Functions (OCR GCSE Maths: Higher): Exam Questions

Here is function A.

The output of function A is y.
Write an algebraic expression, in terms of y, for the input of function A.

Here is function A.

The diagram shows a composite function with an input, n, and an output of 96.

Find the value of n.

n = .....................................................

Here is a function.

The output of function A is x.

Write an algebraic expression, in terms of x, for the input of function A.

A number, , is put into function A.
The output is also .

Find the value of .

= .....................

A function is represented by the following function machine.

A number is input into the machine.
The output is used as a new input.
The second output is 11.

Work out the number that was the first input.

A number is input into the machine.
The output given is the same number.
Work out the number.

Here is function A.

A number, k, is input into function A.
The output is also k.
Find the value of k.

k = .....................................................

Here are two functions.

Composite function C is shown below.

The output from function C is 54.

Work out the input.

The input to function C is x.

Find an expression, in terms of x, for the output from function C.

Here is a function.

Complete the table of values for function A.

Here is another function.

Find the inverse function of function B.

Here is a composite function.

Find an expression for m in terms of p.
Give your answer in its simplest form.

m = ....................................................

A function machine is shown below.

If the Input is 3, the Output is 5.
If the Input is 7, the Output is 25.
Use this information to fill in the two boxes.

A function is given by the equation

Find the equation of the inverse function.

Function 1 is given by 

Function 2 is given by

Show that the equation for the composite function

'Function 1 followed by Function 2'

can be written in the form where and are integers which you should find.

Here are two functions.

i) Jo chooses a number, .
She inputs into each function.
The two outputs are equal.

Work out the value of .

............................[4]

ii) Explain why there is no other input that gives two outputs that are equal.

[1]

Here is function C.

Kai chooses values for p and q so that if he inputs any number into both function A and function C, he will always get two outputs that are equal.

Find the value of p and the value of q.

Here are two functions.

Find an algebraic expression for the output of the inverse of function A when the input is x.

Here is a composite function C.

Find the value x when z = 4x .

x = ..................................................

Here are two function machines, A and B.

Both machines have the same input.

Work out the range of input values for which

                                   the output of A is less than the output of B. 

Function 1 is given by

Function 2 is given by

The inverse of the composite function 'Function 1 followed by Function 2' is given by

Find the value of .

Function 1 is given by

where . Function 2 is given by

Two different composite functions are formed: 'Function 1 followed by Function 2' and 'Function 2 followed by Function 1'.

Find the input, , for which the outputs of the two different composite functions are the same, giving your answer in terms of .