CALCULATORS ARE NOT TO BE USED FOR THIS PAPER

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Mathematics Intermediate Tier Paper 1 November
2002 (2 hours)
CALCULATORS ARE NOT TO BE USED FOR THIS PAPER
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• (a) Consider the following set of numbers.
• 60, 61, 62, 63, 64, 65, 66, 67, 68,
• Using only the numbers in the set, write down
• (i) a prime number

61 or 67
(ii) a cube number
64
(b) Find the value of 0.3 x 0.4
0.12
3
2. A text book costs 6.35. A school wishes to
buy 48 of these text books. Calculate the total
cost of the 48 text books.
6 . 3 5 x 4 8
25400 (x 40)
5080 (x 8 )
30480
4
3. A cone is labelled A. A cuboid is labelled
B. A square-based pyramid is labelled C and a
tetrahedron labelled D. Complete the following
table. One has been done for you.
A
C
D
B
5
4. The daigram below represents a number machine.
INPUT
Subtract 8
Divide by 3
OUTPUT
If the input is n, write down the output in terms
of n.
n 8 3
6
5. Simplify 5x 9 3x 4
2x - 5
(b) What is the value of 6d 7e when d -3 and
e 2?
6 x -3 7 x 2
-18 -14
- 32
7
6. A black bag contains four disks numbered as
shown.
1
2
5
6
A green bag contains five disks numbered as shown.
8
1
2
4
7
In a game a player chooses a disc from the black
bag and then a disc from the green bag. The
numbers on the disc are multiplied together to
obtain the score. (a) Complete the following
table to show all the possible scores.
8
Green bag
Black bag
(b) (i) What is the probability that a player
scores less than 25?
16 20
(ii) What is the probability that a player scores
25 or more?
4 20
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A player wins a prize by scoring 6 or less. (c)
Mae Delyth yn chwaraer gêm unwaith. Beth ywr
tebygolrwydd y bydd hin ennill gwobr?
7 20
(ch) (i) 300 people each play the game
once. Approximately how many would you expect to
win a prize?
7 x 15
7 x 300 20
105
(ii) It costs 2 to play the game once. The prize
for winning is 5. If the 300 people each play
the game once, approximately how much profit do
you expect the game to make?
2 x 300 - 5 x 105
600 - 525
75
10

• 7. A rectangle has length 5 cm and width 2 cm.
• Write down the dimensions of the triangle after
  each has been enlarged by a factor of 4.

Length 20cm, Width 8cm
(b) How many times bigger is the area of the
enlarged rectangle than the area of the original
rectangle?
Area small rectangle 5 x 2 10 cm²
Area large rectangle 20 x 8 160 cm²
160 10
16
Or (scale factor ²) 4² 16
11
8. P and Q are two ports with Q due South of P.
Another port is at a point R on a bearing of 230
(S 50 W) from P and 300 (N 60 W) from Q. By
drawing suitable lines, mark the position R on
your diagram.
P
G N
230
x
R
300
Q
12
9. Solve the following equations. (a) 6x 8 10
(b) 4x 5 30 3x
4x 3x 30 5
7x 35
6x 10 8
6x 18
x 35 7
x 18 6
(c) 4(x 2) 36
x 5
x 3
4x 8 36
4x 36 - 8
4x 28
x 28 4
x 7
13
10. Show clearly how you would obtain an ESTIMATE
for the following calculation 594.3 x 7.6
38.7
600 x 8 40
600 5
120
14
11.
DVD Player 280
Sale 35 Off
A DVD player was priced at 280. In a sale it was
offered at a reduction of 35. How much does it
cost in the sale?
35 x 280 100
Neu 10 28
5 14
7 x 28 2
35 28 28 28 14
98
7 x 14
98
Sale price 280 - 98
182
Pris yn y sêl 280 - 98
182
15
12. Twice a day Chris gives his dog Kola 2/3 of a
bowl of biscuits. A 2.5kg bag of biscuits has
enough biscuits to last Kola 15 days. Find the
weight, in grams, of the biscuits in a full bowl
of biscuits.
2.5 kg 2500g
1 day 2500 g 15
2 x bowl 2500 g 3 15
bowl 2500 x 3 15 2
250g
16
13. Arwyn, Betty and Clive share out 3600 in the
ratio of 459. How much do they each get?
Number of parts 459 18
1 part 3600 18
200
Arwyn gets 4 x 200 800
Betty gets 5 x 200 1000
Clive gets 9 x 200 1800
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14. In quadrilateral PQRS, the line PQ is
parallel to SR, with PQ 16cm and SR 18cm. The
perpendicular distance between PQ and SR is
8cm. Calculate the area of the quadrilateral PQRS.
S
18cm
R
8cm
Diagram not drawn to scale.
Q
P
16cm
Area of a trapesium (a b) x h 2
(18 16) x 8 2
34 x 8 2
34 x 4
136cm²
18
15. The masses of 8 people who went on a diet
were measured before and after the diet. The
results were as shown in the following table.
(a) On the graph paper opposite, draw a scatter
diagram to display these results.
(b) What type of correlation does your scatter
diagram show?
Positive
(c) The mean mass of the 8 people before the diet
was 84kg and after the diet it was 72kg. Use this
information to draw a line of best fit on your
scatter diagram.
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140
120
Mass after the diet (kg)
(d) Use your line of best fit to estimate the
mass after the diet for a person whose mass was
95kg before going on the diet.
100
80
60
80kg
40
M
M
60
70
80
90
100
130
120
50
110
Mass before the diet (kg)
20

• 16. The table shows some of the values of y 3x²
  - 2x 6 for values of x
• from -3 to 3.
• Complete the table by finding the value of y when
  x -2.

