IB Maths: Applications and Interpretation chapter 2: Functions MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

34 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.

34 questions · 4 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. What is the gradient of a line perpendicular to y = 3x − 4?

  1. A
    3
  2. B
    −3
  3. C
    1/3
  4. D
    −1/3
Show answer

Answer: D. Perpendicular gradients multiply to −1, so m = −1/3. 3 is the gradient of a parallel line.

2. Find the range of f(x) = x2 + 3 for the domain −2 ≤ x ≤ 4.

  1. A
    7 ≤ f(x) ≤ 19
  2. B
    3 ≤ f(x) ≤ 19
  3. C
    −2 ≤ f(x) ≤ 4
  4. D
    f(x) ≥ 3
Show answer

Answer: B. The minimum is at x = 0, where f = 3, and the maximum at x = 4, where f = 19. Using only the end points gives 7 to 19 and misses the vertex.

3. For the open box with volume V = x(20 − 2x)2 cm3, 0 < x < 10, use technology to find the maximum volume.

  1. A
    588 cm3
  2. B
    593 cm3
  3. C
    500 cm3
  4. D
    3.33 cm3
Show answer

Answer: B. The graph has a maximum at x = 3.33, where V = 592.6 ≈ 593 cm3. 588 is V at x = 3 only, and 3.33 is the value of x, not V.

4. A taxi charges $4 for the first 2 km and $1.50 for each km after that. Using this piecewise linear model, find the cost of a 7 km journey.

  1. A
    $14.50
  2. B
    $11.50
  3. C
    $10.50
  4. D
    $7.50
Show answer

Answer: B. The first 2 km cost $4 and the remaining 5 km cost 5 × 1.50 = $7.50, so $11.50. $14.50 charges all 7 km at $1.50 on top of the $4.

5. The temperature of a cup of coffee is modelled by T = 20 + 70(0.9)t °C, t minutes after it is made. What temperature does the coffee approach in the long term?

  1. A
    20 °C
  2. B
    90 °C
  3. C
    70 °C
  4. D
    0 °C
Show answer

Answer: A. As t grows, 0.9t tends to 0, so T tends to 20 °C, the horizontal asymptote (room temperature). 90 °C is the starting temperature.

6. y varies directly as the square of x, and y = 18 when x = 3. Find y when x = 5.

  1. A
    30
  2. B
    6.48
  3. C
    50
  4. D
    25
Show answer

Answer: C. y = kx2, so 18 = 9k and k = 2. Then y = 2 × 25 = 50. 30 comes from assuming y is proportional to x, not x2.

7. The graph of y = f−1(x) is a reflection of the graph of y = f(x) in which line?

  1. A
    the x-axis
  2. B
    the y-axis
  3. C
    the line y = x
  4. D
    the line y = −x
Show answer

Answer: C. The inverse swaps x and y, so each point (a, b) becomes (b, a): a reflection in y = x.

8. A linear model gives the cost of producing n T-shirts as C = 2.5n + 40 dollars. Find the cost of producing 100 T-shirts.

  1. A
    $250
  2. B
    $42.50
  3. C
    $4250
  4. D
    $290
Show answer

Answer: D. C = 2.5 × 100 + 40 = 250 + 40 = $290. $250 forgets the fixed cost of $40.

9. Find the equation of the line with gradient 4 that passes through (2, −1).

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

Answer: D. y − (−1) = 4(x − 2) gives y + 1 = 4x − 8, so y = 4x − 9. Using y − 1 instead of y + 1 gives y = 4x − 7.

10. A quadratic model passes through (0, 5), (2, 9) and (4, 5). Find its equation.

  1. A
    y = −x2 + 4x + 5
  2. B
    y = x2 − 4x + 5
  3. C
    y = −x2 + 2x + 5
  4. D
    y = −x2 + 4x + 9
Show answer

Answer: A. By symmetry the vertex is (2, 9), so y = −(x − 2)2 + 9 = −x2 + 4x + 5. Check (4, 5): −16 + 16 + 5 = 5.

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Ways to practise this chapter

Functions: questions students ask

How many Functions MCQs are there?

34, each with the answer and a short explanation, across 4 topics: SL2.1 Equations of straight lines, SL2.2, SL2.3, SL2.4 Functions, graphs and their key features, SL2.5 Linear, quadratic, cubic and variation models, SL2.5, SL2.6 Exponential and sinusoidal models; the modelling process. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Applications and Interpretation 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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