IB Maths: Analysis and Approaches chapter 2: Functions MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

57 exam-style questions on Functions, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

57 questions · 6 topics · 10 per test

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What chapter 2 covers

Ten Functions questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. How many real solutions does the equation ex = x + 2 have?

  1. A
    0
  2. B
    1
  3. C
    2
  4. D
    3
Show answer

Answer: C. At x = 0 the line (2) is above the curve (1), but for large positive or negative x the curve is above the line, so they cross twice (at about x = −1.84 and x = 1.15, as a GDC confirms).

2. The mass of a substance is A = 80e−kt grams. When t = 10, A = 20. Find k.

  1. A
    0.0602
  2. B
    −0.139
  3. C
    0.139
  4. D
    0.4
Show answer

Answer: C. 20 = 80e−10k gives e−10k = 1/4, so 10k = ln 4 and k = (ln 4)/10 ≈ 0.139. The minus sign is already in the model, so k is positive.

3. Find the equations of the asymptotes of y = (2x + 1)/(x − 3).

  1. A
    x = −3 and y = 2
  2. B
    x = 3 and y = 2
  3. C
    x = 3 and y = −1/3
  4. D
    x = 2 and y = 3
Show answer

Answer: B. Vertical asymptote where the denominator is zero: x = 3. Horizontal asymptote y = a/c = 2/1 = 2, since for large x the constants hardly matter.

4. Find the equation of the axis of symmetry of y = x2 − 8x + 3.

  1. A
    x = −4
  2. B
    x = 4
  3. C
    x = 8
  4. D
    x = 3
Show answer

Answer: B. x = −b/(2a) = 8/2 = 4. The sign of b must be changed.

5. Describe the transformation that maps y = f(x) onto y = f(x − 3).

  1. A
    translation of 3 units to the left
  2. B
    translation of 3 units to the right
  3. C
    translation of 3 units down
  4. D
    horizontal stretch with scale factor 3
Show answer

Answer: B. y = f(x − a) is a horizontal translation of a units to the right. The minus inside the bracket moves the graph the positive way.

6. Solve log2 x + log2(x − 2) = 3.

  1. A
    x = 4 or x = −2
  2. B
    x = 5
  3. C
    x = 4
  4. D
    x = −2
Show answer

Answer: C. log2[x(x − 2)] = 3 gives x2 − 2x = 8, so (x − 4)(x + 2) = 0. x = −2 is rejected because log2(−2) is undefined; x = 4.

7. Describe the transformation that maps y = f(x) onto y = f(−x).

  1. A
    reflection in the x-axis
  2. B
    reflection in the line y = x
  3. C
    rotation of 180° about the origin
  4. D
    reflection in the y-axis
Show answer

Answer: D. Replacing x by −x swaps left and right: (a, b) goes to (−a, b), a reflection in the y-axis. −f(x) would reflect in the x-axis.

8. Find the equation of the line with gradient 3 through (−2, 5), in the form ax + by + d = 0.

  1. A
    3x − y − 11 = 0
  2. B
    3x − y + 11 = 0
  3. C
    3x + y + 1 = 0
  4. D
    x − 3y + 17 = 0
Show answer

Answer: B. y − 5 = 3(x + 2) gives y = 3x + 11, so 3x − y + 11 = 0. Check: 3(−2) − 5 + 11 = 0. Using (x − 2) instead of (x + 2) is the usual sign slip.

9. Find the equation of the line perpendicular to y = 2x − 5 that passes through (4, 1).

  1. A
    y = 2x − 7
  2. B
    y = ½x − 1
  3. C
    y = −2x + 9
  4. D
    y = −½x + 3
Show answer

Answer: D. Perpendicular gradient = −1/2 (so that 2 × −½ = −1). y − 1 = −½(x − 4) gives y = −½x + 3. Using −2 just changes the sign without taking the reciprocal.

10. What does the discriminant tell you about the roots of 3x2 − 4x + 2 = 0?

  1. A
    Δ = −8, so there are no real roots
  2. B
    Δ = 40, so there are two distinct real roots
  3. C
    Δ = −8, so there are two equal roots
  4. D
    Δ = 8, so there are two distinct real roots
Show answer

Answer: A. Δ = b2 − 4ac = 16 − 24 = −8 < 0, so no real roots. Equal roots need Δ = 0.

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Ways to practise this chapter

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How many Functions MCQs are there?

57, each with the answer and a short explanation, across 6 topics: SL2.1 Equations of straight lines, SL2.2 to SL2.5 Functions, graphs, composites and inverses, SL2.6, SL2.7 Quadratic functions, equations and inequalities, SL2.8 Reciprocal and rational functions, SL2.9, SL2.10 Exponential and logarithmic functions; solving equations, SL2.11 Transformations of graphs. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Analysis and Approaches chapter 2 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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