. Make x the subject of the formula in y = mx+c.

Option
A. (y-c)/m.

Option
B. y-c/m.

Option
C. y-m/c.

Correct
Answer is. (y-c)/m.

Explanation. Basic
transposition.

Question
Number. 16. Make c the subject of the formula in y = mx+c.

Option
A. y-mx.

Option
B. mx-y.

Option
C. y+mx.

Correct
Answer is. y-mx.

Explanation. Basic
transposition.

Question
Number. 17. Octal is to the base of.

Option
A. 2.

Option
B. 16.

Option
C. 8.

Correct
Answer is. 8.

Explanation. Octal
is base 8 numbering system.

Question
Number. 18. 101110 in binary is.

Option
A. 46 base 8.

Option
B. 46 base 2.

Option
C. 46 base 10.

Correct
Answer is. 46

_{10. }
Explanation. In
binary, each term means 32, 16, 8, 4, 2, 1. Write down 101110
underneath and add up the numbers above the 1's.

Question
Number. 19. What is octal 13 in base 10?.

Option
A. 11.

Option
B. 5.

Option
C. 4.

Correct
Answer is. 11.

Explanation. Octal
numbering is 64, 8, 1 etc. So 13 is 1 x 8's, and 3 x 1's = 11.

Question
Number. 20. What type of equation is this? ax

^{2 }+bx+c = 0.
Option
A. Quadratic equation.

Option
B. Polynomic equation.

Option
C. Gradient of the line.

Correct
Answer is. Quadratic equation.

Explanation. Quadratic.

Question
Number. 21. What is (X

^{2 }x X^{3 })^{3 }?.
Option
A. X

^{36. }
Option
B. X

^{15. }
Option
C. X

^{10. }
Correct
Answer is. X

^{15. }
Explanation. X

^{2 }* X^{3 }= X^{5 }X^{5 }raised to the power 3 is X^{15. }
Question
Number. 22. Hexadecimal is base.

Option
A. 16.

Option
B. 8.

Option
C. 2.

Correct
Answer is. 16.

Explanation. Hexadecimal
is base 16.

Question
Number. 23. y=mx+c can also be written.

Option
A. x=y-c/m.

Option
B. x=y/m+c.

Option
C. x=y/m-c.

Correct
Answer is. x=y-c/m.

Explanation. Basic
transposition.

Question
Number. 24. (x+y)

^{2 }÷ (x + y)^{8 }has a base and exponent of.
Option
A. (x+y)

^{10. }
Option
B. (x+y)-

^{6. }
Option
C. (x+y)

^{1/4. }
Correct
Answer is. (x+y)-

^{6 }.
Explanation. If
the bases are the same, keep it the same, but subtract the indices
(exponents) if dividing.(Add the indices if multiplying).

Question
Number. 25. Rewrite the following with a positive index: z pwr-2 and
x pwr-3.

Option
A. (ZX

^{2 })^{2 }; and (X)^{3 }
Option
B. 1/z

^{2 }and 1/x^{3 }.
Option
C. Z/22; and 1/X

Correct
Answer is. 1/Z

^{2 }and 1/X^{3 }.
Explanation. Invert
the variable (e.g. 1/z and write the power with the opposite sign).

Question
Number. 26. 10011

_{2 }=.
Option
A. 29

_{2 }.
Option
B. 19

_{10. }
Option
C. 35

_{10. }
Correct
Answer is. 19

_{10. }
Explanation. (1
* 16) + (0 * 8) + (0 * 4) + (1 * 2) + (1 * 1) = 19.

Question
Number. 27. y = 2x + 4, When x = -1, y =.

Option
A. 4.

Option
B. 2.

Option
C. 0.5.

Correct
Answer is. 2.

Explanation. y=2(-1)+4=-2+4
=+2.

Question
Number. 28. What is 011100001

_{2 }in Octal?.
Option
A. 341.

Option
B. 324.

Option
C. 452.

Correct
Answer is. 341.

Explanation. A
binary number ending in 1 must be an odd number when converted to any
base.

Question
Number. 29. BCD format of numbering system has a base of.

Option
A. 8.

Option
B. 2.

Option
C. 10.

Correct
Answer is. 2.

Explanation. BCD
is base 2.

Question
Number. 30. The characteristic of Log 0.698 is.

Option
A. 1.

Option
B. -1.

Option
C. -2.

Correct
Answer is. -1.

Explanation. The
characteristic of a logarithm is the integral part of the logarithm.
The mantissa is the decimal part. So, for example Log8(29345) =
4.94694 the characteristic is 4 and the mantissa 0.94694. The log
definition y=bx, logb(y)=x. So 0.698 = 10powerx. x must be -1.***
(i.e minus one-point-something).

Question
Number. 31. Log 59,000 is equal to.

Option
A. 0.77452.

Option
B. 4.7745.

Option
C. 5.77452.

Correct
Answer is. 4.7745.

Explanation. Log
10=1, Log 100 = 2, Log 1000=3. Log 59,000 = Log 59+Log 1000 =
something between 1 and 2, + 3.

Question
Number. 32. If 2x

^{2 }+ kx-8 = 0 has two equal real roots, then.
Option
A. k is an imaginary number.

Option
B. k=±8.

Option
C. k=-8.

Correct
Answer is. k is an imaginary number.

Explanation. Because
of the +/- part of the quadratic solution formula, it is not possible
for the equation to have two equal roots. k is therefore an imaginary
number.

Question
Number. 33. Given the log of A exceeds that of B by 4, find the
correct statement about A and B.

Option
A. A is 4000 times the value of B.

Option
B. A is 10,000 times the value of B.

