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13+ EXAMINATION 2012
(THIRD FORM ENTRY)
MATHEMATICS
Time allowed: 1 HOUR
NON-CALCULATOR
CANDIDATE NO:
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO
Answer as many questions as you can.
There are t w o sections to this paper. Section A is multiple choice.
In Section B you should write the answers in the space provided.
Marks can be obtained for correct methods so show your working
clearly in the space near the question.
If you are not sure about a question leave it and go on to the next one.
You can return to any you have missed out at the end if you have time.
MARKS
Section A
25
Section B
60
TOTAL
85
%
SECTION A – MULTIPLE CHOICE
Answer ALL TWENTY-FIVE questions by circling the correct answer.
If you wish to change your answer, put a cross through the previous choice and
circle your new answer.
USE THIS SPACE FOR ANY WORKING OUT YOU NEED TO DO
1
A café had 23578 customers last year.
Round the number 23578 to the nearest ten.
A
23572
2
B
23570
C
23580
D
23500
E
23600
D
21
E
22
Here is a sequence of numbers
5
9
13
17
Find the next number in the sequence.
A
18
3
B
19
C
20
Look at the shaded rectangle on the centimetre grid below.
What is the area of the shaded rectangle?
A
3 cm²
4
C
6 cm²
D
10 cm²
E
12 cm²
Martin bought a calculator for £5.75 and a pencil case for £1.45
Work out his total bill
A
£6.10
5
B
5 cm²
B
£6.20
C
£6.30
D
£6.15
E
£7.20
C
11
D
13
E
15
What is the 7th odd number?
A
7
B
9
6
Which of these is an obtuse angle?
A
7
C
Which of these numbers is equivalent to
A
0.7
8
B
B
9
12
C
2
3
D
E
D
E
7
8
3
?
4
0.12
Sam buys a bus ticket for £1.25 and a train ticket for £14.80. She pays with a
£20 note.
How much change should she receive?
A
£4.95
B
£16.05
C
£4.05
D
£3.95
E
£18.75
C
(–1, –2)
D
(–1, 2)
E
(2, –1)
9
What are the coordinate of P?
A
(–2, 1)
B
(1, –2)
10
Look at the number line below.
What is the number indicated by the arrow?
A
1.2
11
B
1.21
C
1.22
D
1.23
E
1.25
Here are the first five terms in a sequence of numbers.
7
10
13
16
19
What is the 10th term in this sequence?
A
25
B
30
C
31
D
34
E
37
D
130°
E
360°
12
What is the size of the angle marked x?
A
30°
13
B
90°
C
100°
There are 48 packets of crisps in each box of crisps.
Work out the total number of packets of crisps in 234 boxes.
A
2808
B
10000
C
11196
D
11232
E
11238
14
Here is a list of numbers.
1.232
1.33
1.23
1.323
1.22
The numbers are going to be written in order, smallest number first.
Which of these numbers would be the 4th on the list?
A
1.232
15
C
1.23
D
1.323
E
1.22
A train leaves Manchester at 07 45 and arrives in London at 10 20.
How long does it take the train to make the journey?
A
2 hours
25 minutes
16
B
1.33
B
2 hours
35 minutes
C
3 hours
15 minutes
D
3 hours
25 minutes
E
3 hours
35 minutes
Here is a sequence of numbers.
5
10
8
13
11
Work out the next number in this sequence.
A
9
B
11
C
15
D
16
E
18
C
80°
D
140°
E
180°
17
In the triangle ABC, AB = AC
Work out the size of angle x.
A
40°
B
70°
18
Which of these numbers is a prime number?
A
2
19
B
6
C
9
D
21
E
15
D
4
E
5
Adult cinema tickets cost £3.50
Child cinema tickets cost £2.20
Mr Brown buys some tickets for £14.90
He buys 2 child cinema tickets.
How many adult cinema tickets does he buy?
A
1
20
B
2
C
3
This diagram shows a rectangular garden patio.
A gardener has square paving slabs.
The length of the sides of a slab is 50 cm.
How many square paving slabs are needed to completely cover the patio?
A
15
B
16
C
30
D
40
E
60
C
7 m²
D
12 m²
E
60 m²
21
Work out the area of this triangle.
A
6 m²
B
7½ m²
22
The sketch shows the coordinates of the endpoints of the line AB.
Work out the coordinates of the midpoint of the line AB.
A
(4, 3½)
23
C
(3½, 2½)
D
(2, 3½)
E
(3, 1½)
C
524
D
5240
E
52400
Work out 1572 ÷ 0.3
A
5.24
24
B
(3, 3)
B
52.4
Here is an arithmetic sequence
1
4
7
10
13
Work out the expression, in terms of n, for the nth term of the sequence.
A
3n + 2
25
B
2n – 3
C
3n
D
3n – 2
E
2n
Work out the Highest Common Factor (HCF) of 30 and 72.
