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0580/33 May/Jun 2022, Question 5: Upper and Lower Bounds

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

A set of short arithmetic and number questions covering weeks to days, height difference, integer pairs, fraction conversions, reciprocals, powers, roots, standard form and error bounds.

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

Part (a) · 1 mark

Convert seven weeks into a number of days.

  1. 17 × 7 = 49 days

Answer49

Part (b) · 1 mark

Find the height difference between Everest at 8848 m and Ayding Lake at 154 m below sea level.

  1. 18848 − (−154) = 8848 + 154 = 9002 m

Answer9002

Part (c) · 1 mark

Find two integers whose sum is −12 and whose product is 32.

  1. 1(−8) + (−4) = −12 and (−8) × (−4) = 32
  2. 2−8 and −4

Answer−8 and −4

Part (di) · 1 mark

Express the fraction 3/8 as a decimal.

  1. 13 ÷ 8 = 0.375

Answer0.375

Part (dii) · 1 mark

Express the fraction 3/8 as a percentage.

  1. 10.375 × 100 = 37.5%

Answer37.5

Part (e) · 1 mark

State the reciprocal of 1/9.

  1. 1Reciprocal of 1/9 = 1 ÷ 1/9 = 9

Answer9

Part (fi) · 1 mark

Evaluate 4⁵.

  1. 14⁵ = 4 × 4 × 4 × 4 × 4 = 1024

Answer1024

Part (fii) · 1 mark

Evaluate the cube root of 512.

  1. 18 × 8 × 8 = 512, so ∛512 = 8

Answer8

Part (gi) · 1 mark

Write 587 000 in standard form.

  1. 1587 000 = 5.87 × 100 000 = 5.87 × 10⁵

Answer5.87 × 10⁵

Part (gii) · 1 mark

Add 4.9 × 10⁻³ and 8.1 × 10⁻⁴, giving the result in standard form.

  1. 10.0049 + 0.00081 = 0.00571
  2. 2= 5.71 × 10⁻³

Answer5.71 × 10⁻³

Part (h) · 2 marks

Given h = 2.43 m to the nearest centimetre, complete the lower and upper bounds for h.

  1. 1Nearest centimetre: half of 0.01 m = 0.005 m
  2. 22.43 − 0.005 = 2.425, 2.43 + 0.005 = 2.435
  3. 32.425 ≤ h < 2.435

Answer2.425 and 2.435

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Also searched as: 0580/33/M/J/22 · 0580_s22_qp_33 · 0580 s22 33 · question 5.
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