Option
C. A is 1000 times the value of B.

Correct
Answer is. A is 10,000 times the value of B.

Explanation. log
10=1, log 100=2, log 1000=3, log 10000=4, log 100,000=5.

Question
Number. 34. What is 11110001 base2 in Octal?.

Option
A. 72.

Option
B. 684.

Option
C. 361.

Correct
Answer is. 361.

Explanation. Divide
into blocks of 3 (from right to left), and convert each block into
DECIMAL - you have just converted to OCTAL. (Note: 'c' is
automatically out, since you cannot have '7' in octal).

Question
Number. 35. If x

^{2 }-3=6, then x=.
Option
A. ±3.

Option
B. 18.

Option
C. ± 2.

Correct
Answer is. ±3.

Explanation. x

^{2 }=6 +3, x^{2 }=9, x=+/-3.
Question
Number. 36. Given that s=0, solve the equation s=ut+½at

^{2}^{ }for the two possible values of t.
Option
A. t=0, t=2u/a.

Option
B. t=0, t=a/2u.

Option
C. t=0, t=-2u/a.

Correct
Answer is. t=0, t=-2u/a.

Explanation. s=ut+½at2
Make s=0, 0=ut+½at

^{2 }Divide all terms by u, 0 = t + a/2ut^{2 }Factorise, 0=t(1+a/2ut) So either t=0, or -2u/a=0 (so everything in the brackets=0).
Question
Number. 37. What is Log 9-Log 3 + Log 4.

Option
A. Log 12.

Option
B. Log 10.

Option
C. Log 16.

Correct
Answer is. Log 12.

Explanation. Log
9 = 2Log3, therefore 2Log3-Log3 + Log 4 = Log3 + Log4 = Log(3 x 4) =
Log12.

Question
Number. 38. What is log 0.1?.

Option
A. -0.1.

Option
B. 0.

Option
C. -1.

Correct
Answer is. -1.

Explanation. Log
of 0.1 is always -1, (log 0.01 = -2, log 0.001 = -3 etc).

Question
Number. 39. What is log 1?.

Option
A. 10.

Option
B. 1.

Option
C. 0.

Correct
Answer is. 0.

Explanation. Log
of 1 is always 0.

Question
Number. 40. What is the log of 20000.2?.

Option
A. 0.47892.

Option
B. 4.7892.

Option
C. 47.892.

Correct
Answer is. 4.7892.

Explanation. Log
of a 5-figure number (not including the decimal) is always 4 point
something.

Question
Number. 41. A quadratic equation has the real roots x=6 and x=9.
Determine the equation which is satisfied by these roots.

Option
A. x

^{2 }-54x+15=0.
Option
B. x

^{2 }-15x+54=0.
Option
C. x

^{2 }+15x-15=0.
Correct
Answer is. X

^{2 }-15x+54=0.
Explanation. Change
the sign of each root -6, -9. Coefficient of x is the addition, the
constant is the multiplication.
http://www.themathpage.com/alg/quadratic-equations.htm.

Question
Number. 42. What is 10111

_{2 }^{ }-1001_{2 }?.
Option
A. 1100

_{2 }.
Option
B. 1110

_{2 }.
Option
C. 1010

_{2 }.
Correct
Answer is. 1110

_{2 }.
Explanation. NIL.

Question
Number. 43. What is the characteristic of 5.74?.

Option
A. 1.

Option
B. -1.

Option
C. 0.

Correct
Answer is. 0.

Explanation. If
you find the Log of 5.74, it will be 0.--- The '0' is the
characteristic.

Question
Number. 44. What is log63?.

Option
A. 6log3.

Option
B. log18.

Option
C. 3log6.

Correct
Answer is. 3log6.

Explanation. 3log6.

Question
Number. 45. Solve for x: 5x-7=3.

Option
A. x=-4/5.

Option
B. x=-2.

Option
C. x=2.

Correct
Answer is. x=2.

Explanation. 5x-7
= 3add 7 to both sides to give 5x = 10 divide both sides by 5 to give
x = 2.

Question
Number. 46. Octal is the word given to what base?.

Option
A. 8.

Option
B. 2.

Option
C. 16.

Correct
Answer is. 8.

Explanation. NIL.

Question
Number. 47. Which of the following is a quadratic equation?.

Option
A. 3x

^{2 }+2x+1=0.
Option
B. 3x+2y+4=0.

Option
C. 3x

^{3 }+3x-2 = 0.
Correct
Answer is. 3x

^{2 }+2x+1=0.
Explanation. A
quadratic equation has only one unknown and the highest power is
two.

Question
Number. 48. What is log 1000?.

Option
A. 2.0787.

Option
B. 1.0787.

Option
C. 3.0787.

Correct
Answer is. 3.0787.

Explanation. Log
10 = 1 Log 100 = 2 Log 1000 = 3 Log 10000 = 4 etc.

Question
Number. 49. What is log AB?.

Option
A. log (A+B).

Option
B. log A+log B.

Option
C. Log A-Log B.

Correct
Answer is. log A+log B.

Explanation. External
website.

Question
Number. 50. What is LogA/B?.

Option
A. log A+Log B.

Option
B. log A-Log B.

Option
C. Log (A-B).

Correct
Answer is. log A-Log B.

Explanation. External
website.

Question
Number. 51. log 100+2 =.

Option
A. 4.

Option
B. Log 200.

Option
C. Log 200.

Correct
Answer is. 4.

Explanation. log
100=2, 2+2 = 4.

Question
Number. 52. Log 100/2 =.

Option
A. Log 200.

Option
B. Log 98.

Option
C. 1.

