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Q1. Place value (incl. decimals) [4 marks]

Non-calculator

(a) What is the value of the digit 5 in 0.40507? →

(b) Complete the expansion: 0.307 = × 0.1 + × 0.01 + × 0.001

Q2. Rounding (nearest, d.p., s.f.) [3 marks]

Non-calculator

(a) Round 73846 to the nearest thousand. →

(b) Round 3.468 to 1 decimal place. →

(c) Round 0.007986 to 2 significant figures. →

Q3. Add & subtract numbers [4 marks]

Non-calculator

(a) 48761939 =

(b) −3.4 + 7.28 =

Q4. Multiply & divide numbers (written methods) [4 marks]

Non-calculator

(a) 307 × 24 =

(b) 5268 ÷ 12 =

Q5. Fractions — Fraction of an amount & reverse fraction [3 marks]

Non-calculator

(a) Find 35 of 210. →

(b) 35 of a number is 210. Find the number. →

Q6. Fractions — Add & subtract (give answers in simplest form) [4 marks]

Non-calculator

(a) 38+512 =

(b) 71015 =

Q7. Fractions — Multiply & divide (simplify) [5 marks]

Non-calculator

(a) 23×1528 =

(b) 56÷310 =

Q8. Convert between fractions, decimals & percentages (+ % of an amount) [5 marks]

Non-calculator

(a) Write 0.375 as a fraction in simplest form and as a percentage: and %

(b) Write 720 as a decimal. →

(c) Write 12% as a fraction in simplest form:

(d) Find 15% of 160. →

Q9. Estimation & approximation (1 s.f.) [3 marks]

Non-calculator

By rounding to 1 significant figure, estimate 39.7 × 0.51.

Rounded numbers used: × → Estimate =

Q10. Measures & accuracy (units & error intervals) [5 marks]

Non-calculator

(a) Convert: 3.5 kg = g    and   2.4 m = cm

(b) A rope is measured as 8.4 m to the nearest 0.1 m. Give the error interval for its actual length (enter numbers only):

Lower bound = m    Upper bound = m

Note: interpret as lower ≤ length < upper.

Q11. Factors & multiples — Prime factors, HCF & LCM [6 marks]

Non-calculator

(a) Write 84 as a product of prime factors (index form allowed). →

(b) Write 60 as a product of prime factors. →

(c) Hence find HCF of 84 and 60. →

(d) Hence find LCM of 84 and 60. →

Q12. Powers & roots [3 marks]

Non-calculator

(a) Evaluate 5³. →

(b) Evaluate √196. →

(c) Hence find 5³ − √196. →

Q13. Roots & indices (laws) [4 marks]

Non-calculator

(a) Simplify to a single power of 2: 25 × 23 ÷ 24 = 2 00

(b) Express 96= 2a × 3b . Give integers a and b: a = , b =

Q14. Standard form — Convert [3 marks]

Non-calculator

(a) Write 0.00036 in standard form.

= × 10 00

(b) Write 5.2×104 as an ordinary number. →

Q15. Standard form — Calculate [6 marks]

Non-calculator

(a) (3×105) × (2×103) — give your answer in standard form:

= × 10 00

(b) (6×107) ÷ (3×102) — give your answer in standard form:

= × 10 00

(c) (7×106) + (3×105) — give your answer in standard form:

= × 10 00

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