Lemmara logoLemmaraWorked solution

4024/21 Oct/Nov 2020, Question 4: Exponential Functions

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a table for y = 4/5 × 2ˣ, plot the curve for −3 ≤ x ≤ 3, estimate the gradient at x = 2 using a tangent, and solve 4 × 2ˣ = 5 from the graph.

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

Part (a) · 1 mark

Fill in the missing y-value in the table for y = 4/5 × 2ˣ at the given x values.

  1. 1x = −3: y = 4/5 × 2⁻³ = 0.8 × 1/8 = 0.1

Answer0.1

Part (b) · 3 marks

Draw the graph of y = 4/5 × 2ˣ on the grid for x from −3 to 3.

  1. 1Plot (−3, 0.1), (−2, 0.2), (−1, 0.4), (0, 0.8), (1, 1.6), (2, 3.2), (3, 6.4)
  2. 2Join with a smooth curve rising more steeply to the right

AnswerCorrect smooth curve

Part (c) · 2 marks

Draw a tangent to the curve at x = 2 and use it to estimate the gradient.

  1. 1Draw the tangent to the curve at (2, 3.2)
  2. 2Gradient = rise ÷ run of the tangent ≈ 2.2

Answer1.8 to 2.4

Part (d) · 1 mark

Use the drawn graph to estimate the x-value solving 4 × 2ˣ = 5.

  1. 14 × 2ˣ = 5 means 4/5 × 2ˣ = 1
  2. 2Read across from y = 1 to the curve: x ≈ 0.32

Answer0.25 to 0.4

Stuck on a step? Read the free lesson: Exponential Functions

Practise more exponential functions 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 exponential functions

Also searched as: 4024/21/O/N/20 · 4024_w20_qp_21 · 4024 w20 21 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.