Correct
Answer is. 1.

Explanation. log
100=2, 2/2 = 1.

Question
Number. 53. Log 100+cos60.

Option
A. 0.25.

Option
B. 25.

Option
C. 2.5.

Correct
Answer is. 2.5.

Explanation. Log
100=2, cos60=0.5, 2+0.5=2.5.

**1.3a Geometry.**
Question
Number. 1. What is the external angle indicated on the figure
below?.

Option
A. 60.

Option
B. 120.

Option
C. 30.

Correct
Answer is. 120.

Explanation. NIL.

Question
Number. 2. If a wheel of radius R revolves 1/2 a turn, how many
radians does it turn through?.

Option
A. 2π radians.

Option
B. 2R

^{2 }radians.
Option
C. π radians.

Correct
Answer is. π radians.

Explanation. There
are 2π radians in one complete turn (i.e. 360 degrees).

Question
Number. 3. If there are two similar angles in a right triangle, these
angles are.

Option
A. supplementary.

Option
B. subordinate.

Option
C. complementary.

Correct
Answer is. complementary.

Explanation. Complementary
angles add up to 90 degrees. Supplementary angles add up to 180
degrees. A right (angled) triangle already has one 90 degree angles
so the other 2 must add up to 90.

Question
Number. 4. An equilateral triangle has.

Option
A. no equal sides.

Option
B. 2 equal sides.

Option
C. 3 equal sides.

Correct
Answer is. 3 equal sides.

Explanation. Triangle
definitions.

Question
Number. 5. The three angles of a triangle summed together equal.

Option
A. 90

^{o }.
Option
B. 180

^{o }.
Option
C. 360

^{o }.
Correct
Answer is. 180

^{o }.
Explanation. The
sum of the angles of a triangle ar 180 degrees.

Question
Number. 6. The circumference of a circle is found by.

Option
A. multiplying the diameter by 3.142.

Option
B. multiplying the radius by 3.142.

Option
C. dividing the diameter by 3.142.

Correct
Answer is. multiplying the diameter by 3.142.

Explanation. Circumference
= π x diameter.

Question
Number. 7. Calculate the height of an obtuse triangle whose base is X
cm and the area is Y square cm.

Option
A. Y x 2/X.

Option
B. Y + X/2.

Option
C. Y * 2 * X.

Correct
Answer is. Y * 2/X.

Explanation. Y
= 1/(Y+2) 2X * h, h = Y * 2/X.

Question
Number. 8. A right-angled triangle has sides of 3 inches and 4
inches, what will the third side be?.

Option
A. 5 inches.

Option
B. 5.5 inches.

Option
C. 6 inches.

Correct
Answer is. 5 inches.

Explanation. 3,4,5
triangle.

Question
Number. 9. To work out the circumference of a circle use.

Option
A. D * 0.3142.

Option
B. D * 3.142.

Option
C. D-3.142.

Correct
Answer is. D * 3.142.

Explanation. Circumference
= 3.14 * diameter.

Question
Number. 10. An equilateral triangle has.

Option
A. two equal side.

Option
B. no equal sides.

Option
C. three equal sides.

Correct
Answer is. three equal sides.

Explanation. Triangle
definition.

Question
Number. 11. A quadrilateral with only two parallel sides is a.

Option
A. Trapezium.

Option
B. Trapezoid.

Option
C. Rhombus.

Correct
Answer is. Trapezoid.

Explanation. Shape
definitions.

Question
Number. 12. A triangle with equal angles is called.

Option
A. right angled.

Option
B. equilateral.

Option
C. isosceles.

Correct
Answer is. equilateral.

Explanation. Triangle
definitions.

Question
Number. 13. Two gears are in mesh, one is larger than the other, the
smaller gear rotates.

Option
A. at a faster speed.

Option
B. at a lower speed.

Option
C. at the same speed.

Correct
Answer is. at a faster speed.

Explanation. The
smallest gear rotates the fastest.

Question
Number. 14. The name given to this shape.

Option
A. Trapezoid.

Option
B. Parallelogram.

Option
C. Rhombus.

Correct
Answer is. Parallelogram.

Explanation. Shape
definition.

Question
Number. 15. A triangle with equal sides is.

Option
A. isosceles.

Option
B. equilateral.

Option
C. acute.

Correct
Answer is. equilateral.

Explanation. NIL.

Question
Number. 16. Two gears are in mesh, one has twice the number of teeth
as the other.

Option
A. the two gears rotate at the same speed.

Option
B. the gear with fewer teeth rotates faster than the other.

Option
C. the gear with fewer teeth rotates slower than the other.

Correct
Answer is. the gear with fewer teeth rotates faster than the other.

Explanation. The
smaller gear rotates at twice the speed of the larger gear.

Question
Number. 17. Locus points plotted equidistant from a central points
represent.

Option
A. circumference.

Option
B. diameter.

Option
C. radius.

Correct
Answer is. circumference.

Explanation. Locus
is the line scribed by points moving equidistant from a point - in
this case it will scribe the circumference of a circle.

Question
Number. 18. A circle contains.

Option
A. 2πr radians.

Option
B. 2π radians.

Option
C. 4π radians.

Correct
Answer is. 2π radians.

Explanation. There
are 2π radians in 360°.

Question
Number. 19. An oblique pyramid is one which has its axis.

Option
A. perpendicular to its base.

Option
B. not perpendicular to its base.

Option
C. parallel to its base.

Correct
Answer is. not perpendicular to its base.

Explanation. Nil.

Question
Number. 20. An input gear has 20 teeth and the output gear has 120
teeth. If the input gear rotates 360°, the output gear will
rotate.

