plumiFunctions: CAIE A‑Level Maths questions
Every CAIE A-Level Maths exam question on 1.2 Functions, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![Specimen Paper 1, question 2: Functions f and g are defined by f : x ↦ 3x + 2, x ∈ ℝ, g : x ↦ 4x – 12, x ∈ ℝ. Solve the equation f –1(x) = gf(x). [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970901-spec-02-qp.webp)
![Specimen Paper 1, question 5: (a) The curve y = x2 + 3x + 4 is translated by 2 f p. 5 0 Find and simplify the equation of the translated curve. [2] (b) The graph of y = f(x) is transformed t](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970901-spec-05-qp.webp)
![Specimen Paper 1, question 11: 11 The function f is defined, for x ∈ ℝ, by f : x ↦ x2 + ax + b, where a and b are constants. (a) It is given that a = 6 and b = –8. Find the range of f. [3] (b](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970901-spec-11-qp.webp)
All 5 questions on Functions, as a list
- June 2024, Paper 1, Q2 (6 marks): y 1 x O 1 r 3 2 r 5 3r 7 2 r r 2 r 2 r 2 – 1 – 2 – 3 – 4 – 5 The diagram shows two curves. One curve has equation y sin x and the other curve has = equation y f
- June 2024, Paper 1, Q6 (7 marks): y O x 2 The function f is defined by f x ( ) + for x 4 1 0 . The diagram shows the graph of y f ( ) x . = = x 2 (a) On this diagram, sketch the graph of y f - 1
- Specimen, Paper 1, Q2 (4 marks): Functions f and g are defined by f : x ↦ 3x + 2, x ∈ ℝ, g : x ↦ 4x – 12, x ∈ ℝ. Solve the equation f –1(x) = gf(x). [4]
- Specimen, Paper 1, Q5 (5 marks): (a) The curve y = x2 + 3x + 4 is translated by 2 f p. 5 0 Find and simplify the equation of the translated curve. [2] (b) The graph of y = f(x) is transformed t
- Specimen, Paper 1, Q11 (9 marks): 11 The function f is defined, for x ∈ ℝ, by f : x ↦ x2 + ax + b, where a and b are constants. (a) It is given that a = 6 and b = –8. Find the range of f. [3] (b
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