A-Level & Admissions

Interactive practice · A-Level Maths

Interactive Exam Questions
Edexcel A-Level Maths

Ten exam-style questions, worked one line at a time. Open a question, and each line is revealed only after you commit to the previous one, just like building a solution under exam conditions. You're then marked the way Edexcel marks it: method (M) and accuracy (A) marks adding up to the question's real total, with feedback on every slip.

Subject A-Level Maths Further Maths
Board Edexcel OCR AQA
1 · Open a questionEach is an Edexcel-style question with its real mark total. Try it on paper first.
2 · Build the solutionPick each line; the next appears once you commit. Wrong options mirror real, common mistakes.
3 · Get your marksPress Mark to see your score out of the total, line-by-line M1/A1 awards and feedback.

Marks follow Edexcel conventions: M = method mark (correct approach), A = accuracy mark (correct result; needs the method), dM = a method mark that depends on the previous one. Each question shows its total, exactly as on the paper.

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The 10 Edexcel questions on this page

Every question below is fully interactive above: open it, build the solution line by line, and be marked against an authentic Edexcel-style mark scheme with per-line feedback. The stems are listed here in full.

  1. Q1. Differentiate using the chain rule (Paper 1 (Pure) · typically 2 marks, 2 marks · Pure · Differentiation)
    Given \(y=(3x^{2}+1)^{5}\), find \(\dfrac{dy}{dx}\).
    Show worked solution & mark scheme

    Chain rule: \(\frac{dy}{dx}=5(3x^{2}+1)^{4}\times 6x\) (M1) \(=\) \(30x(3x^{2}+1)^{4}\) (A1). Total: 2 marks.

  2. Q2. Evaluate a definite integral (Paper 1 (Pure) · typically 4 marks, 4 marks · Pure · Integration)
    Evaluate \(\displaystyle\int_{1}^{2}\left(6x^{2}-2\right)\,dx\).
    Show worked solution & mark scheme

    \(\int_{1}^{2}(6x^{2}-2)\,dx=[\,2x^{3}-2x\,]_{1}^{2}\) (M1 A1) \(=(16-4)-(2-2)\) (dM1) \(=\) 12 (A1). Total: 4 marks.

  3. Q3. Binomial expansion, first three terms (Paper 2 (Pure) · typically 3 marks, 3 marks · Pure · Binomial)
    Find the first three terms, in ascending powers of \(x\), of \((1+2x)^{8}\).
    Show worked solution & mark scheme

    \((1+2x)^{8}=1+\binom{8}{1}(2x)+\binom{8}{2}(2x)^{2}+\dots\) (M1) \(=\) \(1+16x+112x^{2}\) (A1, A1). Total: 3 marks.

  4. Q4. Solve a logarithmic equation (Paper 2 (Pure) · typically 4 marks, 4 marks · Pure · Logarithms)
    Solve \(\log_{10}x+\log_{10}(x-3)=1\).
    Show worked solution & mark scheme

    \(\log_{10}[x(x-3)]=1\) (M1) \(\Rightarrow x(x-3)=10\) (M1) \(\Rightarrow x^{2}-3x-10=0\Rightarrow(x-5)(x+2)=0\) (A1). Reject \(x=-2\): \(x=5\) (A1). Total: 4 marks.

  5. Q5. Differentiate a product (Paper 1 (Pure) · typically 3 marks, 3 marks · Pure · Differentiation)
    Differentiate \(y=x^{2}e^{x}\).
    Show worked solution & mark scheme

    \(\frac{dy}{dx}=2xe^{x}+x^{2}e^{x}\) (M1 A1) \(=\) \(xe^{x}(x+2)\) (A1). Total: 3 marks.

  6. Q6. Sum to infinity of a geometric series (Paper 2 (Pure) · typically 2 marks, 2 marks · Pure · Sequences & series)
    A geometric series has first term \(a=12\) and common ratio \(r=\tfrac{3}{4}\). Find the sum to infinity \(S_{\infty}\).
    Show worked solution & mark scheme

    \(|r|=\tfrac34<1\), so \(S_{\infty}=\dfrac{a}{1-r}=\dfrac{12}{\tfrac14}=\) 48 (M1 A1). Total: 2 marks.

  7. Q7. Solve a trigonometric equation (Paper 1 (Pure) · typically 4 marks, 4 marks · Pure · Trigonometry)
    Solve \(2\sin^{2}x+\sin x-1=0\) for \(0^{\circ}\le x<360^{\circ}\).
    Show worked solution & mark scheme

    \((2\sin x-1)(\sin x+1)=0\) (M1) \(\Rightarrow\sin x=\tfrac12\) or \(-1\) (A1). So \(x=30^{\circ},150^{\circ}\) (A1) and \(x=270^{\circ}\) (A1). \(x=30^{\circ},150^{\circ},270^{\circ}\). Total: 4 marks.

  8. Q8. Find the stationary points (Paper 1 (Pure) · typically 4 marks, 4 marks · Pure · Differentiation)
    Find the \(x\)-coordinates of the stationary points of \(y=2x^{3}-3x^{2}-12x\).
    Show worked solution & mark scheme

    \(\frac{dy}{dx}=6x^{2}-6x-12\) (M1) \(=0\Rightarrow x^{2}-x-2=0\) (A1) \(\Rightarrow(x-2)(x+1)=0\) (dM1). \(x=2,\ x=-1\) (A1). Total: 4 marks.

  9. Q9. Sum of an arithmetic series (Paper 2 (Pure) · typically 2 marks, 2 marks · Pure · Sequences & series)
    An arithmetic series has first term \(a=5\) and common difference \(d=3\). Find the sum of the first 30 terms, \(S_{30}\).
    Show worked solution & mark scheme

    \(S_{30}=\frac{30}{2}[2(5)+29(3)]=15(10+87)=15\times97=\) 1455 (M1 A1). Total: 2 marks.

  10. Q10. Binomial distribution probability (Paper 3 (Statistics) · typically 2 marks, 2 marks · Statistics · Distributions)
    The random variable \(X\sim B(10,\,0.3)\). Find \(P(X=4)\), to 3 significant figures.
    Show worked solution & mark scheme

    \(P(X=4)=\binom{10}{4}(0.3)^{4}(0.7)^{6}=210\times0.0081\times0.117649\approx\) 0.200 (M1 A1). Total: 2 marks.

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