# (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

Assessment
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Produced by Al Reynolds - September 2001 - Revised March 2003