Autumn

Yr 12  ENTRY EXAM
Non-Calculator

Instructions
•	Use black ink or black ball-point pen. Draw diagrams in pencil.
•	Fill in the boxes at the bottom of this page.
•	Answer all questions.
•	You must answer the questions in the space provided. 
•	Do all rough work in this book. Cross through any work that you do
		not want to be marked.
•	In all calculations, show clearly how you work out your answer.

Information
•	The marks for questions are shown in brackets.
•	The maximum mark for this paper is 69.
•	You may ask for more answer paper, graph paper and/or tracing paper.
		These must be tagged securely to this answer booklet.

Please write clearly, in CAPITALS.

Surname __________________________________________________________

Forename(s) ______________________________________________________

Teacher(s): ________________________________________________________

Class: _____________________________________________________________

Date: ______________________________________________________________

Result	Percentage	Grade	Target	

				
Tracking comment: 

Year 12 Maths Entry Test: GCSE Review
Strictly NON calculator: Where appropriate, enough working must be shown to illustrate your answer.

1.	(a)	Work out 

………………………
(2)
 
(b)	Work out 5 – 2

………………………
(3)
(Total 5 marks)

2.	

Diagram NOT accurately drawn
	AB is parallel to CD.
	Explain why angle x is 72º.
................................................................................................................................................
................................................................................................................................................
(Total 2 marks)

3.	Tayub said, “When x = 3, then the value of 4x2 is 144”.
	Bryani said, “When x = 3, then the value of 4x2 is 36”.
(a)	Who was right?
Explain why.

(2)
(b)	Work out the value of 4(x + 1)2 when x = 3.

.................................
(1)
(Total 3 marks)

4.	

	A has coordinates (0, 3).
B has coordinates (2, 7).
	Work out the gradient of the line that passes through A and B.

.....................................
(Total 2 marks)

5.	

	The diagram represents a garden in the shape of a rectangle.
All measurements are given in metres.
The garden has a flowerbed in one corner.
The flowerbed is a square of side x.
(a)	Write down an expression, in terms of x, for the shortest side of the garden.

.....................................
(1)
(b)	Find an expression, in terms of x, for the perimeter of the garden.
Give your answer in its simplest form.

.....................................
(2)
 
	The perimeter of the garden is 20 metres.
(c)	Find the value of x.

.....................................
(2)
(Total 5 marks)

6.	(a)	Simplify
(i)	3g + 5g
.................................
(ii)	2r × 5p
.................................
(2)
(b)	Expand	5(2y – 3)
.................................
(1)

(c)	Expand and simplify
2(3x + 4) – 3(4x – 5)

.................................
(2)
(Total 5 marks)

7.	Ben bought a car for £12 000.

	Each year the value of the car depreciated by 10%.
	Work out the value of the car two years after he bought it.

£ ………………….
(Total 3 marks)

8.	

Diagram NOT accurately drawn
	In the diagram, all measurements are in centimetres.
	ABC is an isosceles triangle.
AB = 2x
AC = 2x
BC = 10
 
(a)	Find an expression, in terms of x, for the perimeter of the triangle.
Simplify your expression.

………………………
(2)
	The perimeter of the triangle is 34 cm.
 
(b)	Find the value of x.

x =………………………
(2)
(Total 4 marks)

9.	(a)	Solve	7p + 2 = 5p + 8

p = ............................
(2)
(b)	Solve	7r + 2 = 5(r – 4)

r = ...........................
(2)
(Total 4 marks)

10.	Solve
2x – 3y = 11
5x + 2y = 18

x = ......................
y = ......................

(Total 4 marks)

11.	(a)	Simplify	a3 × a4

…………………….
(1)
 
(b)	Simplify   3x2y × 5xy 3

…………………….
(2)
 
(c)	Simplify   

…………………….
(1)
 
(d)	Factorise   x2 – 9

…………………….
(1)
(Total 5 marks)

12.	A straight line has equation	y = x +1
	The point P lies on the straight line.
P has a y-coordinate of 5.
(a)	Find the x-coordinate of P.

............................
(2)
 
(b)	Write down the equation of a different straight line that is parallel to y = x + 1.

.........................................
(1)
 
(c)	Rearrange y = x + 1 to make x the subject.

.................................
(2)
(Total 5 marks)

13.	(a)	Factorise
9x2 – 6x + 1

……………………………
(2)
 
(b)	Simplify

……………………………
(3)
(Total 5 marks)

14.	

	The line with equation 6y + 5x = 15 is drawn on the grid above.
(a)	Rearrange the equation 6y + 5x = 15 to make y the subject.

y = .........................
(2)
 
(b)	The point (–21, k) lies on the line.
Find the value of k.

k = .........................
(2)

 
15.	Bill said that the line y = 6 cuts the curve x2 + y2 = 25 at two points.
(a)	By eliminating y show that Bill is incorrect.

(2)
           (b)	By eliminating y, find the solutions to the simultaneous equations
x2 + y2 = 25
y = 2x – 2

x = ........................ y = ...................
or x = ........................ y = ...................
(6)
(Total 8 marks)

16.	

	Cylinder A and cylinder B are mathematically similar.
The length of cylinder A is 4 cm and the length of cylinder B is 6 cm.
The volume of cylinder A is 80 cm3.
	Calculate the volume of cylinder B.

………………………… cm3
(Total 3 marks)