Free Part 66 Module 1 sample questions

What is ³⁄₄ of 60?

• 40
• ✓ 45
• 48

Answer: 60 ÷ 4 = 15, then 15 × 3 = 45.

What is 15% of 240?

• 24
• ✓ 36
• 48

Answer: 15% = 0.15, and 0.15 × 240 = 36.

£50 is split in the ratio 2:3. What is the larger share?

• £20
• £25
• ✓ £30

Answer: There are 2 + 3 = 5 parts. 50 ÷ 5 = 10 per part, so the larger share is 3 × 10 = £30.

What is the mean of 4, 8, 10 and 14?

• 8
• ✓ 9
• 10

Answer: Sum = 36, and 36 ÷ 4 = 9.

What is 2⁵?

• 10
• 25
• ✓ 32

Answer: 2 × 2 × 2 × 2 × 2 = 32.

What is the square root of 144?

• ✓ 12
• 14
• 72

Answer: 12 × 12 = 144, so √144 = 12.

Solve for x: 3x + 7 = 22.

• 3
• ✓ 5
• 7

Answer: Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.

Rearrange v = u + at to make a the subject.

• ✓ a = (v − u)/t
• a = (v + u)/t
• a = v − u − t

Answer: Subtract u from both sides: v − u = at. Divide by t: a = (v − u)/t.

What is the binary number 1011 in decimal?

• 9
• ✓ 11
• 13

Answer: 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11.

Simplify 2³ × 2².

• ✓ 2⁵
• 2⁶
• 4⁵

Answer: When multiplying powers of the same base, add the indices: 3 + 2 = 5, giving 2⁵.

Solve x² = 49 (take the positive root).

• ✓ 7
• 24.5
• 2401

Answer: x = √49 = 7.

What is log₁₀(1000)?

• 2
• ✓ 3
• 100

Answer: 10³ = 1000, so log₁₀(1000) = 3.

A right-angled triangle has legs 3 cm and 4 cm. What is the length of the hypotenuse?

• ✓ 5 cm
• 7 cm
• 12 cm

Answer: Hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

What is the area of a triangle with base 10 cm and height 6 cm?

• 16 cm²
• ✓ 30 cm²
• 60 cm²

Answer: Area = ½ × base × height = ½ × 10 × 6 = 30 cm².

What is sin 30°?

• ✓ 0.5
• 0.866
• 1

Answer: sin 30° = 0.5 — one of the standard exact values worth memorising.

Two angles of a triangle are 40° and 60°. What is the third angle?

• ✓ 80°
• 90°
• 100°

Answer: Angles in a triangle sum to 180°: 180 − 40 − 60 = 80°.