Educerie · IB Diploma · Mathematics: applications and interpretation

Topic 1 — Topic test

Paper 1 style · technology required · 20 marks · 30 minutes

Give all answers to three significant figures unless otherwise stated, or as an exact value. Show your working: an unsupported answer earns no method marks.

1. A student measures the volume of a container as 240 cm³. Its true volume is 254 cm³.

(a) Calculate the percentage error in the measurement. [2]

(b) Write the true volume in the form a × 10^k, where 1 ≤ a < 10 and k ∈ ℤ. [2]

2. The population of a town is 42 000 and is increasing by 3.2 % each year.

(a) Find the population after 5 years. [2]

(b) Find the least number of whole years after which the population exceeds 60 000. [3]

(c) State one assumption made in this model. [1]

3. $8000 is invested at a nominal annual interest rate of 4.5 %, compounded quarterly.

(a) Find the value of the investment after 6 years. [3]

(b) Find the total interest earned. [1]

(c) Over the same period, inflation averages 2 % per year. Comment on what this means for the investor. [2]

4. A stadium stand has 24 seats in the first row. Each subsequent row has 3 more seats than the one in front of it. There are 20 rows in total.

(a) Find the number of seats in the 20th row. [2]

(b) Find the total number of seats in the stand. [2]

Total: 20 marks

Command words in this test. Question 2(c) says state — one short sentence, no justification needed. Question 3(c) says comment on, which requires a sentence about the investor's situation, not a restatement of the arithmetic.

Educerie · original questions written against the published IB syllabus structure for Mathematics: applications and interpretation Topic 1, first assessment 2021. All values are our own. Last reviewed 5 September 2026.