IGCSE Maths 4MA1 Foundation Number Questions

• B1 (a) 17 and 23 only
• B1 (b) 6, 9, 21 and 27 only

1. A prime number has exactly two factors. 6, 9, 14, 21 and 27 all have other factors, so the primes are 17 and 23.
2. A multiple of 3 is in the 3 times table: 6 = 2 × 3, 9 = 3 × 3, 21 = 7 × 3, 27 = 9 × 3.

Answer: (a) \(17, 23\) (b) \(6, 9, 21, 27\)

• M1 (a) for a correct method to find the prime factors, e.g. a factor tree with at least two correct branches
• A1 (a) 2³ × 3² × 5²
• B1 (b) 2

1. (a) 1800 = 18 × 100 = (2 × 3²) × (2² × 5²) = 2³ × 3² × 5².
2. (b) A square number has every power even. 3² and 5² are already even powers; 2³ needs one more 2.
3. So n = 2: 1800 × 2 = 3600 = 60².

Answer: (a) \(2^3 \times 3^2 \times 5^2\) (b) \(n = 2\)

• M1 for 3 × 4.80 (= 14.40) or 4 × 1.35 (= 5.40)
• M1 for 50 − (14.40 + 5.40) (= 30.20)
• M1 for their 30.20 ÷ 2
• A1 £15.10

1. Notebooks: 3 × £4.80 = £14.40
2. Pens: 4 × £1.35 = £5.40
3. Total spent: £14.40 + £5.40 = £19.80
4. Left: £50 − £19.80 = £30.20
5. Each brother: £30.20 ÷ 2 = £15.10

Answer: £15.10

• B1 3/5

1. The highest common factor of 24 and 40 is 8.
2. 24 ÷ 8 = 3 and 40 ÷ 8 = 5, so 24/40 = 3/5.

Answer: \(\frac{3}{5}\)

• M1 for 45/120 (both in minutes)
• A1 3/8

1. Use the same units: 2 hours = 120 minutes.
2. 45/120 = 3/8 (dividing by 15).

Answer: \(\frac{3}{8}\)

• M1 for 5/8 − 1/4 (= 3/8) or 5/8 × 240 (= 150) or 1/4 × 240 (= 60)
• M1 for 3/8 × 240 or 150 − 60
• A1 90

1. At the start: 5/8 × 240 = 150 litres.
2. At the end: 1/4 × 240 = 60 litres.
3. Used: 150 − 60 = 90 litres.

Answer: \(90\) litres

• B1 0.035, 0.305, 0.35, 0.5, 0.53

1. Write each to 3 decimal places: 0.350, 0.305, 0.530, 0.035, 0.500.
2. Order: 0.035, 0.305, 0.350, 0.500, 0.530.

Answer: \(0.035, 0.305, 0.35, 0.5, 0.53\)

• B1 (a) 11.61
• B1 (b) 430

1. (a) 4.3 × 2.7 = (43 ÷ 10) × (27 ÷ 10) = 1161 ÷ 100 = 11.61
2. (b) 1161 ÷ 27 = 43, so 116.1 ÷ 0.27 = (1161 ÷ 10) ÷ (27 ÷ 100) = 43 × 10 = 430

Answer: (a) \(11.61\) (b) \(430\)

• M1 for 2.40 ÷ 8 (= 0.30) or comparing a bag with 8 × 0.35 (= 2.80)
• M1 for 2 bags + 4 single apples: 2 × 2.40 + 4 × 0.35
• M1 for comparing with 3 bags (= 7.20)
• A1 £6.20

1. A bag works out at £2.40 ÷ 8 = £0.30 an apple, cheaper than £0.35.
2. 2 bags give 16 apples for £4.80; 4 more single apples cost 4 × £0.35 = £1.40, total £6.20.
3. 3 bags (24 apples) would cost £7.20, which is more.
4. So the least he can pay is £6.20.

Answer: £6.20

• B1 (a) 16, 25, 64
• B1 (b) 8, 27, 64

1. (a) 16 = 4², 25 = 5², 64 = 8².
2. (b) 8 = 2³, 27 = 3³, 64 = 4³ (64 is both a square and a cube).

Answer: (a) \(16, 25, 64\) (b) \(8, 27, 64\)

• B1 (a) 8
• B1 (b) 7
• B1 (c) −3

1. (a) n + 3 = 11, so n = 8.
2. (b) 9 − n = 2, so n = 7.
3. (c) 0.001 = 1/1000 = 1/10³ = 10⁻³, so n = −3.

