Download DAY WATERMAN COLLEGE ENTRANCE EXAM JANUARY 2010

DAY WATERMAN COLLEGE
ENTRANCE EXAM
JANUARY 2010
NAME:
SCHOOL:
DATE OF BIRTH:
EXAM DATE:
CENTRE:
MATHEMATICS EXAMINATION (SAMPLE PAPER)
TIME ALLOWED: 1 HOUR
TOTAL MARKS: 50
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. Write your answers correctly.
2. Calculators must NOT be used.
3. Do all of Section A before attempting Section B.
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Mathematics Sample Paper
Section A
60 min
50 marks
No calculators. Do all of Section A before attempting Section B
1.
Write each word in the correct box.
faces
edges
vertices
1 mark
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2.
Ben wants to buy a packet of biscuits.
He gives the shopkeeper 65p
The shopkeeper says,
‘You need 25p more to buy the biscuits’.
How much do the biscuits cost?
p
1 mark
3.
Join the dots which are 10 centimetres apart.
You may use a ruler.
1 mark
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3
4.
Some children in Class 4 are in a club.
This table shows the club they are in.
How many more children go to recorder than chess?
children
This graph should show the same data as the table.
Shade in the correct number of blocks for computer club.
2 marks
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4
5.
Circle one number in each box to make a total of 1000
150
150
250
200
250
350
400
350
450
450
1 mark
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5
6.
The line on the grid is one side of a square.
On the grid, draw the other three sides of the square.
Use a ruler.
1 mark
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7.
A square always has four sides.
Is it true that a four-sided shape is always a square?
Yes / No
Circle Yes or No.
Explain how you know.
1 mark
8.
Write in the missing numbers.
(3 × 4) +
= 19
1 mark
(5 × 5) –
= 23
1 mark
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9.
There are four shapes on this diagram.
The diagram is turned to the new position below.
Draw the three missing shapes.
2 marks
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10.
Here are four digit cards.
7
5
2
1
Choose two cards each time to make the following two-digit numbers.
The first one is done for you.
an even number
5
2
a multiple of 9
a square number
a factor of 96
2 marks
11.
Here are six quadrilaterals with their mathematical names.
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square
parallelogram
rhombus
oblong
kite
trapezium
9
Lara chooses one of the quadrilaterals.
She says,
‘It has two acute angles.
All four sides are the same length’.
Which quadrilateral did Lara choose?
..................................................................
1 mark
Stefan chooses one of the quadrilaterals.
He says,
‘It has more than one obtuse angle.
It has no parallel sides’.
Which quadrilateral did Stefan choose?
..................................................................
1 mark
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12.
Here are four labels.
even
multiples of 9
not even
not
multiples of 9
Write each label in the correct position on the sorting diagram below.
72
56
84
54
63
45
49
75
1 mark
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13.
Here are two thermometers.
They show two different temperatures.
ºC
20
0
–5
5
10
–10
10
–15
0
15
ºC
What is the difference between the two temperatures?
degrees
1 mark
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12
14.
Here is a number chart.
Circle the smallest number on the chart that is a multiple of both 2 and 7
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
1 mark
Here is the same number chart.
Circle the largest number that is not a multiple of 2 or 3 or 5
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
1 mark
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15.
Class 6 did a survey of birthday dates.
This chart shows the number of people with birthdays in each three months of the year.
20
Number
of people
10
0
Jan
Feb
March
April
May
June
July
Aug
Sep
Oct
Nov
Dec
Months
From the chart, how many people have a birthday before July?
1 mark
Nobody has a birthday in October.
Six people have a birthday in November.
How many people have a birthday in December?
1 mark
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16.
A cube has shaded shapes on three of its faces.
Here is a net of the cube.
Draw in the two missing shaded shapes.
1 mark
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17.
The numbers in this sequence increase by 7 each time.
1
8
15
22
29
....
The sequence continues in the same way.
Will the number 777 be in the sequence?
Yes / No
Circle Yes or No.
Explain how you know.
1 mark
18.
Here is a regular octagon with two vertices joined to make the line AB.
Join two other vertices to draw one line that is parallel to the line AB.
A
B
1 mark
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Here is the octagon again.
Join two vertices to draw one line that is perpendicular to the line AB.
A
B
1 mark
19.
Find two square numbers that total 45
+
=
45
1 mark
20.
ABCD is a rectangle drawn on coordinate axes.
The sides of the rectangle are parallel to the axes.
y
A
E
B
(– 10, 8)
x
0
D
C
(14, – 4)
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What are the coordinates of D and E?
D is
(
,
)
1 mark
E is
(
,
)
1 mark
21.
Here are five calculations.
A
720 ÷ 64
B
820 ÷ 75
C
920 ÷ 80
D
1020 ÷ 90
E
1120 ÷ 100
Write the letter of the calculation that has the greatest answer.
.......................
1 mark
Write the letter of the calculation that has an answer closest to 11
.......................
1 mark
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22.
A and B are two numbers on the number line below.
The difference between A and B is 140
Write the values of A and B.
2 marks
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23.
Calculate 143
× 37
Show
your working.
You may get
a mark.
2 marks
24.
A shop sells notebooks and pens.
Hassan bought a notebook and a pen.
He paid £1.10
Kate bought a notebook and 2 pens.
She paid £1.45
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20
Calculate the cost of a notebook.
Show
your working.
You may get
a mark.
2 marks
25.
Part of this number line is shaded.
0
1
2
Circle all the numbers below that belong in the shaded part of the number line.
1.1
1.4
11
3
11
5
1 mark
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~
Part B Extension
Answer as many questions as you can. The
questions get harder as you go on.
26.
The diagram shows a right-angled triangle and three parallel lines.
x
145º
Not to scale
35º
y
Calculate the size of angle x and angle y
Do not use a protractor (angle measurer).
x=
1 mark
y=
1 mark
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27.
Two numbers are in the ratio 3 : 2
One of the numbers is 0.6
There are two possible answers for the other number.
What are the two possible answers?
2 marks
28.
150 people take part in a walk.
This chart shows the number of people still walking at different times.
150
140
130
120
110
100
90
Number 80
of walkers
70
60
50
40
30
20
10
0
9 am
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10 am
11 am
12 pm
Time
1 pm
2 pm
3 pm
23
Use the chart to estimate the time when two-thirds of the people are still on the walk.
1 mark
What percentage of the people who started are still on the walk at 3pm?
Show
your method.
You may get
a mark.
%
2 marks
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29.
Here is a sequence of shapes made from squares and circles.
shape
number (n)
1
2
3
4
number of
circles (c)
2
5
8
11
number of
squares (s)
3
5
7
9
The sequence continues in the same way.
The formula for the number of circles (c)
in shape number (n) is
c = 3n – 1
Use the formula to work out the shape number which has 104 circles.
Show
your method.
You may get
a mark.
2 marks
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25
Write the formula for the number of squares (s) in shape number (n).
S = ..............................................
1 mark
30.
Here is a circle with its centre at the point (1, 1)
The point (1, 7) is on the circumference of the circle.
y
(1, 7)
(1, 1)
0
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x
26
For each of these points, put a tick ( ) to show if it is inside the circle, on the circle or
outside the circle.
One has been done for you.
inside
the circle
on the
circle
outside
the circle
(3, 7)
(7, 1)
(1, –7)
(–2, –2)
2 marks
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