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0580/31 Oct/Nov 2021, Question 1: Number Review: Mixed Practice

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 12 marks

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The question, in short

Use the given number list and number properties to answer parts on square roots, factors, multiples, consecutive numbers, brackets, reciprocals, indices and roots.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 1 mark

From the list, identify the number equal to the square root of 289.

  1. 117 × 17 = 289
  2. 2√289 = 17

Answer17

Part (aii) · 1 mark

From the list, choose a number that is a factor of 81.

  1. 181 ÷ 27 = 3 exactly
  2. 227 is a factor of 81

Answer27

Part (aiii) · 1 mark

From the list, choose a number that is a common multiple of 3 and 5.

  1. 1Common multiples of 3 and 5 are multiples of 15
  2. 230 = 2 × 15 is in the list

Answer30

Part (b) · 2 marks

Find three consecutive whole numbers A, B, C where A is prime, B is a cube, C is a square, and A+B+C is under 40.

  1. 1Cube numbers: 1, 8, 27
  2. 2B = 8: A = 7 (prime), C = 9 (square)
  3. 37 + 8 + 9 = 24 < 40
  4. 4A = 7, B = 8, C = 9

AnswerA = 7, B = 8, C = 9

Part (ci) · 1 mark

Insert one pair of brackets into 4 × 3 + 7 ÷ 2 = 20 to make it true.

  1. 14 × (3 + 7) ÷ 2 = 4 × 10 ÷ 2
  2. 2= 40 ÷ 2 = 20

Answer4 × (3 + 7) ÷ 2 = 20

Part (cii) · 1 mark

Insert one pair of brackets into 51 − 12 ÷ 3 + 6 = 19 to make it true.

  1. 1(51 − 12) ÷ 3 + 6 = 39 ÷ 3 + 6
  2. 2= 13 + 6 = 19

Answer(51 − 12) ÷ 3 + 6 = 19

Part (di) · 1 mark

State the reciprocal of 8.

  1. 1Reciprocal of 8 = 1 ÷ 8
  2. 2= 1/8

Answer1/8 or 0.125

Part (dii) · 1 mark

State the value of 14 to the power 0.

  1. 1Any non-zero number to the power 0 is 1
  2. 214⁰ = 1

Answer1

Part (ei) · 1 mark

Calculate 5 to the power 4.

  1. 15⁴ = 5 × 5 × 5 × 5
  2. 2= 625

Answer625

Part (eii) · 1 mark

Calculate the cube root of 6859.

  1. 119 × 19 × 19 = 6859
  2. 2∛6859 = 19

Answer19

Part (eiii) · 1 mark

Calculate 16 to the power negative one half.

  1. 116^(1/2) = √16 = 4
  2. 216^(−1/2) = 1/4

Answer1/4 or 0.25

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Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 1.
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