AQA A-level Mathematics – Practice Examination Paper (Paper 3 Style) 2026 updated Advanced Level (Year 13 Standard) Complete Questions And Correct worked solutions Answers (Expert Verified Exam)

AQA A-level Mathematics – Practice
Examination Paper (Paper 3 Style) 2026
updated
Advanced Level (Year 13 Standard) Complete
Questions And Correct worked solutions
Answers (Expert Verified Exam)
Time allowed: 2 hours (for full 100-question
paper simulation)
Total marks: 100

Instructions
• Answer all questions
• Show all your working clearly
• You may use a calculator unless otherwise stated
• Final answers should be given to a suitable degree of accuracy
• Diagrams are not drawn to scale unless stated


SECTION A: PURE MATHEMATICS (Q1–Q50)
Q1 (1 mark)
Simplify 2𝑥 3 ⋅ 𝑥 4

,Answer:
Working:
2𝑥 3+4 = 2𝑥 7
Final Answer: 2x⁷


Q2 (2 marks)
Solve 𝑥 2 − 5𝑥 = 0
Working:
𝑥(𝑥 − 5) = 0
So:
𝑥 = 0or 𝑥 = 5
Final Answer: x = 0, 5


Q3 (2 marks)
Differentiate 𝑦 = 3𝑥 2 − 4𝑥 + 7
Working:
𝑑𝑦
= 6𝑥 − 4
𝑑𝑥
Final Answer: 6x − 4


Q4 (3 marks)
Find the stationary points of 𝑦 = 𝑥 3 − 3𝑥 2
Working:
𝑑𝑦
= 3𝑥 2 − 6𝑥
𝑑𝑥
Factor:

, 3𝑥(𝑥 − 2) = 0
So:
𝑥 = 0,2
Substitute:
• 𝑥=0⇒𝑦=0
• 𝑥 = 2 ⇒ 𝑦 = 8 − 12 = −4
Final Answer: (0, 0), (2, -4)


Q5 (2 marks)
Solve ln⁡ 𝑥 = 3
Working:
𝑥 = 𝑒3
Final Answer: e³


Q6 (3 marks)
Expand (𝑥 + 2)2
Working:
𝑥 2 + 4𝑥 + 4
Final Answer: x² + 4x + 4


Q7 (4 marks)
Solve 2𝑥+1 = 16
Working:
16 = 24
So: