MEDIUM
AS and A Level
IMPORTANT
Earn 100

By sketching graphs of and determine the number of roots of the equation

Important Questions on Numerical Solutions of Equations
HARD
AS and A Level
IMPORTANT
Show, by calculation, that has a root that lies between and

HARD
AS and A Level
IMPORTANT
Show, by calculation, that has a root between and

MEDIUM
AS and A Level
IMPORTANT
Show, by sketching the graph of and one other suitable graph, that this is the only root of this equation.

HARD
AS and A Level
IMPORTANT
Show by calculation that the equation has a root where

HARD
AS and A Level
IMPORTANT
The diagram shows the graph of where
By drawing a suitable graph on a copy of the diagram, show that is the only root of for

HARD
AS and A Level
IMPORTANT
The curve with equation where intersects the line at the point
By sketching the graph of for radians and one other suitable graph, deduce that this is the only point where the curve intersects the line

HARD
AS and A Level
IMPORTANT
The curve with equation where intersects the line at the point
Using calculations, show that

MEDIUM
AS and A Level
IMPORTANT
By sketching a suitable pair of graphs, show that the equation has only one root for
