Lemmara logoLemmaraWorked solution

4024/22 Oct/Nov 2023, Question 6: Exponential Functions

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a table and draw the curve y = 4ˣ/10, then use it to solve an equation, estimate a gradient by tangent, and find a and b from a parabola sketch.

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

Part (ai) · 1 mark

Fill in the missing y value in the table for y = 4ˣ/10 at x = 0.

  1. 1x = 0: y = 4⁰/10 = 1/10 = 0.1

Answer0.1

Part (aii) · 3 marks

Plot the graph of y = 4ˣ/10 for x from 0 to 3 on the grid.

  1. 1Plot (0, 0.1), (0.5, 0.2), (1, 0.4), (1.5, 0.8), (2, 1.6), (2.5, 3.2), (3, 6.4)
  2. 2Join with a smooth curve getting steeper

AnswerCorrect smooth curve

Part (aiii) · 1 mark

Use your graph to solve 4ˣ/10 = 5.

  1. 1Draw y = 5 and read down where it meets the curve
  2. 2x ≈ 2.8 (exactly 4ˣ = 50 gives 2.82…)

Answer2.8 (accept 2.75 to 2.9)

Part (aiv) · 2 marks

Draw a tangent at x = 2 and estimate the gradient of the curve there.

  1. 1Draw a tangent touching the curve at (2, 1.6)
  2. 2Gradient = rise ÷ run from two points on the tangent
  3. 3Gradient ≈ 2.2

Answer1.7 to 2.5

Part (b) · 3 marks

From the sketch of y = x² + ax + b crossing the x-axis at 2 and 5, find a and b.

  1. 1Crosses x-axis at 2 and 5, so y = (x − 2)(x − 5)
  2. 2= x² − 7x + 10
  3. 3a = −7, b = 10

Answera = −7, b = 10

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: 4024/22/O/N/23 · 4024_w23_qp_22 · 4024 w23 22 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.