Number

What is 7 × 8?

• A56✓
• B54
• C63
• D49

Answer: 7 × 8 = 56. A key times-table fact to know by heart.

What is the value of 3² + 4²?

• A14
• B7
• C25✓
• D49

Answer: 3² = 9 and 4² = 16, so 9 + 16 = 25.

Write 0.75 as a fraction in its simplest form.

• A3/4✓
• B1/4
• C7/5
• D7/10

Answer: 0.75 = 75/100, and dividing the top and bottom by 25 gives 3/4.

What is the lowest common multiple (LCM) of 4 and 6?

• A2
• B24
• C10
• D12✓

Answer: Multiples of 4: 4, 8, 12… Multiples of 6: 6, 12… The lowest common multiple is 12.

What is 15% of 200?

• A3
• B15
• C30✓
• D35

Answer: 10% of 200 = 20, and 5% = 10, so 15% = 20 + 10 = 30.

What is −6 + 10?

• A−16
• B4✓
• C−4
• D16

Answer: Starting at −6 and adding 10 moves up the number line to 4.

Round 4,672 to the nearest hundred.

• A4,670
• B5,000
• C4,700✓
• D4,600

Answer: The tens digit is 7, so we round up: 4,672 → 4,700.

What is the cube root of 27?

• A13.5
• B6
• C9
• D3✓

Answer: 3 × 3 × 3 = 27, so the cube root of 27 is 3.

What is −4 × −3?

• A12✓
• B−12
• C7
• D−7

Answer: A negative multiplied by a negative gives a positive: −4 × −3 = 12.

Simplify 3⁴ × 3⁵, giving your answer as a single power of 3.

• A3⁹✓
• B3²⁰
• C9⁹
• D3¹

Answer: Multiplying powers of the same base means adding the indices: 4 + 5 = 9, so the result is 3⁹. Multiplying the indices, or multiplying the bases as well, are the two usual slips.

Simplify 2¹⁰ ÷ 2³, giving your answer as a single power of 2.

• A2¹³
• B2³⁰
• C2⁷✓
• D1⁷

Answer: Dividing powers of the same base means subtracting the indices: 10 - 3 = 7, giving 2⁷. The base itself is never divided, so it stays as 2.

Simplify (5³)², giving your answer as a single power of 5.

• A5⁵
• B5⁶✓
• C5⁹
• D25⁶

Answer: A power raised to another power means the indices multiply: 3 × 2 = 6, so (5³)² = 5⁶. Adding the indices would give 5⁵, which is the common error.

Which of these is 47,000 written correctly in standard form?

• A4.7 × 10³
• B47 × 10³
• C4.7 × 10⁴✓
• D4.7 × 10⁵

Answer: Standard form needs a number that is at least 1 but less than 10, times a power of ten. The digits 4.7 must be multiplied by 10,000 to reach 47,000, so the index is 4. Writing 47 in front breaks the rule about the first number.

Write 0.0026 in standard form.

• A2.6 × 10⁻³✓
• B2.6 × 10³
• C26 × 10⁻⁴
• D2.6 × 10⁻⁴

Answer: 0.0026 is 2.6 divided by 1000, and dividing by 10³ gives an index of −3, so the answer is 2.6 × 10⁻³. Count the places the decimal point moves. Writing 26 × 10⁻⁴ has the right value, but the first number must be at least 1 and less than 10, so it is not standard form.

Write 84 as a product of its prime factors.

• A2² × 3 × 7✓
• B2 × 3 × 7
• C2² × 21
• D4 × 3 × 7

Answer: Dividing repeatedly by primes gives 84 = 2 × 2 × 3 × 7, and grouping the twos writes this as 2² × 3 × 7. Every number in the product must itself be prime, which rules out 21 and 4, and the factor 2 appears twice.

Given that 36 = 2² × 3² and 60 = 2² × 3 × 5, what is the highest common factor of 36 and 60?

• A6
• B12✓
• C180
• D4

Answer: The highest common factor uses the lowest power of each prime that appears in both: 2² × 3 = 12. Taking the highest powers instead gives the lowest common multiple, which is 180.

What is the lowest common multiple of 8 and 12?

• A96
• B24✓
• C4
• D48

Answer: The multiples of 8 run 8, 16, 24 and the multiples of 12 run 12, 24, so the smallest one they share is 24. Multiplying 8 by 12 gives 96, which is a common multiple but not the lowest.

Round 0.04837 to 2 significant figures.

• A0.05
• B0.048✓
• C0.04
• D0.0484

Answer: Leading zeros are not significant, so the first significant figure is the 4 and the second is the 8. The next digit is 3, which is below 5, so the value rounds down to 0.048.

By rounding each number to 1 significant figure, estimate 19.7 × 4.1.

• A60
• B24
• C100
• D80✓

Answer: To 1 significant figure 19.7 becomes 20 and 4.1 becomes 4, so the estimate is 20 × 4 = 80. Adding the rounded values instead of multiplying them gives 24.