Lemmara logoLemmaraWorked solution

4024/21 May/Jun 2021, Question 3: Constructing Equations

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 13 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Answer six short algebra questions: evaluate a formula, expand and simplify, solve an equation, find an exponent, then use a 30 cm by 24 cm card net to find x and the fraction of the open box filled by 1000 cm³ of sand.

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

Part (a) · 2 marks

Substitute q = 15 and r = −4 into p = (3q + 5)/r² and calculate p.

  1. 1p = (3 × 15 + 5)/(−4)²
  2. 2= 50/16
  3. 3= 3.125

Answer3.125 or 25/8 or 3 1/8

Part (b) · 2 marks

Expand and simplify 3(2x + 1) + 4(x − 5).

  1. 13(2x + 1) = 6x + 3, 4(x − 5) = 4x − 20
  2. 26x + 3 + 4x − 20 = 10x − 17

Answer10x − 17

Part (c) · 2 marks

Solve (3 − k)/4 = 1 for k.

  1. 13 − k = 4
  2. 2k = 3 − 4 = −1

Answer−1

Part (d) · 1 mark

Given x⁶/xᵐ = x⁻³, find the value of m.

  1. 1x⁶ ÷ xᵐ = x⁶⁻ᵐ
  2. 26 − m = −3
  3. 3m = 9

Answer9

Part (ei) · 3 marks

With squares of side x removed from each corner of a 30 cm by 24 cm card, and net area 576 cm², form and solve an equation for x.

  1. 1Area of net = 24 × 30 − 4x² = 576
  2. 2720 − 4x² = 576
  3. 34x² = 144, x² = 36
  4. 4x = 6

Answer6

Part (eii) · 3 marks

For the open box made from the net, find the fraction of its volume filled by 1000 cm³ of sand, in simplest form.

  1. 1Box is (30 − 12) by (24 − 12) by 6 = 18 by 12 by 6
  2. 2Volume = 18 × 12 × 6 = 1296 cm³
  3. 3Fraction = 1000/1296
  4. 4= 125/162

Answer125/162

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

Practise more constructing equations questions

Real 4024 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: 4024/21/M/J/21 · 4024_s21_qp_21 · 4024 s21 21 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.