Option
A. 60°.

Option
B. 45°.

Option
C. 90°.

Correct
Answer is. 60°.

Explanation. Ratio
1:6. The big gear will rotate 1/6 of the small gear. 360/6 = 60°.

Question
Number. 21. A line from the centre of a circle is called.

Option
A. diameter.

Option
B. its segment.

Option
C. radius.

Correct
Answer is. radius.

Explanation. NIL.

Question
Number. 22. Give the name of the triangle, which has two sides equal
in length and two equal angles.

Option
A. Equilateral.

Option
B. Isosceles.

Option
C. Obtuse.

Correct
Answer is. Isosceles.

Explanation. NIL.

Question
Number. 23. In an equilateral triangle, all of the angles are equal,
to.

Option
A. π divided by 3.

Option
B. π divided by 4.

Option
C. π divided by 2.

Correct
Answer is. π divided by 3.

Explanation. Since
360° = 2π radians, 180° = π radians. The angles of an equilatrial
triangle are each 180/3 (60°) or π/3.

Question
Number. 24. What is an obtuse angle?.

Option
A. One greater than 180

^{o }.
Option
B. One less than 90

^{o }.
Option
C. One greater than 90°, but less than 180

^{o }.
Correct
Answer is. One greater than 90°, but less than 180.

Explanation. NIL.

Question
Number. 25. A congruent triangle has.

Option
A. same shape and size.

Option
B. same size different shape.

Option
C. same shape different size.

Correct
Answer is. same shape and size.

Explanation. Congruent
triangles have the same sides AND the same angles.

Question
Number. 26. Which shape has no parallel sides?.

Option
A. Trapezoid.

Option
B. Kite.

Option
C. Rhombus.

Correct
Answer is. Kite.

Explanation. NIL.

Question
Number. 27. The properties of a scalene triangle are.

Option
A. acute angle.

Option
B. all sides different lengths.

Option
C. all sides are equal.

Correct
Answer is. all sides different lengths.

Explanation. A
Scalene triangle has all different sides.

Question
Number. 28. What is the height of an oblique pyramid?.

Option
A. The height is angled to the base.

Option
B. The height is perpendicular to the base.

Option
C. The height is parallel to the sides.

Correct
Answer is. The height is perpendicular to the base.

Explanation. Height
is always measured perpendicular (90 degrees) to the base.

Question
Number. 29. What is the value of in the diagram shown?.

Option
A. 30°.

Option
B. 35°.

Option
C. 40°.

Correct
Answer is. 35°.

Explanation. x
+ 3x + 4x + 80 = 360, 8x +80 = 360, 8x = 360-80, x = 280/8 = 35.

Question
Number. 30. How many degrees are there in the smaller of the
segments, where AB is one sixth of AC?.

Option
A. 15°.

Option
B. 14.5°.

Option
C. 10°.

Correct
Answer is. 15°.

Explanation. 90/6
= 15 degrees.

Question
Number. 31. In a parallelogram, if all the sides are of equal length
and 1 angle is 90°, it is a.

Option
A. rhomboid.

Option
B. quadrilateral.

Option
C. square.

Correct
Answer is. square.

Explanation. A
square.

Question
Number. 32. In a rhombus.

Option
A. all sides are different length with no angles 90°.

Option
B. all sides are equal length with no angles 90°.

Option
C. adjacent sides are different lengths with no angles 90°.

Correct
Answer is. all sides are equal length with no angles 90°.

Explanation. A
rhombus is a square on the tilt.

Question
Number. 33. An isosceles triangle has the following properties:.

Option
A. Two sides parallel.

Option
B. Three sides the same length.

Option
C. Two sides the same length.

Correct
Answer is. Two sides the same length.

Explanation. An
isoscelese triangle has 2 sides and 2 angles the same.

Question
Number. 34. In an oblique triangle the axis is.

Option
A. perpendicular to the base.

Option
B. at a slant to the base.

Option
C. parallel to the base.

Correct
Answer is. at a slant to the base.

Explanation. An
oblique triangle is on the slant.

Question
Number. 35. How far does a wheel of 7m radius travel in one
revolution?.

Option
A. 14.

Option
B. 22m.

Option
C. 44m.

Correct
Answer is. 44m.

Explanation. C
= 2πR = 2 * 3.14 * 7 = 44 (approx.).

Question
Number. 36. For a scalene triangle which is true?.

Option
A. 2 sides are equal.

Option
B. No 2 sides are equal.

Option
C. One angle is acute.

Correct
Answer is. No 2 sides are equal.

Explanation. A
scalene triangle has no sides equal.

Question
Number. 37. A line to create a segment from the centre of a circle is
a.

Option
A. radius.

Option
B. diameter.

Option
C. chord.

Correct
Answer is. diameter.

Explanation. A
chord does not go through the centre of the circle. A radius does not
produce a segment.

Question
Number. 38. A shape with 4 equal sides and one 90° angle is a.

Option
A. parallelogram.

Option
B. rhombus.

Option
C. square.

Correct
Answer is. square.

Explanation. Neither
a parallelogram (a pushed-over rectangle) nor a rhombus (a
pushed-over square) has any 90° angles. A square has (at least) one
90° angle.

Question
Number. 39. In a right angled triangle the longest side is 20cm long,
the shortest side is 12cm. What length is the last side?.

Option
A. 13.6cm.

Option
B. 18cm.

Option
C. 16cm.

Correct
Answer is. 16cm.

Explanation. 12-16-20
triangle is a 3-4-5 triangle.

Question
Number. 40. The sum of the internal angles of a triangle is.

