GCSE Mathematics Unit M4 - Higher Tier Assessment - (With calculator) Paper

Q: How many questions are in the Unit M4 assessment paper?

There are twenty-four questions. All questions must be answered in the provided spaces.

Q: Is a calculator allowed for this paper?

Yes. The paper states that you may use a calculator for this assessment.

Q: What marking guidance is given for working shown?

All working should be clearly shown in the spaces provided, and marks may be awarded for partially correct solutions.

Sep 5, 2026

Upload by Bill Black

GCSE Mathematics Unit M4 higher tier assessment paper focused on solving algebraic equations, interpreting grouped frequency tables, and applying key number theory concepts such as primality. Questions also cover depreciation with percentage change, cost and distance modelling using tables and graphs (including fixed charges and per-mile rates), and geometry involving semicircles inside a large circle to calculate shaded area. The test includes 24 questions, requires clear working, and allows calculator use.

LanguageEnglish

CategoryExam

FormatPDF

Pages32

Reading Time1 h 21 min

AccessFree to download

Instructions to candidates

Assessment information

Questions

Algebra and equations

Statistics: grouped frequency and median class

Number theory: primes

Percentage depreciation

Graphs and cost modelling

Geometry: semicircles area

| |

General Certificate of Secondary Education | | |
Centre Number

Candidate Number
| | --- | --- | --- | --- | --- | | Mathematics
Unit M4
(With calculator)
Higher Tier
[GMC41] Assessment | | | *GMC41*
*GMC41* | | | Assessment Level of Control: | | | | | |
TIME
2 hours. | | Tick the relevant box (3)
Controlled Conditions Other | | | |
INSTRUCTIONS TO CANDIDATES
Write your Centre Number and Candidate Number in the spaces provided at the top of this page.
You must answer the questions in the spaces provided.
Do not write outside the boxed area on each page or on blank pages.
Complete in black ink only. Do not write with a gel pen.
Answer all twenty-four questions.
All working should be clearly shown in the spaces provided. Marks may be awarded for partially correct solutions.
You may use a calculator for this paper.

INFORMATION FOR CANDIDATES
The total mark for this paper is 100.
Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question.
You should have a calculator, ruler, compasses and a protractor.
The Formula Sheet is on page 2. | | | | | |
12371
| | | | | *32GMC4101* *32GMC4101* | | | | | | | | --- | --- | --- | --- | --- | --- | | | | | | | | | | |
| | | | | | | | | | | | | |
| | | | | 12371

| | | | | | *32GMC4102* *32GMC4102* 1 Solve 2(3x − 1) + 5 = 4(x + 2) Answer x = [3] [Turn over 12371 *32GMC4103* *32GMC4103* | | 2 Data on the weights of 16 players on a sports team is recorded in the grouped frequency table.
Weight (W kg) Frequency 60 < W ≤ 70 1 70 < W ≤ 80 5 80 < W ≤ 90 4 90 < W ≤ 100 6 | | | | --- | --- | --- | --- | | The manager states that “the estimated mean weight of the team lies within the median class”.
Is his statement correct? You must justify your answer fully.
[4] | | | | | 12371

| | | | *32GMC4104* *32GMC4104* | | 3 Which of these numbers is prime?
Explain your reasoning clearly for each number below. | | | --- | --- | --- | | Number 11 111 1111 Yes/No Reason
[2] | | | | [Turn over
12371

| | | *32GMC4105* *32GMC4105* 4 A caravan depreciates in value by 15% each year. Two years ago Malcolm bought a new caravan costing £24 000 (a) What is its value now? Answer £ [2] (b) Malcolm states his caravan has depreciated by 30% over the two years. Is he correct? Explain your answer clearly. [3] 12371 *32GMC4106* *32GMC4106* BLANK PAGE DO NOT WRITE ON THIS PAGE (Questions continue overleaf) [Turn over 12371 *32GMC4107* *32GMC4107* | | 5 Martine wants to hire a van.
The table shows the costs for hiring the van.
Distance (d miles) 50 100 150 200 250 Total cost (£ C) 50 60 70 80 90
| |
250 | [2] | | | --- | --- | --- | --- | --- | --- | | 12371

| | | | | | *32GMC4108* *32GMC4108* (b) Use the graph to find (i) the initial fixed charge for hiring the van, Answer £ _____________ [ 1] (ii) the cost per mile, in pence, for using the van. Answer _____________ p [ 1] (c) Work out the total cost if the van travels 450 miles. Answer £ [2] [Turn over 12371 *32GMC4109* *32GMC4109* 6 A large circle has three semicircles of equal diameters placed across its diameter as shown. The radius of each of the small semicircles is 2 cm. Work out the area shaded. Answer cm2 [5] 12371 *32GMC4110* *32GMC4110*

FAQs

How many questions are in the Unit M4 assessment paper?

There are twenty-four questions. All questions must be answered in the provided spaces.

Is a calculator allowed for this paper?

Yes. The paper states that you may use a calculator for this assessment.

What marking guidance is given for working shown?

All working should be clearly shown in the spaces provided, and marks may be awarded for partially correct solutions.

Sep 5, 2026

Upload by Bill Black