IB Maths: Analysis and Approaches chapter 1: Number and algebra MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

48 exam-style questions on Number and algebra, 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.

48 questions · 5 topics · 10 per test

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What chapter 1 covers

Ten Number and algebra questions with answers

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

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. 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.

3. 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.

4. Find the coefficient of x2 in the expansion of (1 − 3x)6.

  1. A
    −135
  2. B
    45
  3. C
    135
  4. D
    −45
Show answer

Answer: C. The term is 6C2(−3x)2 = 15 × 9x2 = 135x2. Squaring −3 gives +9; forgetting to square the 3 gives 45.

5. A theatre has 25 rows. The first row has 18 seats and each row has 2 more seats than the row in front. How many seats are there in total?

  1. A
    1050
  2. B
    1075
  3. C
    2100
  4. D
    66
Show answer

Answer: A. S25 = (25/2)(2 × 18 + 24 × 2) = 12.5 × 84 = 1050. 66 is only the number of seats in the last row.

6. The sum of the first n terms of an arithmetic series is Sn = 2n2 + 3n. Find the 5th term.

  1. A
    65
  2. B
    21
  3. C
    23
  4. D
    17
Show answer

Answer: B. u5 = S5 − S4 = (50 + 15) − (32 + 12) = 65 − 44 = 21. 65 is the sum of five terms, not the fifth term.

7. Which expression in sigma notation represents the series 3 + 7 + 11 + ... + 79?

  1. A
    Σk=179 (4k − 1)
  2. B
    Σk=120 (4k + 3)
  3. C
    Σk=120 (4k − 1)
  4. D
    Σk=119 (4k − 1)
Show answer

Answer: C. The general term is 4k − 1 (k = 1 gives 3). Solving 4k − 1 = 79 gives k = 20, so the upper limit is 20, not the last term 79.

8. A geometric sequence has u2 = 12 and u5 = 96. Find the common ratio r and the first term.

  1. A
    r = 2, u1 = 6
  2. B
    r = 8, u1 = 1.5
  3. C
    r = 2, u1 = 3
  4. D
    r = 4, u1 = 3
Show answer

Answer: A. u5 ÷ u2 = r3 = 8, so r = 2 and u1 = 12 ÷ 2 = 6. The ratio 8 covers three steps, not one.

9. What is the difference between 3x + 2 = 11 and 3(x + 2) ≡ 3x + 6?

  1. A
    the first is an equation true only for x = 3; the second is an identity true for all x
  2. B
    both are identities
  3. C
    the first is an identity; the second is an equation
  4. D
    both are equations with exactly one solution each
Show answer

Answer: A. An equation holds only for certain values (here x = 3). The symbol ≡ marks an identity: both sides are equal for every value of x.

10. Find the value of 6C2.

  1. A
    30
  2. B
    20
  3. C
    15
  4. D
    12
Show answer

Answer: C. 6C2 = 6!/(2! 4!) = (6 × 5)/2 = 15. 30 forgets to divide by 2!.

Start the chapter testAbout the IB Maths: Analysis and Approaches test

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Ways to practise this chapter

Number and algebra: questions students ask

How many Number and algebra MCQs are there?

48, each with the answer and a short explanation, across 5 topics: SL1.2 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. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Analysis and Approaches chapter 1 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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