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(b) On the graph paper opposite, draw the graph
of y 3x² - 2x 6 for values of x between -3
and 3.
(c) Draw the line y 5 on your graph paper and
write down the x-values of the points where your
two graphs intersect.
x -1.7 or x 2.2
(d) Write down the equations in x whose solutions
are the x-values you found in (c).
or 3x² - 2x 11 0
3x² - 2x 6 5
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y
30
20
10
y 5
-2
1
2
3
x
-1
-3
-4
4
-10
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17. Shade in the region of points inside the
triangle ABC which satisfy both of the following
conditions. (i) The points are nearer the point
A than the point B
And (ii) the points are further from B than the
distance BC.
C
A
B
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18. (a) Draw the image of the shape A after a
translation of 3 units in the x direction and -5
in the y direction. Label the image B.
5
4
3
2
A
1
1
-3
x
2
3
4
5
-1
-2
-4
-5
0
-1
-2
-3
B
-4
-5
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(b) Rotate the shape C through 90 clockwise
about the point (1, -2). Label the image D.
5
4
3
D
2
1
1
-3
x
2
3
4
5
-1
-2
-4
-5
0
-1
-2
-3
C
-4
-5
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19. The letters of the word MAESTEG are written
on several cards, one letter per card and placed
in a box. Similarly, the ten letters of
CAERNARFON are written on ten cards and placed in
another box. A person selects one card at random
from each of the two boxes. What is the
probability that the person has the letter E on
both cards?
P (E in MAESTEG) x P (E in CAERNARFON)
2 x 1 7 10
2 70
1 35
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20. Solve the following simultaneous equations by
an algebraic (not graphical) method. Show all
your working. 5 x 2 y 10 2 x 3 y
- 7
Multiply equation 1 x 2 and equation 2 x 5
Substitute y -5 in equation 1
5 x 2 y 10
10x 4y 20
5 x 2 x -5 10
10x 15y - 35
5 x - 10 10
15y 4y - 35 - 20
5x 10 10
11y - 55
5x 20
y - 55 11
x 20 5
y - 5
x 4
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21. (a) Write each of the following numbers in
standard form. (a) 0.0000086
8.6 x 10-6
(ii) 62400 000
6.24 x 107
(b) Find, in standard form, the value of (i) (5
x 10-8) x (3.2 x 10-4)
(ii) (2 x 10-5) (5x107)
2 x 10 (-5 - 7) 5
5 x 3.2 x 10 (-8 -4)
16.0 x 10 -12
0.4 x 10 -12
1.6 x 10 -11
4 x 10 -13
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22. A group of 200 pupils sat an examination. The
table gives a grouped frequency distribution of
their marks in the examination.
(a) Complete the following cumulative frequency
table.
4
18
64
116
162
192
198
200
(b) On the graph paper opposite, draw a
cumulative frequency diagram to show this
information.
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200
(c) Use your cumulative frequency diagram to find
the median.
160
36 Mark
120
(d) The minimum mark for the top grade A was 58.
Use your cumulative frequency diagram to estimate
how many pupils achieved grade A.
Median
Cumulative frequency
80
40
2009 - 192
8 pupils
58
60
20
40
80
Marks
30
23. Each of the following quantities has a
particular number of dimensions. Give the number
of dimensions of each quantity. The first one has
been done for you.
1
3
1
2
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24. (a) Show giving reasons, why the triangles
ABC and PQR below are NOT similar. You must give
all your reasoning.
Q
Diagram not drawn to scale.
B
12cm
18cm
6cm
9cm
C
A
8cm
P
R
10cm
If similar AB AC BC
QR PR PQ
6 8 12 9 10 18
AC is not in the same ratio. PR
2 4 2 3 5 3
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(b) Every cube is similar to every other cube.
Name another 3 dimensional object that has this
property.
Sphere
Regular Tetrahedron
Regular Octahedron
Regular Dodecahedron
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25. Solve the following equation. 2x 6 -
4x 1 1 3 2
2
6 (2x 6) - 6(4x 1) 6 x 1 3
2 2
2(2x 6) - 3(4x 1) 3
4x 12 12x 3 3
-8x 15 3
-8x 3 - 15
-8x -12
x -12 -8
x 1 ½ or 1.5