GCSE Maths - Level 9 Paper (A** Paper) - STAR paper questions

Sep 5, 2026

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GCSE Maths Level 9 Paper (A** Paper) focuses on advanced problem-solving across geometry, algebra, and graphs, structured as practice questions for AQA, OCR, and Edexcel. The guidance emphasizes reading each question carefully, managing time, attempting every problem, and showing full working. Questions cover area calculations with arcs and sectors, relationships in circle sectors, turning points of polynomial graphs, proof of the quadratic formula by completing the square, surface area of cylinders, coordinate geometry in a parallelogram, equation finding for lines with parameters, and solving trigonometric equations from plotted graphs.

LanguageEnglish

CategoryExam

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Guidance

Revision questions

Questions 1-9

AQA, OCR, Edexcel GCSE GCSE Maths Level 9 Paper (A** Paper) Name: Guidance 1. Read each question carefully. 2. Don’t spend too long on each question. 3. Attempt every question. 4. Always show your workings. Revise GCSE Maths: [www.MathsMadeEasy.co.uk/gcse-maths-revision/](www.MathsMadeEasy.co.uk/gcse-maths-revision/) | 1. Calculate the area between the arc CB, the arc EB and the line CE. ECA = 90°

| | --- | | Area = cm2
(3 marks) | | 2. In the diagram below the sectors A, B, and C all subtend the same angle at the centre of the circle.
The radii of the sectors A, B, and C are in the ratio 1: 2: 3.
Calculate the total area of the shape in terms of r, the radius of the circle.

| | --- | | (4 marks) | 3. Quadratic and cubic graphs have one and two turning points respectively. This can be seen on the diagram below. Sketch the graph of a quartic graph. A quartic graph has 􀝔 4 as the leading power of 􀝔 , and three turning points. Describe the general rule for the number of turning points of a graph with a leading power of 􀝔 􀯡 . ………………………………………………………………………………………… ………………………………………………………………………………………… | 4. The quadratic formula
􀝔 = | −􀜾 ± √􀜾2 − 4􀜽􀜿
2􀜽 | | --- | --- | | is a re-arrangement of the general quadratic equation
􀜽􀝔2 + 􀜾􀝔 + 􀜿 = 0
By completing the square on the general quadratic equation , prove this result.
| | | (5 marks) | | | 5. Three cylinders with the same radii have lengths in the ratio 3:4:5 . Calculate the surface areas of the three cylinders.

…………………………………………………………………………………………….
.
. . . . . .
Surface area = | | --- | | (4 marks) | | 6. The following information is known about a parallelogram ABCD.
􀜣 = (0, 6)
AB has gradient 3
AD has gradient − 12 The x-coordinate of B is 2
The y-coordinate of D is 2.
Find the co-ordinates of the point C.

􀜥 = , | | --- | | (4 marks) | | 7. a. The points 􀜣(8, 10) and 􀜤 (􀝀 , 􀝁) form a line AB. Find the equation of the line AB in terms of 􀝀 and 􀝁 .
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
􀜧: 􀝕 = −3􀝔 + 6
b. What is a possible set of values of 􀝀 and 􀝁 if the line segment AB is parallel to E?
……………………………………………………………………………………………
……………………………………………………………………………………………
􀝀 = 􀝁 =
c. What is a possible set of values of 􀝀 and 􀝁 if the line segment AB is perpendicular to E?

􀝀 = 􀝁 = | | --- | | (2 marks, 2 marks, 3 marks) | | 8. The graph of 􀝕 = 􀝏􀝅􀝊 (􀝔) for −180 ≤ 􀝔 ≤ 180 has been drawn on the axes below. A solution to 􀝏􀝅􀝊(􀝔) = 􀜽 is 18° .

Find another solution, and the approximate value of a.
.
. . . The domain of 􀝕 = 􀝏􀝅􀝊 (􀝔) is no longer limited to −180 ≤ 􀝔 ≤ 180.
Write down two more solutions to 􀝏􀝅􀝊(􀝔) = 􀜽 .
. . . . | | --- | | (2 marks, 2 marks) | | 9. A cuboid is pictured below.

􀜦􀜥 = 􀜥􀜩
Using an algebraic argument, show that the shape is not a cube.
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
Find the length CE in terms of 􀝔 .
| | --- | | (2 marks, 2 marks) |

FAQs

What general instructions should be followed when attempting this GCSE Maths paper?

Read each question carefully, don’t spend too long on any single question, attempt every question, and always show workings.

What topics are covered in the revision questions?

The paper includes geometry (areas with arcs/sectors, surface area of cylinders), algebra (quadratic formula proof), graph behavior (turning points of polynomials), coordinate geometry, and trigonometry (solving trig equations from graphs).

How is the quadratic formula question approached?

It asks to prove the quadratic formula by rearranging the general quadratic equation and using completing the square.

Sep 5, 2026

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