Option
A. 180°.

Option
B. 2π radians.

Option
C. 360°.

Correct
Answer is. 180°.

Explanation. Internal
angles of a triangle add up to 180 degrees (note: 360 degrees and 2π
radians are the same thing).

Question
Number. 41. A triangle has angles 67° and 48°. The third angle
is.

Option
A. 115°.

Option
B. 75°.

Option
C. 65°.

Correct
Answer is. 65°.

Explanation. 67+
48 = 115. 180-115 = 65°.

Question
Number. 42. The sum of the angles of a polygon with 'n' sides is.

Option
A. 180 x (n-2).

Option
B. (n/4) x 180.

Option
C. 60 x n.

Correct
Answer is. 180 x (n-2).

Explanation. 180(n-2).

Question
Number. 43. Suppose the earth to be a real sphere with the radius R.
The arc distance from HK (N23) to the North pole is:.

Option
A. 0.9R.

Option
B. 2.2R.

Option
C. 1.2R.

Correct
Answer is. 1.2R.

Explanation. Circumference
= 2πR (take π = 3). Proportion of quoted arc of circumference is
67/360. 67/360 x (2 x 3 x R) = 1.1R (approx, slightly more if you
take π = 3.14)).

Question
Number. 44. One radian is.

Option
A. the angle subtended at the centre of a circle when the arc-length
formed between two radial lines is equal to pi.

Option
B. the angle subtended at the centre of a circle when the arc-length
formed between two radial lines is equal in length to the radius.

Option
C. 66.67°.

Correct
Answer is. the angle subtended at the centre of a circle when the
arc-length formed between two radial lines is equal in length to the
radius.

Explanation. NIL.

Question
Number. 45. How many degrees in π radians ?.

Option
A. 180.

Option
B. 360.

Option
C. 90.

Correct
Answer is. 180.

Explanation. 2π
radians = 360 degrees.

Question
Number. 46. The sum of the external angles of any polygon is.

Option
A. 180 degrees.

Option
B. 540 degrees.

Option
C. 360 degrees.

Correct
Answer is. 360 degrees.

Explanation. External
website.

Question
Number. 47. Which of the 2 angles are called supplementary?.

Option
A. 60 degrees and 120 degrees.

Option
B. 40 degrees and 40 degrees.

Option
C. 30 degrees and 60 degrees.

Correct
Answer is. 60 degrees and 120 degrees.

Explanation. Add
up to 180 degrees.

Question
Number. 48. An acute angle is.

Option
A. less than 90 degrees.

Option
B. less than 180 degrees.

Option
C. more than 90 degrees.

Correct
Answer is. less than 90 degrees.

Explanation. NIL. http://math.about.com/library/bldefacuteangle.htm.

Question
Number. 49. A straight line which goes from one point on the
circumference to another is called.

Option
A. an arc.

Option
B. a tangent.

Option
C. a chord.

Correct
Answer is. a chord.

Explanation. NIL. http://en.wikipedia.org/wiki/Chord_%28geometry%29.

Question
Number. 50. What is the name given to a quadrilateral with two pairs
of adjacent sides equal and the diagonals intersect at right angles?
Note not all the sides are equal?.

Option
A. kite.

Option
B. parallelogram.

Option
C. rhombus.

Correct
Answer is. kite.

Explanation. Draw
the figure to check.

Question
Number. 51. Find the size of the other two angles of an isoscelese
triangle with one angle of 100°.

Option
A. 40°, 40°.

Option
B. 30°, 30°.

Option
C. 100°, 20°.

Correct
Answer is. 40°, 40°.

Explanation. Isoscelese
triangle has 2 angles equal. If one angle is 100° the other two add
up to 80°. These must be the equal angles so each will be 40°.

Question
Number. 52. A triangle always has.

Option
A. exactly one right angle.

Option
B. at least two acute angles.

Option
C. exactly two acute angle.

Correct
Answer is. at least two acute angles.

Explanation. NIL. http://mathforum.org/library/drmath/view/55061.html.

Question
Number. 53. The locus of a point which stays the same distance from a
given point is.

Option
A. a circle.

Option
B. a parallel line.

Option
C. an ellipse.

Correct
Answer is. a circle.

Explanation. A
locus is the path a point travels following a given rule. In this
case imagine the path of the end of a piece of string fixed at the
other end and kept taught.

**1.3b Geometry.**
Question
Number. 1. In the following equation what is the y-intercept? 4y = 2x
+ 8.

Option
A. 2.

Option
B. 4.

Option
C. 8.

Correct
Answer is. 2.

Explanation. First
get rid of the 4 from RHS (divide all by 4) y = 0.5x + 2. Intercept
with y-axis is when x = 0. So put x = 0 and what is left? (remember
that 0.5 x 0 = 0).

Question
Number. 2. How many times does the x-axis get crossed when y = x

^{2 }-3.
Option
A. 3.

Option
B. 1.

Option
C. 2.

Correct
Answer is. 1.

Explanation. y
= x

^{2 }(a quadratic) is a shape like a 'U-curve' where the bottom of the 'U' sits on the (0,0) point. The -3 means the 'U' is shifted down the y-axis 3 places.
Question
Number. 3. On a graph what is the intercept of y when 4y = x + 8.

Option
A. 4.

Option
B. 8.

Option
C. 2.

Correct
Answer is. 2.

Explanation. Use
y = mx + c The 'c' is the y-intercept. 4y = x + 8 must be converted
to y = 1/4x + 8/4".

Question
Number. 4. What is the equation of the line shown?.

Option
A. y = 2x + 2.

Option
B. y = -2-x.

