Lemmara logoLemmaraWorked solution

0580/33 Oct/Nov 2022, Question 5: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 13 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Work through a rectangle with side lengths in x, a box-packing problem with a 65 by 30 by 18 box and 15 by 15 by 6 cuboids, and a cube with surface area 486 cm².

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

Part (ai) · 1 mark

Add the five horizontal lengths of the rectangle and simplify to obtain 5x + 8.

  1. 1AD = x + 4 + x/2 + 2x + x/2 + x + 4
  2. 2= 5x + 8

Answerx + 4 + x/2 + 2x + x/2 + x + 4

Part (aii) · 4 marks

Given the rectangle's area is 360 cm², form an equation using 15 and 5x + 8, then solve for x.

  1. 115(5x + 8) = 360
  2. 25x + 8 = 24
  3. 35x = 16
  4. 4x = 3.2

Answer3.2

Part (aiii) · 1 mark

Using x = 3.2, work out the combined area of the two shaded strips.

  1. 1Shaded = 2 × (x/2) × 15 = 15x
  2. 2= 15 × 3.2 = 48 cm²

Answer48

Part (bi) · 1 mark

Using the dimensions of the box and cuboid, justify that 24 cuboids can be packed inside.

  1. 165 ÷ 15 = 4.3… → 4, 30 ÷ 15 = 2, 18 ÷ 6 = 3
  2. 23 × 2 × 4 = 24

Answer3 × 2 × 4 = 24

Part (bii) · 4 marks

Subtract the total volume of 24 cuboids from the box's volume and state the units.

  1. 1Box = 65 × 30 × 18 = 35 100 cm³
  2. 2Cuboids = 24 × 15 × 15 × 6 = 32 400 cm³
  3. 3Empty space = 35 100 − 32 400 = 2700 cm³

Answer2700 cm³

Part (c) · 2 marks

From a cube's total surface area of 486 cm², determine its side length x.

  1. 16x² = 486
  2. 2x² = 81
  3. 3x = 9

Answer9

Stuck on a step? Read the free lesson: Constructing Equations

Practise more constructing equations questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on constructing equations

Also searched as: 0580/33/O/N/22 · 0580_w22_qp_33 · 0580 w22 33 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.