Upton Court Grammar School – Department of Mathematics
Year 12 Mathematics: Pre-enrolment task
There are two learning objectives for this pre-enrolment task:
1) To develop your independent learning skills as these will be critical to your success at A-level.
2) To identify any gaps in your A and A* GCSE knowledge as this knowledge is needed for the first
part of your A-level.
As such your pre-enrolment task is as follows:
1) Answer the nine A-level past paper questions set out below. Your work must be marked and
corrected in green pen using the attached mark scheme, and a final mark out of 52 recorded.
2) Any additional work you do to help you complete this task should be recorded in the attached
‘Independent Learning Log’ sheet. Additional work might include using resources such as your
GCSE notes and the recommended textbook* named below to help you to complete this
pre-enrolment task.
The above work must be completed and submitted to your teacher in your first Maths lesson in
September. In that lesson you will sit a baseline test covering the same topics as the nine questions
below, and your target will be to score a minimum of 80%.
Anyone either not handing in the work on time or not scoring appropriately in the baseline test will be
immediately put onto an intervention programme in order to support their progress. Use the checklist
below to ensure that you submit everything required.
Dr Ioras
* Recommended textbook:
https://www.amazon.co.uk/Edexcel-AS-Level-Modular-Mathematics/dp/0435519107/ref=sr_1_1?s=books
&ie=UTF8&qid=1465902231&sr=1-1&keywords=edexcel+maths+c1
Checklist for submission
1) Full answers to questions 1-9.
2) All answers marked and corrected in green pen.
3) Score out of 52 recorded.
4) All learning to support this work recorded on the attached ‘Independent Learning
Log’ sheet.
Completed
Q1. (Surds)
Expand and simplify (√7 + 2)(√7 − 2).
(2)
(Total 2 marks)
Q2. (Indices)
(a) Find the value of 8 .
(2)
(b) Simplify
.
(2)
(Total 4 marks)
Q3. (Quadratics)
Factorise completely x − 4x3
(3)
(Total 3 marks)
Q4. (Simultaneous equations)
Solve the simultaneous equations
(7)
(Total 7 marks)
Q5. (Inequalities)
Find the set of values of x for which
(a) 2(3x + 4) > 1 − x
(2)
(b) 3x2 + 8x − 3 < 0
(4)
(Total 6 marks)
Q6. (Reciprocal curve)
Figure 1
Figure 1 shows a sketch of the curve C with equation
y = 1⁄x + 1,
x≠0
The curve C crosses the x-axis at the point A.
(a) State the x coordinate of the point A.
(1)
The curve D has equation y = x2(x − 2), for all real values of x.
(b) A copy of Figure 1 is shown below.
On this copy, sketch a graph of curve D.
Show on the sketch the coordinates of each point where the curve D crosses the coordinate axes.
(3)
(c) Using your sketch, state, giving a reason, the number of real solutions to the equation
x2(x − 2) = 1⁄x + 1.
(1)
Figure 1
(Total 5 marks)
Q7. (Completing the square, curve sketching)
4x2 + 8x + 3 = a(x + b)2 + c
(a) Find the values of the constants a, b and c.
(3)
(b) On the axes below, sketch the curve with equation y = 4x2 + 8x + 3, showing clearly the coordinates of
any points where the curve crosses the coordinate axes.
(4)
(Total 7 marks)
Q8. (Co-ordinate geometry)
The straight line L1 passes through the points (−1, 3) and (11, 12).
(a) Find an equation for L1 in the form ax + by + c = 0,
where a, b and c are integers.
(4)
The line L2 has equation 3y + 4x − 30 = 0.
(b) Find the coordinates of the point of intersection of L1 and L2.
(3)
(Total 7 marks)
Q9. (Co-ordinate geometry)
The line L1 has equation 2y − 3x − k = 0, where k is a constant.
Given that the point A (1, 4) lies on L1, find
(a) the value of k,
(1)
(b) the gradient of L1.
(2)
The line L2 passes through A and is perpendicular to L1
(c) Find an equation of L2 giving your answer in the form ax + by + c = 0, where a, b and c are integers.
(4)
The line L2 crosses the x-axis at the point B.
(d) Find the coordinates of B.
(2)
(e) Find the exact length of AB.
(2)
(Total 11 marks)