ENTRANCE EXAMINATION
13+ SCHOLARSHIP
3rd FORM ENTRY
MATHEMATICS
PAPER 2
1 HOUR
CALCULATOR
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CANDIDATE NUMBER: ______________________________
TODAY’S DATE:
______________________________
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO
Answer as many questions as you can.
Show your working in the space below the question.
Marks are given for clear working out.
Where answers are not exact, they should be given to
three significant figures, unless specified otherwise.
The π button on your calculator should be used for calculations involving π.
13+Schol2
1
(a) Rewrite all the numbers in the following expression correct to 1 significant
figure:
219 – 52.4
4.7 × 3.1
............ – ............
............ × ............
(2 marks) (b)
Calculate the value of your answer to part (a).
..............................
(c)
(1 mark) Writing down all the figures shown on your calculator, find the decimal
value of:
219 – 52.4
4.7 × 3.1
..............................
(d)
(1 mark) Write your answer to part (c)
(i)
correct to two decimal places
..............................
(ii)
(1 mark) correct to three significant figures
..............................
13+ Schol 2
(1 mark) 2
Alfie is on holiday and wants to change £400 into Euros (€)
There are two places where he can change his money.
City Bank
£1 = €1.14
(a)
Travel Superstore
£1 = €1.16
Work out how many Euros he would get at the City Bank.
..............................
(b)
Work out how much extra he would get at the Travel Superstore.
..............................
(c)
(1 mark) The Travel Superstore charges 1% commission on money exchange.
How many Euros would he actually receive for his £400?
..............................
(d)
(2 marks) (2 marks) When he returns to England, he has €75 left over.
The Post Office has displays this exchange rate:
Post Office
£1 = €1.22
How much money in Pounds does he get back?
..............................
(1 mark) 13+ Schol 2
3
(a)
1 kilometre = 0.622 miles
The distance from Stoke-On-Trent to Exeter is 269 kilometres.
Convert this distance to miles, giving your answer correct to the nearest
five miles.
..............................
(2 marks) (b)
1 metre = 3.27 feet
A tennis court is 78 feet long.
Convert this distance to metres, giving your answer correct to one decimal
place.
..............................
(c)
(2 marks) A = 4πr²
is the formula to find the surface area of a sphere, where r is the radius of
the sphere.
A bowling ball has a diameter of 21.8 cm. Calculate its surface area in m² to
two significant figures.
..............................
(3 marks) 13+ Schol 2
4
(a)
Midtown High School has more girls than boys in the Sixth Form. The
ratio of girls to boys is 17 : 14
There are 182 boys. How many girls are there?
..............................
(b)
A ferry carries cars and coaches in the ratio 17 : 6
How many cars are there when the ferry is carrying a total of 368 cars and
coaches?
..............................
(c)
(2 marks) (2 marks) To make 24 pieces of chocolate fudge, Rosie mixes together
450 g icing sugar
100 g butter
100 g dark chocolate
(i)
How much butter will Rosie need if she uses 630 grams of icing
sugar in her chocolate fudge recipe?
..............................
(2 marks) (ii)
How many chocolate fudge pieces can Rosie make if she only has 75
grams of dark chocolate?
..............................
13+ Schol 2
(2 marks) 5
The number of merits awarded to students in Amber’s class last term were:
11
8
(a)
6
7
7
8
9
10
8
5
7
6
5
8
12
7
6
5
6
6
10
6
9
9
5
7
How many students are in Amber’s class?
..............................
(b)
(1 mark) Complete the tally chart below
merits
5
6
7
8
9
10
11
12
tally
frequency
/ / / /
total
(c)
(2 marks) What was the range of merits awarded?
..............................
(d)
What was the modal number of merits?
..............................
(e)
(1 mark) (1 mark) What was the median number of merits?
..............................
13+ Schol 2
(2 marks) (f)
What was the mean number of merits?
..............................
6
(2 marks) Solve:
(a) 3 x – 4 = 17
x = ..............................
(b)
y = 0.75
2
y = ..............................
(c)
(1 mark) 1.8 z + 19 = 27 – 2.2 z
z = ..............................
(d)
(2 marks) (3 marks) 3(4q + 2) = -30
q = ..............................
13+ Schol 2
(3 marks) 7
The diagram shows a replacement blade for a carpet knife.
Diagram NOT accurately drawn (a)
The blade is in the shape of a trapezium.
Find the area of this trapezium.
..............................
(b)
(2 marks) What is the length of the fourth side?
..............................
(3 marks) (c)
If angle p is 42°, what is angle q?
..............................
13+ Schol 2
(1 mark) 8
(a)
In March, bus fares were increased by 6%.
Until then, Robert paid £8 for his return bus ticket to Chester.
How much does he pay for his ticket after the price increase?
..............................
(b)
In the sale at Daisy’s Dresses there is sale with 15% discount off all marked
prices. How much does Alice pay for a ball gown with a marked price of
£120?
..............................
(c)
(3 marks) (3 marks) Before last year’s April increase, Mrs Watson paid £1150 per year Council
Tax. She expected this amount to rise by 6%.
(i)
How much more did Mrs Watson expect to pay?
..............................
(2 marks) (ii)
She actually paid £74.75 more.
What was the actual percentage increase?
..............................
13+ Schol 2
(2 marks) 9
(a)
When y = 8 – x complete the table of values
x
y
0
2
4
6
(2 marks) (b)
On the grid opposite draw the line y = 8 – x
(c)
If y = 1.5 x – 3
(i)
what is the value of y when x = 0?
(2 marks) y = ..............................
(ii)
what is the value of x when y = 0?
x = ..............................
(d)
(1 mark) (1 mark) Using your answers to part (c), or otherwise, on the grid opposite draw
the line y = 1.5 x – 3
(2 marks) (e)
Calculate the area of the quadrilateral which is bounded by the lines
y = 8 – x, y = 1.5 x – 3, and the x and y axes.
..............................
13+ Schol 2
(2 marks) 13+ Schol 2
10
The diagram shows a quadrilateral.
Diagram NOT accurately drawn The lengths of the sides are given in centimetres.
(a)
Find an expression, in terms of x, for the perimeter of the quadrilateral.
Give your answer in its simplest form.
..............................
(b)
(2 marks) The perimeter of the quadrilateral is 34 cm.
Find the length of the longest side of the quadrilateral.
..............................
13+ Schol 2
(3 marks) 11
Simplify
(a) 7 a³ + 2 a³
..............................
(2 marks) (b)
7 b² × 4 b³
..............................
(c)
(2 marks) (4 c³)³
..............................
(2 marks) (d)
9 d³
3d
..............................
(2 marks) 13+ Schol 2
12
A circle has a diameter of 14 centimetres.
14 cm (a)
Calculate the length of the circumference of
the circle.
..............................
(b)
(2 marks) Calculate the area of the circle.
..............................
(c)
A cylindrical container of diameter 14
centimetres and height 18 centimetres is made.
Calculate the volume of liquid it will hold (in cm³)
(2 marks) 14 cm 18 cm ..............................
(2 marks) END OF EXAMINATION
13+ Schol 2