Answer: (a) \(n = 8\) (b) \(n = 7\) (c) \(n = -3\)

• M1 (a) for 420 ÷ 30 (= 14) or 270 ÷ 30 (= 9)
• A1 (a) 126
• M1 (b) for 126 ÷ 20 (= 6.3)
• A1 (b) 7

1. (a) 4.2 m = 420 cm and 2.7 m = 270 cm. Along the length: 420 ÷ 30 = 14 tiles; across: 270 ÷ 30 = 9 tiles.
2. 14 × 9 = 126 tiles.
3. (b) 126 ÷ 20 = 6.3, so 6 boxes are not enough: 7 boxes.

Answer: (a) \(126\) (b) \(7\) boxes

• B1 (a) No, 5 is not a member of A (5 ∉ A)
• B1 (b) even numbers from 2 to 10 oe

1. (a) ∈ means 'is a member of'. 5 is not in the list, so 5 ∉ A.
2. (b) The members are the even numbers from 2 up to 10.

Answer: (a) No, \(5 \notin A\) (b) the even numbers from 2 to 10

• B1 (a) 2
• M1 (b) for P = {2, 3, 5, 7, 11, 13} and E = {2, 4, 6, 8, 10, 12, 14}
• A1 (b) {1, 9, 15}

1. (a) 2 is the only even prime.
2. (b) P ∪ E = {2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14}.
3. Numbers from 1 to 15 not in P ∪ E: 1, 9, 15.

Answer: (a) \(2\) (b) \(\{1, 9, 15\}\)

• B1 (a) F ∩ O: 1, 3
• B1 (a) F only: 2, 4, 6, 12
• B1 (a) O only: 5, 7, 9, 11 and neither: 8, 10
• B1 (b) {5, 7, 9, 11}

1. F = {1, 2, 3, 4, 6, 12}; O = {1, 3, 5, 7, 9, 11}.
2. Both: 1, 3. F only: 2, 4, 6, 12. O only: 5, 7, 9, 11. Neither: 8, 10.
3. (b) F′ ∩ O is odd and not a factor of 12: 5, 7, 9, 11.

Answer: (a) both: \(1, 3\); \(F\) only: \(2, 4, 6, 12\); \(O\) only: \(5, 7, 9, 11\); neither: \(8, 10\) (b) \(\{5, 7, 9, 11\}\)

• M1 for 0.15 × 240 oe
• A1 £36

1. 10% of £240 = £24 and 5% = £12.
2. 15% = £24 + £12 = £36 (or 0.15 × 240 = 36).

Answer: £36

• M1 for 348 ÷ 1.2 oe
• A1 £290

1. Price with VAT = 120% of the price before VAT.
2. 348 ÷ 1.2 = 290.

Answer: £290

• M1 for 800 × 0.04 × 4 (= 128)
• M1 for 800 × 1.038⁴ (= 928.70…)
• M1 for interest 128.70… or comparing totals 928 and 928.70…
• A1 Tom, by £0.71 (accept 71p)

1. Lena (simple interest): 4% of £800 = £32 a year, so 4 × £32 = £128.
2. Tom (compound interest): 800 × 1.038⁴ = 928.708…, so the interest is £128.71.
3. Tom pays £128.71 − £128 = £0.71 more.

Answer: Tom, by £0.71

• B1 2 : 3

1. The HCF of 24 and 36 is 12.
2. 24 ÷ 12 = 2 and 36 ÷ 12 = 3.

Answer: \(2 : 3\)

• M1 for s = 3.5t or a multiplier of 14/4 seen
• A1 35
• A1 18

1. s ÷ t is constant: 14 ÷ 4 = 3.5, so s = 3.5t.
2. When t = 10, s = 35.
3. When s = 63, t = 63 ÷ 3.5 = 18.

Answer: \(s = 35\) when \(t = 10\); \(t = 18\) when \(s = 63\)

• M1 for 15 ÷ 5 (= 3)
• M1 for 6 litres of red or 9 litres of yellow
• M1 for 6 × 6 + 9 × 4.50
• A1 £76.50

1. 15 litres in the ratio 2 : 3: one part = 15 ÷ 5 = 3 litres.
2. Red: 6 litres; yellow: 9 litres.
3. Cost: 6 × £6 + 9 × £4.50 = £36 + £40.50 = £76.50.

Answer: £76.50

• B1 (a) 47 860
• B1 (b) 48 000

1. (a) 47 862 is between 47 860 and 47 870; the units digit 2 rounds down.
2. (b) 47 862 is between 47 000 and 48 000; the hundreds digit 8 rounds up.

