# A-Level Audit: Pure Mathematics

Instructions:
Answer as many questions as possible.
The questions become progressively more difficult.
Give all fractional answers in decimal form unless
otherwise indicated in the question.
Do not put spaces in any of your answers.
Where answers are not rational, round your
response to no more than 3 decimal places.

Question 1
Look at the following equation:

State the value of n:
n =

Question 2
Consider this equation, where a and b are constants:

State the values of a and b:
a =
b =

Question 3
Look at this quadratic equation:

How many real solutions does the equation have?
solutions

Question 4
Consider this equation:

What is the value of p?
p =

Question 5
Consider this function:

What is the range of the function? Choose from the options below:

Type the letter of your choice in this box:

Question 6
The graph of    y = |a + bx| + c    is shown below:

State the values of a, b and c:
a =
b =
c =

Question 7
The graph of y = f(x) is shown below:

The graph is transformed to give this graph:

Which of these expressions is the equation of the new graph?

Type the letter of your choice in this box:

Question 8
The equations of two lines are given below:

Which of the following statements is true?

Type the letter of your choice in this box:

Question 9
An infinite geometric series begins:
5 + 2.5 + 1.25 + 0.625 + ...

What is the sum of this series?
(write INFINITE in the box if you believe the sum of the series is infinite)

Question 10
An arithmetic series has 20 terms. The first term is 2 and the last term is 44.

What is the sum of the series?

Question 11
Four graphs are shown below.
The equation of each graph is of the form y = a sin(bx).
Work out the values of a and b for each graph.

 (a) a = b = (b) a = b = (c) a = b = (d) a = b =

Question 12
Look at the equation below:

How many solutions are there in the interval ?

Question 13
Look at the statements below:

Which of the statements is true for all values of x?
Type the letter of your choice in this box:

Question 14
The graph below has the equation y = a e x + b.

Work out the values of a and b for each graph.
a =
b =

Question 15
Simplify log3(34).

Question 16
The solution of the equation 8 = 2e 5x is of the form x = ln p q,
where p is an integer between 0 and 20 and q is a decimal between 0 and 1.

State the values of p and q. Give q as a decimal.
p =
q =

Question 17
Evaluate 30.

Question 18
If
 dy dx
= 4y, what is y as a function of x?

Pick your answer from the list below. k is a constant.

Type the letter of your choice in this box:

Question 19
The graph of y = f(x) is shown below:

Indicate whether each of the statements below is true or false:
A:      At x = a,
 dy dx
= 0                  True False
B:      At x = a,
 d2y dx2
> 0                  True False
C:      At x = b,
 d2y dx2
> 0                  True False

Question 20
What do you get when you differentiate ln(2x)?

Pick your answer from the list below:
A:
 2 x
B:
 1 x
+ 2
C:
 1 x
Type the letter of your choice in this box:

Question 21
What is ?
Pick your answer from the list below:

Type the letter of your choice in this box:

Question 22
The diagram shows the graph of y = f(x):

Indicate whether each of the statements below is true or false:
 True False True False True False True False

Question 23
The table below gives the values of a continuous function f(x) for different values of x:

Indicate whether each of the statements below is true or false:
 A: There are exactly two solutions to the equation f(x)=0 between -1 and 6. True False B: The equation f(x)=0 has a solution between 3 and 4. True False

Question 24
The graphs of the curves with equations y = x2 and y = (x + a)2 + b are shown below:.

Work out the values of a and b.
a =
b =

Question 25
The derivative of   y = 11x -4 can be written in the form:

Work out the values of p and q, where p and q are integers.
p =
q =

Question 26

Work out the values of p and q, where p and q are integers.
p =
q =

Question 27
,    and   .

Work out the values of p and q, where p and q are integers.
p =

q =

Question 28
and   .

Work out the values of p and q, where p and q are integers.
p =
q =

Question 29
Look at the simultaneous equations below:

Work out the value of q for which the equations above would have an infinite number of solutions.
q =

Assessment
Use the buttons below to have your questions marked and a report produced.

 Mark your answers (WARNING: You can only do this once per test). Generate your report (Do this after you have checked your answers).

Produced by Al Reynolds - October 2003
Updated by Russell Geach - November 2006