IB Maths: Applications and Interpretation chapter 1: Number and algebra MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

52 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.

52 questions · 6 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. 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. $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.

3. 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.

4. In an arithmetic sequence, u3 = 17 and u8 = 42. Find u1 and d.

  1. A
    u1 = 12, d = 5
  2. B
    u1 = 7, d = 5
  3. C
    u1 = 7, d = 25
  4. D
    u1 = 2, d = 5
Show answer

Answer: B. From u3 to u8 is 5 steps: 5d = 25, so d = 5. Then u1 = u3 − 2d = 17 − 10 = 7. Going back 3 steps instead of 2 gives the wrong u1 = 2.

5. Use technology to solve x3 − 4x2 + x + 6 = 0.

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

Answer: B. The polynomial solver gives −1, 2 and 3; it factorises as (x + 1)(x − 2)(x − 3). A cubic can have up to three real roots, so do not stop at two.

6. A town has 25 000 people and its population grows by 3.2% each year. Estimate the population after 10 years, to 3 significant figures.

  1. A
    33 000
  2. B
    33 200
  3. C
    25 800
  4. D
    34 300
Show answer

Answer: D. Multiply by 1.032 each year: 25 000 × 1.03210 = 34 256 ≈ 34 300. 33 000 adds 3.2% of 25 000 each year (linear), and 33 200 uses only 9 years.

7. $5000 is invested at 4% per year compounded annually. Find its value after 6 years, to the nearest cent.

  1. A
    $6200.00
  2. B
    $6326.60
  3. C
    $6083.26
  4. D
    $1326.60
Show answer

Answer: B. FV = 5000 × 1.046 = $6326.60. $6200 is simple interest, and $1326.60 is only the interest earned.

8. A car costs $28 000 and depreciates by 15% each year. Find its value after 4 years, to the nearest cent.

  1. A
    $11 200.00
  2. B
    $17 195.50
  3. C
    $14 616.18
  4. D
    $13 383.83
Show answer

Answer: C. Value = 28 000 × 0.854 = $14 616.18. $11 200 subtracts 15% of the original price each year, and $13 383.83 is the total loss in value.

9. Evaluate Σk=16 5(2)k−1.

  1. A
    320
  2. B
    160
  3. C
    315
  4. D
    635
Show answer

Answer: C. This is 5 + 10 + 20 + 40 + 80 + 160 = 5(26 − 1) ÷ (2 − 1) = 315. 160 is only the 6th term; 635 sums 7 terms.

10. The profit of a company is zero when x = −1.2, 3.5 or 6.1, where x is years since 2020 and the model is valid for 0 ≤ x ≤ 8. Which solutions are meaningful?

  1. A
    x = 3.5 and x = 6.1 only
  2. B
    x = −1.2, 3.5 and 6.1
  3. C
    x = −1.2 only
  4. D
    x = 6.1 only
Show answer

Answer: A. x = −1.2 lies outside the domain 0 ≤ x ≤ 8 (it would be before 2020), so only 3.5 and 6.1 are meaningful in context.

Start the chapter testAbout the IB Maths: Applications and Interpretation test

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Ways to practise this chapter

Number and algebra: questions students ask

How many Number and algebra MCQs are there?

52, each with the answer and a short explanation, across 6 topics: SL1.1, 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). Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Applications and Interpretation 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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