Option
C. y = x-2.

Correct
Answer is. y = -2-x.

Explanation. Slope
(gradient) is 2/2 and is negative (i.e. -1). y-intercept is -2.
Equation of the line (y = mx + c) is y = -1x -2 or y = -2-x.

Question
Number. 5. The graph points (9, 3) and (3, 1) what is the slope?.

Option
A. 9/5.

Option
B. 1/3.

Option
C. 3/1.

Correct
Answer is. 1/3.

Explanation. Slope
= change in Y / change in = (3-1)/(9-3) = 2/6 = 1/3.

Question
Number. 6. A straight line graph has the equation 3y = 12x–3 What
is the gradient?.

Option
A. 1/4.

Option
B. 4/1.

Option
C. 3/4.

Correct
Answer is. 4/1.

Explanation. The
coefficient of x is the gradient, but only when the equation is in
the form y = mx + c. So y = 12/3x -3/3 12/3 = 4/1.

Question
Number. 7. For an equation 2y = 5x + 3 what is the gradient?.

Option
A. 3/5x.

Option
B. 5/2.

Option
C. 5x+3/2.

Correct
Answer is. 5/2.

Explanation. y
= mx + c Gradient is the 'm' (but the coefficient of y must be 1. If
it is not, divide all terms by the coefficient of y).

Question
Number. 8. Using cosine to find the angle of a triangle, which
statement is true?.

Option
A. Opposite/Hyp.

Option
B. Opposite/Adjacent.

Option
C. Adjacent/Hyp.

Correct
Answer is. Adjacent/Hyp.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 9. What type of equation is y = x

^{2 }+ 9x + 14?.
Option
A. Quadratic.

Option
B. Circular.

Option
C. Exponential.

Correct
Answer is. Quadratic.

Explanation. Quadratic
has x2 as its highest order.

Question
Number. 10. 2y = 5x + 3 What is the gradient?.

Option
A. 2/5.

Option
B. 5/2 + 3.

Option
C. 5/2.

Correct
Answer is. 5/2.

Explanation. Gradient
is the m when the formula is in the form y = mx + c.

Question
Number. 11. What is the slope between the points (3,1) and (9,3)?.

Option
A. 1/3.

Option
B. 3/1.

Option
C. 2.

Correct
Answer is. 1/3.

Explanation. (Y2-Y1)/(-),
3-1 = 2, 9-3 = 6. 2/6 = 1/3.

Question
Number. 12. What is commonly referred to as the law of a straight
line?.

Option
A. y = x

^{2 }plus 180.
Option
B. The line must pass through the 180 degree datum.

Option
C. y = mx + c.

Correct
Answer is. y = mx + c.

Explanation. NIL.

Question
Number. 13. The y intercept of 4y = 4x + 8 is.

Option
A. 4.

Option
B. 8.

Option
C. 2.

Correct
Answer is. 2.

Explanation. Must
be in form y = Mx + C, C is y-intercept. y = x + 2 in this case.

Question
Number. 14. A straight line passes through the two points (1,4) and
(6,1). What is the gradient of the line?.

Option
A. 3/5.

Option
B. -3/5.

Option
C. 2/5.

Correct
Answer is. -3/5.

Explanation. The
gradient is found by dividing the difference between the y
coordinates by the difference between the x coordinates. In this case
it will be 4-1/1-6 = 3/-5 =-3/5.

Question
Number. 15. What is the equation of a straight line with gradient m
and intercept on the y axis c?.

Option
A. y = mx + c.

Option
B. x = y + mc.

Option
C. y = cx + m.

Correct
Answer is. y = mx + c.

Explanation. NIL.

Question
Number. 16. What is the gadient of the straight line whose equation
is 2y + 3x = 6?.

Option
A. 3.

Option
B. 3/2.

Option
C. -3/2.

Correct
Answer is. -3/2.

Explanation. First
put into the form y = mx + c, i.e. y = -3x/2 +3 m = gradient hence
gradient is -3/2.

Question
Number. 17. Two lines with equations y = 3x-6 and y = 3x + 4 ?.

Option
A. meet when y = 3.

Option
B. are at right angles.

Option
C. are parallel.

Correct
Answer is. are parallel.

Explanation. They
both have the same gradient i.e. 3 and hence are parallel.

Question
Number. 18. What is the equation of a straight line that passes
through the two points (0,0) and (3,2).

Option
A. y = 3x + 2.

Option
B. y = 2x + 3.

Option
C. y =2x/3.

Correct
Answer is. y =2x/3.

Explanation. Gradient
of the line is (2-0)/(3-0) = 2/3 this is the difference in the y
values divided by the difference in the x values; m =2/3, The
intercept on the y axis is 0, that is when x = 0 ; c = 0, The
gradient of a straight line is of the form y = mx + c so we get y =
2x/3 +0 = 2x/3.

Question
Number. 19. The line with equation x = 3 is.

Option
A. at 45° to both axes.

Option
B. parallel to the x axis.

Option
C. parallel to the y axis.

Correct
Answer is. parallel to the y axis.

Explanation. If
x = 3 then the line will pass through all points where x=3 i.e.
(3,0); (3,1);(3,2) that is a line parallel to the y axis.

Question
Number. 20. What is the equation of the graph shown?.

Option
A. y = -2.

Option
B. x = -2.

Option
C. y = 2x.

Correct
Answer is. y = -2.

Explanation. All
the points on he line have a y value of -2, hence the equation is y =
-2.

Question
Number. 21. Use the graphs to solve the simultaneous equations y = x
+ 2 and 3y + 2x = 6.

Option
A. x = 2, y = 0.