A
2
B
3
C
6
D
30
E
360
SECTION B
ANSWER ALL QUESTIONS IN THE SPACES PROVIDED
REMEMBER TO SHOW WORKING WHERE NECESSARY
26
a.
What fraction of this shape is shaded?
..................................
b.
(1 mark)
Shade in an area equal to 0.3 of this shape:
(1 mark)
27
Find the value of these expressions when a = –3 and b = 4.
a.
2a + 2.5b
..................................
b.
1
b
–
(2 marks)
1
a
..................................
(2 marks)
28
Rob asked two groups of people what their favourite flavour of ice lolly is.
He decided to display the results of his survey using pie charts.
a.
Group 1 had 200 people in it.
Complete this frequency table showing Group 1’s lolly preferences.
Flavour
Frequency
Orange
Strawberry
50
Lemon
b.
(2 marks)
Group 2 had 100 people in it.
Complete this frequency table showing Group 2’s lolly preferences.
Flavour
Frequency
Orange
Strawberry
Lemon
c.
40
(2 marks)
Rob says “25% of the people I questioned said that strawberry is their
favourite ice lolly flavour.” Is he correct? Explain your answer.
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(1 mark)
29
The formula used for finding the area of a rectangle is:
Area = length × width
Find the missing length, x, in this shape.
Total area of
shape = 47 cm²
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(3 marks)
30
Polly wants to learn to drive.
At her nearest driving school, a one-hour lesson costs £21.50.
a.
If Polly has 30 hours of driving lessons, how much will they cost her?
……………………………………………………………………………………………………………
…………………………………………………………………………………………………………… (2 marks)
b.
The driving school offers Polly a discount if she books all her lessons in
advance. She can have 30 lessons for £600.
If Polly does this, how much cheaper will each individual lesson be?
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(2 marks)
31
Triangle A is enlarged to make Triangle B.
Use the diagram to help you complete the following sentences.
Triangle A was enlarged by a scale factor of ……………… to make Triangle B.
The centre of enlargement was (………… , …………)
(2 marks)
32
The shaded faces of these two cuboids have the same area.
The volume of Cuboid A is 150 cm³.
Find the volume of Cuboid B.
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
(3 marks)
33
Janet puts 8 pink pegs, 2 green pegs and 4 blue pegs in a bag.
She pulls one of the pegs out of the bag at random.
a.
What is the probability that Janet picked a blue peg?
……………………………………………………………………………………………………………
(1 mark)
b.
Janet returns the peg to the bag, and puts some more blue pegs in.
Now the probability that a randomly selected peg will be blue is 3/8.
How many more blue pegs did Janet add to the bag?
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(3 marks)
34
a.
Simplify 2a + 3a
……………………………………………………………………………………………………………
(1 mark)
b.
Expand and simplify 5a + 2b – 7b + 3 (3b – 2a)
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(3 marks)
c.
Factorise completely 3x² + 15x
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(2 marks)
35
Solve these equations:
a.
2k + 3 = 11
k = ………………
(2 marks)
b.
17 = 3y + 2
y = ………………
c.
(2 marks)
20 + x = 39 – x
x = ………………
(3 marks)
36
ABCD is a parallelogram with A (1, 5), B (5, 5) and C (7, 9).
Write down:
a.
The coordinates of D
( …………… , …………… )
(1 mark)
b.
The equation of line p
………………………
(1 mark)
37
In this diagram of a 2-dimensional shape, AB is parallel to DE.
a.
Find angle CDF, giving a reason for your answer
……………………………………………………………………………………………………………
(2 marks)
b.
Find angle ADF, giving a reason for your answer
……………………………………………………………………………………………………………
(2 marks)
c.
Find angle ACB
……………………
d.
Find angle FCE
(1 mark)
……………………
e.
Name the two angles equal to DFC
angle …………………… and angle ……………………
(1 mark)
(2 marks)
38
David went for a walk along a straight road that passes his house.
This graph shows how far he was from his house at every point during the
walk.
a.
How far did David walk in total?
……………… km
(1 mark)
b.
For how many minutes did David rest during his walk?
……………… minutes
(1 mark)
c.
David was furthest from home at point A.
What was his average speed between point A and point B?
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………… km / hour
(3 marks)
39
Andi measures the lengths of 9 leaves, to the nearest cm, for a Science project.
These are the results:
8 cm
a.
10 cm
5 cm
6 cm
11 cm
13 cm
9 cm
7 cm
3 cm
Andi says 11 cm is the median because it is the number in the middle of
the list above. Without finding the median, explain why Andi’s answer is
likely to be wrong.
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(1 mark)
b.
Find the range of lengths.
……………… cm
(2 marks)
c.
Calculate the mean length.
……………… cm
(2 marks)
END OF EXAMINATION
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