Question 1Structured · 3 marksA* challenge
Find the term independent of x in the expansion of (2x − 1x)6.
Show answers and mark scheme
| Part | Answer and marking points | Marks |
|---|---|---|
| -160 general term M1 r = 3 M1 -160 A1 | 3 |
8 free IGCSE Additional Mathematics Series & Counting questions written in the style of Cambridge Additional Mathematics papers, each with its answer and mark scheme. 2 of them are A* challenge questions, built to catch the mistakes strong students still make.
This topic covers Permutations & combinations, Binomial expansion, Arithmetic & geometric progressions. Work through the questions below, then generate a full Series & Counting paper with a fresh set every time.
Generate a full Series & Counting paper →Find the term independent of x in the expansion of (2x − 1x)6.
| Part | Answer and marking points | Marks |
|---|---|---|
| -160 general term M1 r = 3 M1 -160 A1 | 3 |
The second term of a geometric progression is 18 and the fifth term is 163. Find the first term, the common ratio and the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| a = 27, r = ⅔, S∞ = 81 r3 = 163 ÷ 18 = 827 M1 r = ⅔ A1 a = 27 A1 S∞ = 81 A1 | 4 |
The first term of an arithmetic progression is 11 and the common difference is 5.
Find the 30th term.
Find the sum of the first 30 terms.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 156 156 B1 | 1 |
| (b) | 2505 S = n2(2a + (n − 1)d) M1 2505 A1 | 2 |
The letters of the word FRIEND are arranged.
Find the number of different arrangements.
Find the number of arrangements that begin and end with a vowel.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 720 720 B1 | 1 |
| (b) | 48 2 × 4! = 48 M1 48 A1 | 2 |
Find the first three terms in the expansion of (3 − 2x)7, in ascending powers of x.
Hence find the coefficient of x2 in the expansion of (1 + 2x)(3 − 2x)7.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2187 − 10206x + 20412x2 2187 B1 −10206x B1 20412x2 B1 | 3 |
| (b) | 0 20412 + (2)(−10206) M1 0 A1 | 2 |
The first term of a geometric progression is 24 and the common ratio is 13.
Find the sum to infinity.
Find the least number of terms whose sum exceeds 99% of the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 36 a ÷ (1 − r) M1 36 A1 | 2 |
| (b) | 5 1 − rn > 0.99 M1 logs M1 5 A1 | 3 |
A team of 3 is to be chosen from 8 people, including Ali and Bea.
Find the number of different teams.
Find the number of teams that include Ali but not Bea.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 56 56 B1 | 1 |
| (b) | 15 6C2 M1 15 A1 | 2 |
Find the number of different arrangements of the 6 letters of the word MONDAY.
Find the number of these arrangements that begin and end with a consonant.
A team of 4 is chosen from 7 boys and 4 girls. Find the number of teams with exactly 2 girls.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 720 720 B1 | 1 |
| (b) | 288 4 × 3 × 4! M1 288 A1 | 2 |
| (c) | 126 7C2 × 4C2 M1 126 A1 | 2 |
In the 0606 syllabus, Series & Counting covers Permutations & combinations, Binomial expansion, Arithmetic & geometric progressions.
This page has 8 Series & Counting questions with answers. For more, the free generator on mentorriyaz.in builds a new Series & Counting paper with a full mark scheme each time you click.
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in