(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?


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


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


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Produced by Al Reynolds - September 2001 - Revised March 2003