(a) Number and Algebra

(iv) Equations, Functions and Graphs

Question 1
Packages can be sent by motorcycle courier.
The total cost consists of a fixed charge of £ plus £ for every kilometre travelled.

If the total cost is £y and the distance travelled is x km,

(a)	Express y as a function of x
	y =
(b)	What is the cost of sending a package a distance of
	(i) kilometres? £ (ii) kilometres? £
(c)	If it costs £ to send a package, how far was the package sent?
	kilometres

Question 2
Solve each of these equations for x :

(a)	x + =	x =
(b)	2x - =	x =
(c)	2x + = x +	x =

Question 3
Solve these simultaneous equations to find x and y :

		Solutions:	x =
			y =

Question 4
Work out which of the following equations are linear in x and mark them with a tick (like this ).

(a)
(b)		(a, b and c are constants)
(c)
(d)		(a and b are constants)
(e)

Question 5
Write down the equation of each line below (in its simplest form):

	(A)	y =
	(B)	y =
	(C)	y =

Question 6
Write down the coordinates of the points marked on the grid below:

	(A)	( , )
	(B)	( , )
	(C)	( , )
	(D)	( , )
	(E)	( , )
	(F)	( , )

Question 7

(a)	Choose the statement which represents the inverse of the function "multiply by "
	The inverse is
(b)	If the result of multiplying a whole number by and then adding is , what was the original number?
	The original number was

Question 8
The graph below illustrates two equations.

The simultaneous equations are: From the graph, estimate the solution of these simultaneous equations to one decimal place: x = y =

Question 9
The graph below shows the data for the extension of a spring (in centimetres) for given weights (in grams).

	A line has been drawn through the points to help you answer these questions:
	(a)	Estimate the extension for a weight of 80 grams:	cm
	(b)	Estimate the weight which would give an extension of 2.5 cm:	g