Option
B. x = 0, y = 2.

Option
C. x = 0, y = 0.

Correct
Answer is. x = 0, y = 2.

Explanation. This
is easy. The solution is the point when the lines cross, i.e. (0,2):
x=0, y=2.

Question
Number. 22. The plot of the equation y = 1/x is a.

Option
A. straight line.

Option
B. curve with one turning point.

Option
C. curve with two turning points.

Correct
Answer is. curve with two turning points.

Explanation. y
= 1/x is a curve with two turning point. Try plotting it with values
of x of -2, -1, 0, 1, 2 and you will see that it appears in the no.1
and no.3 quadrants and goes off to infinity.

Question
Number. 23. Which of the graphs shown is given by the equation y = x

^{2 }+ 3?.
Correct
Answer is. C is correct.

Explanation. y
= ax + b is a straight line, y = ax

^{2 }+ b is a quadratic which has one turning point, y = ax^{3 }+ bx + c has two turning points.
Question
Number. 24. Which of the graphs shown is given by the equation; 2y =
4x +6 ?.

Correct
Answer is. B is correct because y = ax + b, is equation of straight
line.

Explanation. y
= ax + b is a straight line, y = ax

^{2 }+ b is a quadratic which has one turning point y = ax^{3 }+ bx + c has two turning points.
Question
Number. 25. Which of the graphs shown is given by the equation; y =
2x

^{3 }+ 4x + 3 ?.
Correct
Answer is. Graph in C is correct, because it has two turning points.

Explanation. y
= ax + b is a straight line, y = ax

^{2 }+ b is a quadratic which has one turning point, y = ax^{3 }+ bx + c has two turning points.

**1.3c Geometry.**
Question
Number. 1. What is the tangent of 90

^{o }?.
Option
A. Negative infinity.

Option
B. 0.

Option
C. Positive infinity.

Correct
Answer is. Positive infinity.

Explanation. Technically,
the tan curve goes off the graph to + infinity at 90 degrees, but
then comes back on at - infinity at the same point. Choose + infinity
for the answer here (since it goes to +infinity first).

Question
Number. 2. Two angles of a triangle are 68

^{o }and 32^{o }. Therefore the third angle must be.
Option
A. 114

^{o }.
Option
B. 80

^{o }.
Option
C. 63

^{o }.
Correct
Answer is. 80

^{o }.
Explanation. The
sum of all the angles in a triangle is 180 degrees.

Question
Number. 3. Which of the following formulae are correct for the
triangle shown?.

Option
A. A

^{2 }= C^{2 }+ B^{2 }.
Option
B. B

^{2 }= C^{2 }+ A^{2 }.
Option
C. C

^{2 }= A^{2 }+ B^{2 }.
Correct
Answer is. C

^{2 }= A^{2 }+ B^{2 }.
Explanation. Pythagoras
theorem.

Question
Number. 4. In a right-angled triangle the other two angles are both
45°. The length of the opposite side can be calculated by.

Option
A. cos 45° x length of the adjacent side of the triangle.

Option
B. cos 45° x length of the adjacent side of the triangle.

Option
C. sin 45° x length of the hypotenuse side of the triangle.

Correct
Answer is. sin 45° x length of the hypotenuse side of the triangle.

Explanation. sin
45

^{o }= opp/hyp opp = sin 45^{o }/ hyp.
Question
Number. 5. Sin ø =.

Option
A. A/C.

Option
B. B/C.

Option
C. C/A.

Correct
Answer is. A /C.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 6. Cos A =.

Option
A. 1.2.

Option
B. 0.6.

Option
C. 0.8.

Correct
Answer is. 0.8.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 7. In a right-angle triangle, the sine of an angle is.

Option
A. opposite divided by hypotenuse.

Option
B. adjacent divided by hypotenuse.

Option
C. opposite divided by adjacent.

Correct
Answer is. opposite divided by hypotenuse.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 8. In a right-angle triangle, the tangent of an angle is.

Option
A. opposite divided by adjacent.

Option
B. adjacent divided by hypotenuse.

Option
C. opposite divided by hypotenuse.

Correct
Answer is. opposite divided by adjacent.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 9. In a right-angle triangle, the cosine of an angle is.

Option
A. opposite divided by hypotenuse.

Option
B. adjacent divided by hypotenuse.

Option
C. opposite divided by adjacent.

Correct
Answer is. adjacent divided by hypotenuse.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 10. On a right angle triangle, the longest side is 20 cm and
the shortest is 12 cm. What is the other side?.

Option
A. 13 cm.

Option
B. 18 cm.

Option
C. 16 cm.

Correct
Answer is. 16 cm.

Explanation. 3,4,5
triangle. Also applies to multiples of 3,4,5 such as 6,8,10 and
12,16,20.

Question
Number. 11. In a right triangle, SINE theta =.

Option
A. adjacent divided by hypotenuse.

Option
B. opposite divided by adjacent.

Option
C. opposite divided by hypotenuse.

Correct
Answer is. opposite divided by hypotenuse.

Explanation. SOHCAHTOA.

Question
Number. 12. Complete the following: SINE a =.

Option
A. a squared times b squared.

Option
B. opposite side divided by the hypotenuse side.

Option
C. adjacent side divided by the opposite side.

Correct
Answer is. opposite side divided by the hypotenuse side.

Explanation. S.O.H.C.A.H.T.O.A.

Question
Number. 13. A sector with angle A is subtended to the centre point of
a circle. Area of the sector is proportional to:.

Option
A. Angle A.

Option
B. Cos A.

Option
C. Sin A.

Correct
Answer is. Angle A.

