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IB Maths: Analysis and Approaches MCQs with answers

Practise IB Maths: Analysis and Approaches (SL / HL) with 282 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.

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IB Maths: Analysis and Approaches MCQs with answers

Practise IB Maths: Analysis and Approaches (SL / HL) with 282 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.

282 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 48 questionsSL1.2 Arithmetic sequences and series, SL1.3, SL1.4, SL1.8 Geometric sequences, series and financial applications, SL1.1, SL1.5, SL1.7 Standard form, exponents and logarithms, SL1.6 Simple deductive proof, SL1.9 The binomial theorem
  2. Functions 57 questionsSL2.1 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
  3. Geometry and trigonometry 51 questionsSL3.1 Three-dimensional geometry, SL3.2, SL3.3 Trigonometry of triangles and its applications, SL3.4, SL3.5 Radians, the unit circle and exact values, SL3.6, SL3.8 Trigonometric identities and equations, SL3.7 Circular functions and their graphs
  4. Statistics and probability 66 questionsSL4.1 Collecting data and sampling, SL4.2, SL4.3 Presenting and summarising data, SL4.4, SL4.10 Correlation and regression, SL4.5, SL4.6 Probability and combined events, SL4.6, SL4.11 Conditional probability and independence, SL4.7, SL4.8 Discrete random variables and the binomial distribution, SL4.9, SL4.12 The normal distribution
  5. Calculus 60 questionsSL5.1 to SL5.4 Introduction to differentiation, tangents and normals, SL5.6 Further differentiation, SL5.7, SL5.8 Second derivative, stationary points and optimisation, SL5.5, SL5.10 Anti-differentiation and indefinite integrals, SL5.5, SL5.11 Definite integrals and areas, SL5.9 Kinematics
Sample IB Maths: Analysis and Approaches MCQs with answers 12 questions

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

1. Given that log2 x = 5, find x.

  1. A
    32
  2. B
    10
  3. C
    25
  4. D
    2.5
Show answer

Answer: A. log2 x = 5 means 25 = x, so x = 32.

2. 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).

3. A solid is made of a right cone of radius 3 cm and height 4 cm on top of a hemisphere of radius 3 cm, with flat faces joined. Find its volume, in terms of π.

  1. A
    48π cm3
  2. B
    54π cm3
  3. C
    18π cm3
  4. D
    30π cm3
Show answer

Answer: D. Cone = (1/3)π(9)(4) = 12π and hemisphere = (2/3)π(27) = 18π, total 30π cm3. Using a full sphere gives 48π.

4. A bag has 5 red and 3 blue counters. Two are taken at random without replacement. Find the probability that they are different colours.

  1. A
    15/32
  2. B
    15/56
  3. C
    1/2
  4. D
    15/28
Show answer

Answer: D. P(RB) + P(BR) = (5/8)(3/7) + (3/8)(5/7) = 30/56 = 15/28. Both orders count, and the second draw is out of 7.

5. Find the equation of the tangent to y = x2 + 3x at x = 1.

  1. A
    y = 5x + 4
  2. B
    y = 2x + 2
  3. C
    y = −⅕x + 4.2
  4. D
    y = 5x − 1
Show answer

Answer: D. At x = 1, y = 4 and dy/dx = 2x + 3 = 5. y − 4 = 5(x − 1) gives y = 5x − 1. y = −⅕x + 4.2 is the normal.

6. Which is a correctly laid out proof that (n + 1)2 − (n − 1)2 ≡ 4n?

  1. A
    (n + 1)2 − (n − 1)2 = 4n, so expanding both sides gives 4n = 4n, which is true
  2. B
    LHS = (n2 + 2n + 1) − (n2 − 2n + 1) = 4n = RHS
  3. C
    LHS = (n2 + 1) − (n2 + 1) = 0
  4. D
    LHS = n2 + 2n + 1 − n2 − 2n + 1 = 2 = RHS
Show answer

Answer: B. Start from one side and transform it into the other: LHS = n2 + 2n + 1 − n2 + 2n − 1 = 4n = RHS. Starting from the result you want to prove assumes it is true.

7. 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.

8. A sector has radius 10 cm and angle 0.8 radians. Find its perimeter.

  1. A
    8 cm
  2. B
    18 cm
  3. C
    28 cm
  4. D
    40 cm
Show answer

Answer: C. Arc = 10 × 0.8 = 8 cm, and the perimeter also includes two radii: 8 + 10 + 10 = 28 cm.

9. X takes the values 1, 2, 3, 4 with probabilities 0.1, 0.3, k, 0.2. Find k.

  1. A
    0.4
  2. B
    0.6
  3. C
    0.25
  4. D
    0.2
Show answer

Answer: A. The probabilities must sum to 1: 0.1 + 0.3 + k + 0.2 = 1, so k = 0.4.

10. f′(x) = 3x2 − 2 and f(1) = 4. Find f(x).

  1. A
    x3 − 2x + 4
  2. B
    x3 − 2x + 3
  3. C
    6x − 2
  4. D
    x3 − 2x + 5
Show answer

Answer: D. f(x) = x3 − 2x + C, and f(1) = 1 − 2 + C = 4 gives C = 5.

11. Which row of Pascal’s triangle gives the coefficients in the expansion of (a + b)5?

  1. A
    1, 4, 6, 4, 1
  2. B
    1, 5, 10, 10, 5, 1
  3. C
    1, 5, 10, 5, 1
  4. D
    1, 6, 15, 20, 15, 6, 1
Show answer

Answer: B. (a + b)n has n + 1 terms, so power 5 needs six coefficients: 1, 5, 10, 10, 5, 1.

12. 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.

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Ways to practise 5 ways

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The 282 MCQs are our own, written to the syllabus in the style of the exam.

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