Series: worked exam questions
15 solved series questions, each worked line by line the way the 0606 mark scheme rewards. Learn the method in the Series topic notes, then see it applied here.
A Geometric Series Problem: The Bouncing Ball
Find the total distance a bouncing ball travels using a geometric series and sum to infinity, a classic 0606 applied GP question.
An Arithmetic Progression Savings Problem
Model a weekly savings plan as an arithmetic progression and find the total saved, a 0606 applied AP question testing the translation to a and d.
Arithmetic Progression from Two Given Terms
Given the 5th and 12th terms of an AP, find the first term, common difference and the sum of 20 terms, a 0606 question solved by simultaneous equations.
Binomial Expansion: Finding an Unknown Constant
Given the coefficient of x² in (2 + kx)⁶, find k, a 0606 binomial question that isolates one term with the general term rather than expanding everything.
Binomial: The Term Independent of x
Find the constant term in a binomial expansion by setting the power of x to zero, a 0606 question using the general term to target one specific term.
Coefficient in a Product with a Binomial Expansion
Find the coefficient of x² in (1+2x)(1−x)⁶ by expanding only the terms that can produce x², a common 0606 binomial question.
Finding n and a from Binomial Coefficients
Given two coefficients in the expansion of (1+ax)ⁿ, set up simultaneous equations to find n and a, a frequently examined 0606 binomial question.
Finding the First Term of an AP from a Sum
Given the sum of the first n terms and the common difference, find the first term of an arithmetic progression, a 0606 question running the sum formula in reverse.
Geometric Progression from Two Given Terms
Given the 2nd and 5th terms of a GP, find the common ratio, first term and the sum of 8 terms, a 0606 question solved by dividing the term equations.
Geometric Series: Salary with Annual Rises
A salary rising by a fixed percentage each year forms a geometric progression; find a later year's pay and the total over ten years, a 0606 series application.
How Many AP Terms Are Needed to Exceed a Value
Find how many terms of an arithmetic progression are needed for the sum to first exceed 200, a 0606 question that ends in a quadratic inequality in n.
Recurring Decimal as a Geometric Series
Convert 0.474747… to a fraction using the sum to infinity of a geometric series, a neat 0606 application of S∞ = a/(1−r).
Sum of Multiples in a Range
Add up all the multiples of 3 below 100 by treating them as an arithmetic progression, finding n first, then applying the sum formula, a 0606 series question.
Sum to Infinity of a Geometric Progression
Given the first term and sum to infinity of a GP, find the common ratio and a later term, a 0606 question testing the |r| < 1 convergence condition.
The First Negative Term of an AP
Find the first negative term of a decreasing arithmetic progression by solving an inequality for n, a 0606 question ending with a whole-number check.
Worked examples show the routine. A tutor builds it into your child.
Weekly 1-to-1 classes with a founder-vetted 0606 specialist, your child's own working marked line by line against real mark schemes. A 1-hour trial class first, always.