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IGCSE Maths · Edexcel 4XMA1 · Unit 2 Higher · Graphs

Transformations of Graphs — Practice Questions

12 exam-style questions (32 marks), building from warm-up to grade 8–9. Show full working: Edexcel gives method marks even when the final answer is wrong.

Section A — Warm-up (grades 5–6)
  1. (3 marks)The point (3, 4) lies on the curve y = f(x). Write down the coordinates of the image of this point on
    (a) y = f(x) + 2 (b) y = f(x − 1) (c) y = −f(x).
  2. (2 marks)Describe fully the single transformation that maps y = x² onto y = (x − 4)² + 1.
  3. (2 marks)The graph of y = sin x is transformed to y = 3 sin x.
    (a) Describe the transformation. (b) Write down the maximum value of y = 3 sin x.
  4. (2 marks)The graph of y = cos x is transformed to y = cos 2x. Describe the transformation, and state the period of y = cos 2x.
Section B — Core (grades 6–7)
  1. (4 marks)The curve y = f(x) has a turning point at (2, −5). Write down the turning point of
    (a) y = f(x + 3) (b) y = f(x) − 4 (c) y = 2f(x) (d) y = f(−x).
  2. (3 marks)f(x) = x² − 4x. Show that f(x + 2) = x² − 4.
  3. (3 marks)The maximum point of y = sin x for 0 ≤ x ≤ 360 is (90, 1). Find the maximum point of y = sin(x − 60) + 2.
  4. (2 marks)The diagram shows the curve y = x² − 2x and the tangent to the curve at (3, 3). The tangent also passes through (4, 7). Find the gradient of the curve at x = 3.
    xy-112345-2-1123456789(3, 3)(4, 7)
  5. (3 marks)The graph of y = x² − 2x − 3 has been drawn. Find the equation of the straight line you would draw to solve x² − 3x − 4 = 0, and write down the solutions.
Section C — Stretch (grades 8–9)
  1. (2 marks)The graph of y = f(x) passes through (0, 3) and (4, 0). Find the coordinates of the images of these points on y = 2f(x − 1).
  2. (3 marks)f(x) = x². Show that the graph of y = f(2x) is the same as the graph of y = 4f(x), and describe both as single transformations of y = f(x).
  3. (3 marks)The graph of y = a cos x + b, where a > 0, has a maximum value of 5 and a minimum value of 1. Find a and b.
When you’re doneRevise the method in the notes, then mark your answers with the worked solutions.
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