Series — IGCSE Mathematics - Additional (0606) questions by topic
Series questions ask you to find unknown constants in a binomial expansion written in descending or ascending powers of x, expand an expression using an appropriate quadratic factorisation first, and find how many terms an arithmetic progression written with logarithms needs before its sum exceeds a given value. Find, show and write are the top command words, each requiring careful algebraic setup before any expansion or summation begins.
Marks range from 5 to 12 across the 8 real questions gathered here, from 2025 papers. Binomial and logarithmic series problems chain several algebraic steps together, so submit your workings for instant marking to catch a misidentified coefficient or index slip early, before it invalidates the rest of the expansion.
May–June 2025, Paper 11
An arithmetic progression has common difference d. The 3rd term of this progression is 10. Write down expressions for the 1st term and the 2nd term of this progression. Give your…
Answer this question and get it marked →May–June 2025, Paper 12
A geometric progression has a 4th term of (8k^6)/27 and a 6th term of (32k^10)/243, where k is a constant. The common ratio of this geometric progression is positive. Find the…
Answer this question and get it marked →May–June 2025, Paper 21
Using an appropriate quadratic factorisation, find the first three terms in the binomial expansion of (9x^2 + 12x + 4)^5, in ascending powers of x. You must simplify your…
Answer this question and get it marked →A geometric progression has first term a and common ratio r, where r 0. The sum of the 2nd and 3rd terms of the progression is 168. The sum of the 4th and 5th terms of the…
Answer this question and get it marked →May–June 2025, Paper 22
The first three terms of an arithmetic progression can be written as 2 ln(x^3), 5 ln(x^2), 2 ln(x^7). Given that x 1, find the least number of terms for the sum of this…
Answer this question and get it marked →The first three terms, in descending powers of x, in the expansion of (3x^2 - a)^n (1 + 1/x^2)^2 can be written as 729 x^12 + 972 x^10 + b x^8, where a, b and n are constants.…
Answer this question and get it marked →May–June 2025, Paper 23
Find the term independent of x in the expansion of (x^2 − 3/x^4)^15.
Answer this question and get it marked →The 1st term of an arithmetic progression is 9. The last term of this progression is 159. The sum of all the terms is 2604. The 12th term of this arithmetic progression is the 1st…
Answer this question and get it marked →