Educerie · IB Diploma · Mathematics: analysis and approaches

Topic 1 — Topic test

Paper 1 style · no technology · 20 marks · 30 minutes

Answers must be given in exact form. Show all working: an unsupported answer earns no method marks even when it is correct.

1. An arithmetic sequence has third term u₃ = 11 and eighth term u₈ = 31.

(a) Find the common difference d. [2]

(b) Find the first term u₁. [1]

(c) Find the sum of the first 15 terms. [2]

2. A geometric sequence has u₁ = 24 and u₄ = 3.

(a) Show that r = 1/2. [2]

(b) Hence find S₆, giving your answer as an exact fraction. [2]

(c) Explain why the sum to infinity exists, and find its value. [2]

3. Solve the equation log₅(x) + log₅(x − 4) = 1. [4]

4. Find the term in x⁴ in the expansion of (3x − 2)⁶. [5]

Total: 20 marks

Command words in this test. Question 2(a) says show that — the answer is printed, so every mark is in the route to it, and you may not assume r = 1/2 in order to prove r = 1/2. Question 2(b) says hence, which obliges you to use the r from part (a); an independent method scores nothing. Question 2(c) says explain, so a sentence is required, not just a number.

A proof question rotates into this slot. Topic 1 also assesses simple deductive proof, which is not sampled in this particular test. See Example 6 in worked-examples.md for the structure a proof answer must have.

Educerie · original questions written against the published IB syllabus structure for Mathematics: analysis and approaches Topic 1, first assessment 2021. All values are our own. Sources consulted: none. Last reviewed 5 September 2026.