Modelling with sequences and seriesAQA A-Level Maths: Flashcards

What these 12 flashcards ask

When is a model arithmetic?
When is a model geometric?
Multiplier for a p\% increase?
Multiplier for a 20\% decrease?
Total distance for a bouncing ball (drop h, ratio r)?
Why is a bouncing-ball total distance doubled?
£1000 at the start of each year at 4\%: value at the end of year n?
How do you find when a geometric sum first exceeds a target?
How do you find when an arithmetic sum reaches a target?
How do you find the total of the last k terms?
Why must you check the boundary term when asked for the first term that exceeds a value?
Name one limitation of an arithmetic profit model.

Exam questions on Modelling with sequences and series

A company's profit in year $1$ is £ $40\,000$ and it increases by £ $5\,000$ each year.
Find the first year in which the profit exceeds £ $200\,000$ .2 marks
A ball is dropped from a height of $2$ m. After each bounce it rises to $70\%$ of the height from which it last fell.
Find the total distance travelled by the ball before it comes to rest.2 marks
A person invests £ $1000$ at the start of year $1$ and a further £ $1000$ at the start of each following year. Interest of $4\%$ per year is added at the end of each year.
Find the total value of the investment at the end of year $5$ , to the nearest pound.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).