0580/31 May/Jun 2023, Question 1: Reciprocals

Part (a) · 1 mark

Write forty thousand and thirty-three using digits.

1. 1Forty thousand = 40 000, plus thirty-three = 33
2. 240 000 + 33 = 40033

Answer40033

Part (b) · 1 mark

Evaluate the cube root of 729.

1. 19 × 9 × 9 = 729
2. 2∛729 = 9

Answer9

Part (c) · 2 marks

Find the reciprocal of 7/9 as a decimal rounded to 3 decimal places.

1. 1Reciprocal of 7/9 = 9/7
2. 29 ÷ 7 = 1.28571…
3. 3≈ 1.286 (3 d.p.)

Answer1.286

Part (d) · 2 marks

Calculate 6⁵ ÷ 3⁴.

1. 16⁵ = 7776 and 3⁴ = 81
2. 27776 ÷ 81 = 96

Answer96

Part (e) · 1 mark

Work out (−9) × (−7) ÷ (−3).

1. 1(−9) × (−7) = 63
2. 263 ÷ (−3) = −21

Answer−21

Part (fi) · 1 mark

Evaluate 11 + 9 × 5 − 4 using the correct order of operations.

1. 1Multiply first: 9 × 5 = 45
2. 211 + 45 − 4 = 52

Answer52

Part (fii) · 1 mark

Evaluate (11 + 9) × 5 − 4, respecting the brackets.

1. 1Brackets first: 11 + 9 = 20
2. 220 × 5 − 4 = 100 − 4 = 96

Answer96

Part (g) · 1 mark

From the given list, identify which value is irrational.

1. 1√49 = 7, −0.67, 5/9 and 3.142 can all be written as fractions
2. 2123 is not a square number, so √123 cannot be written as a fraction
3. 3Irrational number: √123

Answer√123

Part (hi) · 2 marks

Find the lowest common multiple of 24 and 104.

1. 124 = 2 × 2 × 2 × 3 = 2³ × 3
2. 2104 = 2 × 2 × 2 × 13 = 2³ × 13
3. 3LCM = 2³ × 3 × 13 = 312

Answer312

Part (hii) · 2 marks

Find the highest common factor of 24 and 104.

1. 124 = 2³ × 3 and 104 = 2³ × 13
2. 2Common factors: 2 × 2 × 2
3. 3HCF = 8

Answer8

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