Graphs of functions, asymptotes and proportional relationshipsEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

What happens at a repeated root?
What happens at a single root?
End behaviour of y=x^3?
End behaviour of y=x^4?
Asymptotes of y=\frac ax?
Where is y=\frac{a}{x^2} for a0?
Asymptotes of y=\frac{2}{x+a}+b?
Asymptotes of y=\frac{3}{x-2}+1?
What do intersections of y=f(x) and y=g(x) give?
Why not divide by (x-4) when solving x^2(x-4)=x-4?
What is the graph of C=kd?
How does y=\frac kx appear if you plot y against \frac1x?
Where does y=x^2(2x-1)^2 meet the x-axis?

Exam questions on Graphs of functions, asymptotes and proportional relationships

The curve $C$ has equation $y=x^2(2x-1)^2$ .
Solve $x^2(2x-1)^2=1$ , and hence state how many times the line $y=1$ meets $C$ .2 marks
The curve $H$ has equation $y=\frac{3}{x-2}+1$ .
Find the coordinates of the points where $H$ meets the line $y=x+1$ .2 marks
A fixed mass of gas is kept at constant temperature. Its pressure $P$ kPa is inversely proportional to its volume $V$ litres, and $P=150$ when $V=2$ .
Find an equation for $P$ in terms of $V$ , and hence find the pressure when $V=5$ .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).