Answer: (a) \(47\,860\) (b) \(48\,000\)

• B1 (a) 3450
• B1 (b) 3549

1. To the nearest 100, the number is within 50 of 3500: from 3450 up to (but not including) 3550.
2. People are counted in whole numbers, so the greatest possible number is 3549.

Answer: (a) \(3450\) (b) \(3549\)

• B1 (a) 8.5 (cm)
• M1 (b) for 2 × (8.5 + 5.5)
• A1 (b) 28 (cm)

1. (a) 8 cm to the nearest centimetre: upper bound 8.5 cm.
2. (b) Upper bounds: 8.5 cm and 5.5 cm. Perimeter = 2 × (8.5 + 5.5) = 28 cm.

Answer: (a) \(8.5\) cm (b) \(28\) cm

• B1 5.3 × 10⁶

1. Move the decimal point 6 places so the first number is between 1 and 10: 5.3.
2. 5 300 000 = 5.3 × 10⁶.

Answer: \(5.3 \times 10^6\)

• M1 for 6.7 × 3 × 10⁻⁴⁺⁶ or 20.1 × 10²
• A1 2.01 × 10³

1. 6.7 × 3 = 20.1 and 10⁻⁴ × 10⁶ = 10².
2. 20.1 × 10² = 2.01 × 10³ grams (2010 g).

Answer: \(2.01 \times 10^3\) grams

• M1 (a) for 272 000 000 − 68 000 000
• A1 (a) 2.04 × 10⁸
• M1 (b) for (2.72 × 10⁸) ÷ (6.8 × 10⁷)
• A1 (b) 4

1. (a) 272 000 000 − 68 000 000 = 204 000 000 = 2.04 × 10⁸.
2. (b) 2.72 × 10⁸ ÷ 6.8 × 10⁷ = (27.2 ÷ 6.8) × 10⁷ ÷ 10⁷ = 4.

Answer: (a) \(2.04 \times 10^8\) (b) \(k = 4\)

• B1 (a) 3500 (g)
• B1 (b) 2.4 (litres)
• B1 (c) 0.85 (m)

1. (a) 1 kg = 1000 g: 3.5 × 1000 = 3500 g.
2. (b) 1 litre = 1000 ml: 2400 ÷ 1000 = 2.4 litres.
3. (c) 1 m = 100 cm: 85 ÷ 100 = 0.85 m.

Answer: (a) \(3500\) g (b) \(2.4\) litres (c) \(0.85\) m

• M1 for 365 ÷ 1.16 (= 314.655…) or 320 × 1.16 (= 371.20)
• M1 for 320 − 314.66 or comparing 371.20 with 365
• A1 Paris, by £5.34

1. Price in Paris in pounds: €365 ÷ 1.16 = £314.655… ≈ £314.66.
2. Difference: £320 − £314.66 = £5.34.
3. The phone is cheaper in Paris.

Answer: Paris, by £5.34

• M1 (a) for 120 × 80 × 50 (= 480 000 cm³)
• A1 (a) 480 (litres)
• M1 (b) for their 480 ÷ 8
• A1 (b) 60 (minutes)

1. (a) In centimetres: 120 × 80 × 50 = 480 000 cm³; 1 litre = 1000 cm³, so 480 litres.
2. (b) 480 ÷ 8 = 60 minutes.

Answer: (a) \(480\) litres (b) \(60\) minutes

• B1 9

1. Work out the top first (use brackets or the fraction key): 8.6 + 4.9 = 13.5.
2. 13.5 ÷ 1.5 = 9.

Answer: \(9\)

• M1 for 38 400 seen
• A1 3.84 × 10⁴

1. 2400 ÷ 0.0625 = 38 400.
2. 38 400 = 3.84 × 10⁴.

Answer: \(3.84 \times 10^4\)

• M1 (a) for 140 ÷ 12 (= 11.66…) or 2.5 × 12 (= 30 m² per tin)
• A1 (a) 5 tins
• M1 (b) for 5 × 14.85 ÷ 140
• A1 (b) £0.53

1. (a) One tin covers 2.5 × 12 = 30 m². 140 ÷ 30 = 4.66…, so he needs 5 tins.
2. (b) 5 tins cost 5 × £14.85 = £74.25; £74.25 ÷ 140 = £0.5303… ≈ £0.53 per m².

Answer: (a) \(5\) tins (b) £0.53 per m\(^2\)