Explanation. Area
of a sector is proportional to the subtended angle of the sector.

Question
Number. 14. Starting from zero amplitude, the cosine curve repeats
itself between.

Option
A. -180 and 180 degree.

Option
B. -90 and 270 degrees.

Option
C. 0 and 360 degree.

Correct
Answer is. -90 and 270 degrees.

Explanation. Sketch
the cosine curve and see. Neither 0 or -180 degrees are zero
amplitude.

Question
Number. 15. Choose the correct statement:.

Option
A. Cosec

^{2 }x-Cot^{2 }x = 1.
Option
B. Sec

^{2 }x+tan^{2 }x = 1.
Option
C. Cos

^{2 }x-Sin^{2 }x = 1.
Correct
Answer is. Cosec

^{2 }x-Cot^{2 }x = 1.
Explanation. See
http://www.ilovemaths.com/2trigid.htm.

Question
Number. 16. A right angled triangle has the two shortest sides of 5cm
and 12 cm. What is the length of the longest side?.

Option
A. 17cm.

Option
B. 15cm.

Option
C. 13cm.

Correct
Answer is. 13cm.

Explanation. Use
Pythagoras theorem The square on the hypotenuse is equal to the sum
of the squares on the other two sides. 52 + 122 = h

^{2 }25 + 144 = h^{2}, h = √169 =13.
Question
Number. 17. The trigonometrical ratio; adjacent divided by hypotenuse
is.

Option
A. Sine.

Option
B. Tangent.

Option
C. Cosine.

Correct
Answer is. Cosine.

Explanation. Sin
= Opp/Hyp, Cos = Adj/Hyp, Tan = Opp/Adj.

Question
Number. 18. 57.3 degrees is equal to.

Option
A. 2 radians.

Option
B. 1 radian.

Option
C. π radians.

Correct
Answer is. 1 radian.

Explanation. This
is worth learning.

Question
Number. 19. A right angled triangle has sides 6cm, 8cm and 10 cm.
What is the sine of the angle between the 8cm side and the 10 cm
side?.

Option
A. 0.75.

Option
B. 0.6.

Option
C. 0.8.

Correct
Answer is. 0.6.

Explanation. A
6,8,10 triangle is 2 x the 3, 4, 5 triangle which is a right angled
triangled triangle with hypotenuse 5. For our triangle the
hypotenuse will be 10. The angle we are considering has an opposite
side of 6 and sine of an angle is the opposite/hypotenuse. Hence the
answer is 6/10 = 0.6.

Question
Number. 20. Sin 90 =.

Option
A. Infinity.

Option
B. 1.

Option
C. 0.

Correct
Answer is. 1.

Explanation. Sin
90 = 1, Cos 90 = 0, tan 90 = infinity.

Question
Number. 21. What size of angle has the same ratio for both the sine
and the cosine?.

Option
A. 60 degrees.

Option
B. 0 degrees.

Option
C. 45 degrees.

Correct
Answer is. 45 degrees.

Explanation. An
isosceles right angled triangle has two 45 degree angles. The size
of the two sides that are not the hypotenuse are the same. This
means that both the sine which is opposite/hypotenuse and the cosine
which is adjacent/hypotenuseis the same as the adjacent = opposite in
this case.

Question
Number. 22. Sin A is equal to.

Option
A. 3/4.

Option
B. 3/5.

Option
C. 4/5.

Correct
Answer is. 3/5.

Explanation. B&C
is opposite to A, A&B is adjacent to A, A&C is hypotenuse,
sin = o/h, cos = a/h , tan= o/a.

Question
Number. 23. If cos 60 is 0.5, what is sin 30?.

Option
A. 0.5.

Option
B. None of the above.

Option
C. 0.866.

Correct
Answer is. 0.5.

Explanation. Cos
θ = sin (90-θ).

**1.4**
Question
Number. 1. 5/16 + 3/32 expressed as a single fraction is.

Option
A. 13/32.

Option
B. 8/48.

Option
C. 15/512.

Correct
Answer is. 13/32.

Explanation. 5/16
= 10/32 , 10/32 + 3/32 = 13/32.

Question
Number. 2. Dividing 41/2 by 2 1/6 gives the answer of.

Option
A. 21/3.

Option
B. 25/12.

Option
C. 54/26.

Correct
Answer is. 54/26.

Explanation. 41/2
= 9/2, 21/6 = 13/6 Turn one fraction up-side-down then multiply 9/2 x
6/13 = 54/26.

Question
Number. 3. 10000 expressed as ten raised to a power would be.

Option
A. 105.

Option
B. 103.

Option
C. 104.

Correct
Answer is. 104.

Explanation. 10
* 10 *10 = 1000, 10 * 10 * 10 * 10 = 10000.

Question
Number. 4. 60 mm expressed as a percentage of 3 metres is.

Option
A. 2 %.

Option
B. 1.8 %.

Option
C. 0.5 %.

Correct
Answer is. 2 %.

Explanation. (60
* 100) / 3000.

Question
Number. 5. The average speed of an aircraft that travels 7200 miles
in 12 hours is.

Option
A. 864 MPH.

Option
B. 167 MPH.

Option
C. 600 MPH.

Correct
Answer is. 600 MPH.

Explanation. 7200
/12.

Question
Number. 6. The sum of complex numbers a+bi and a'+b'i are.

Option
A. (a+b)+(a'+b')i.

Option
B. (a+a')i+(b+b').

Option
C. (a+a')+(b+b')i.

Correct
Answer is. (a+b)+(a'+b')i.

Explanation. Add
the real numbers to each other, then add the imaginary numbers to
each other, and keep them separate.

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