Book a free demo

IB Maths: Applications and Interpretation MCQs with answers

Practise IB Maths: Applications and Interpretation (SL / HL) with 235 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

Loading the test…

IB Maths: Applications and Interpretation MCQs with answers

Practise IB Maths: Applications and Interpretation (SL / HL) with 235 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

235 questions · 5 chapters

What each chapter covers 5 chapters

The questions follow the syllabus chapter by chapter. You can test the whole subject or one chapter at a time.

  1. Number and algebra 52 questionsSL1.1, SL1.6 Standard form, approximation and errors, SL1.2 Arithmetic sequences and series, SL1.3 Geometric sequences and series, SL1.4, SL1.7 Financial applications: compound interest, depreciation, loans and annuities, SL1.5 Exponents and logarithms, SL1.8 Systems of linear equations and polynomial equations (technology)
  2. Functions 34 questionsSL2.1 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
  3. Geometry and trigonometry 36 questionsSL3.1 Three-dimensional geometry: distance, solids and angles, SL3.2 Right-angled and non-right-angled trigonometry, SL3.3, SL3.4 Applications of trigonometry: elevation, bearings, arcs and sectors, SL3.5, SL3.6 Perpendicular bisectors and Voronoi diagrams
  4. Statistics and probability 71 questionsSL4.1 Collecting data and sampling, SL4.2 Presenting data: histograms, cumulative frequency and box plots, SL4.3 Measures of central tendency and dispersion, SL4.4, SL4.10 Correlation and regression, SL4.5, SL4.6 Probability: Venn diagrams, tree diagrams and conditional probability, SL4.7, SL4.8 Discrete random variables and the binomial distribution, SL4.9 The normal distribution, SL4.11 Hypothesis testing: χ² and t-tests
  5. Calculus 42 questionsSL5.1, SL5.2 The derivative as a rate of change; increasing and decreasing functions, SL5.3, SL5.4 Differentiating axⁿ; tangents and normals, SL5.6, SL5.7 Stationary points and optimisation, SL5.5 Integration and areas, SL5.8 The trapezoidal rule
Sample IB Maths: Applications and Interpretation MCQs with answers 12 questions

12 questions from the test, one or two from each chapter. Try each one, then open the answer.

1. A job pays $32 000 in the first year and the salary rises by 4% each year. Find the total earned over the first 10 years, to 3 significant figures.

  1. A
    $45 500
  2. B
    $378 000
  3. C
    $432 000
  4. D
    $384 000
Show answer

Answer: D. S10 = 32 000(1.0410 − 1) ÷ 0.04 = $384 195 ≈ $384 000. $45 500 is the 10th year's salary only, and $432 000 sums 11 years.

2. 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.

3. Find the equation of the perpendicular bisector of (−1, 4) and (5, 2).

  1. A
    y = −3x + 9
  2. B
    y = 3x + 3
  3. C
    y = 3x − 3
  4. D
    y = −x/3 + 11/3
Show answer

Answer: C. Midpoint (2, 3); gradient of the segment = −2 ÷ 6 = −1/3, so the bisector has gradient 3: y − 3 = 3(x − 2), y = 3x − 3. The last option is the line through the two points.

4. A test at the 5% significance level gives a p-value of 0.032. What is the correct conclusion?

  1. A
    Do not reject H0, since 0.032 < 0.05
  2. B
    Reject H0, since 0.032 > 0.01
  3. C
    Reject H0, since 0.032 < 0.05
  4. D
    Do not reject H0, since the p-value is positive
Show answer

Answer: C. If the p-value is less than the significance level, the result is significant and H0 is rejected.

5. Find dy/dx for y = (x2 + 1)/x.

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

Answer: D. Divide first: y = x + x−1, so dy/dx = 1 − x−2. You cannot differentiate the top and bottom separately.

6. $8000 grows to $10 000 in 5 years with interest compounded annually. Find the annual interest rate, to 3 significant figures.

  1. A
    4.56%
  2. B
    5.00%
  3. C
    4.46%
  4. D
    25.0%
Show answer

Answer: A. 1 + r = (10 000 ÷ 8000)1/5 = 1.250.2 = 1.0456, so r = 4.56%. 5.00% is the simple-interest rate, and 25.0% is the total growth.

7. 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.

8. A triangular garden has sides 6 m, 8 m and 11 m. Find its area.

  1. A
    24.0 m2
  2. B
    46.8 m2
  3. C
    33.0 m2
  4. D
    23.4 m2
Show answer

Answer: D. Find an angle first: cos C = (36 + 64 − 121) ÷ 96, so C = 102.6°. Area = ½ × 6 × 8 × sin 102.6° = 23.4 m2. 24.0 m2 wrongly assumes a right angle.

9. A data set has mean 20 and standard deviation 4. Every value is multiplied by 1.5 and then 2 is added. Find the new mean and variance.

  1. A
    mean 32, variance 24
  2. B
    mean 32, variance 36
  3. C
    mean 30, variance 36
  4. D
    mean 32, variance 38
Show answer

Answer: B. New mean = 1.5 × 20 + 2 = 32. The standard deviation becomes 1.5 × 4 = 6, so the variance is 36; adding 2 does not change the spread.

10. Find ∫ (4x3 − 2x + 5) dx.

  1. A
    x4 − x2 + 5x + C
  2. B
    12x2 − 2 + C
  3. C
    x4 − x2 + C
  4. D
    4x4 − 2x2 + 5x + C
Show answer

Answer: A. Integrate term by term: 4x4/4 − 2x2/2 + 5x + C. The constant 5 integrates to 5x, not 0.

11. A rectangular field measures 120 m by 45 m, each correct to the nearest metre. What is the upper bound of its area?

  1. A
    5317.75 m2
  2. B
    5400 m2
  3. C
    5482.75 m2
  4. D
    5460 m2
Show answer

Answer: C. Use both upper bounds: 120.5 × 45.5 = 5482.75 m2. 5317.75 uses both lower bounds, and 5460 only raises one of the lengths.

12. 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.

Try 223 more questions

Ways to practise 5 ways

When you get a question wrong, a short note called "The idea behind this" explains the topic it belongs to, with the rules to remember and a worked example.

Common questions

Is this IB Maths: Applications and Interpretation test free?

Yes. Every test and every explanation is free, and you do not need an account. If you sign in, your results are kept across your devices.

Are these past paper questions?

The 235 MCQs are our own, written to the syllabus in the style of the exam.

How is the test marked?

Instantly. You get your score, the right answer and an explanation for every question, and a list of the topics to work on.

More help with IB Maths: Applications and Interpretation

Other IB Diploma tests

ChemistryBiologyPhysicsMaths: Analysis and Approaches