## 01.1. 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 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 3.

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

Option A. 0.028 m3 .

Option B. 2.88 m3 .

Option C. 0.000288 m3 .

Correct Answer is. 2.88 m3 .

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

Question Number 4.

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.

Question Number 5.

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 6. A rectangle is 11cm x 120cm. What is its area in m2 ?

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 7.

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

Option A. 40π cm2.

Option B. 120π cm2.

Option C. 80π cm2.

Correct Answer is. 40π cm2.

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

Question Number 8.

Evaluate 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 9.

Evaluate 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 10.

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 11.

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 12.

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 13.

143 can be expressed as.

Option A. 14 * 14 * 14.

Option B. 14 x3.

Option C. 14 + 14 + 14.

Correct Answer is. 14 * 14 * 14.

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

Question Number 14.

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 15.

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 16.

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 17.

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 18.

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 19.

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 20.

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 21.

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 22.

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 23.

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 radius2.

Question Number 24.

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 25.

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 26.

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 27.

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

Option A. 2 x 3.142 x r.

Option B. d2 x 3.142.

Option C. r2 x 3.142.

Correct Answer is. r2 x 3.142.

Explanation. Area = πr2.

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 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 3.

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

Option A. 0.028 m3 .

Option B. 2.88 m3 .

Option C. 0.000288 m3 .

Correct Answer is. 2.88 m3 .

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

Question Number 4.

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.

Question Number 5.

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 6. A rectangle is 11cm x 120cm. What is its area in m2 ?

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 7.

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

Option A. 40π cm2.

Option B. 120π cm2.

Option C. 80π cm2.

Correct Answer is. 40π cm2.

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

Question Number 8.

Evaluate 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 9.

Evaluate 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 10.

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 11.

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 12.

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 13.

143 can be expressed as.

Option A. 14 * 14 * 14.

Option B. 14 x3.

Option C. 14 + 14 + 14.

Correct Answer is. 14 * 14 * 14.

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

Question Number 14.

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 15.

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 16.

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 17.

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 18.

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 19.

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 20.

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 21.

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 22.

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 23.

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 radius2.

Question Number 24.

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 25.

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 26.

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 27.

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

Option A. 2 x 3.142 x r.

Option B. d2 x 3.142.

Option C. r2 x 3.142.

Correct Answer is. r2 x 3.142.

Explanation. Area = πr2.