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CAIE A Level Mathematics 9709

Functions questions

Exam-style questions on Functions, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationThe functions f and g are defined as follows: f(x) = x + 1 g(x) = 2x + 2 Evaluate gf(4).
  2. 2 marksFoundationConsider the function f(x) = 3x + 2. Solve f(x) = 5.
  3. 2 marksFoundationGiven functions f(x) = 2x + 2 and g(x) = 2x + 1, find gf(2).
  4. 2 marksFoundationGiven the function f(x) = 6x + 4, solve the equation f(x) = -20.
  5. 3 marksFoundationThe function f is defined by f(x) = 3x + 1, for x in mathbbR.
  6. 3 marksStandardThe function f is defined by f(x) = (x + 1)^2 - 4 for all real x.
  7. 3 marksStandardThe function f is defined by f(x) = (x + 4)^2 + 8 for all real x. Find the least value of f(x).
  8. 4 marksChallengeThe function f is defined by f(x) = frac4x - 2 + 1, x ≠ 2.