CALCULATORS ARE NOT TO BE USED FOR THIS PAPER

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Mathematics Intermediate Tier Paper 1 Summer
2002 (2 hours)
CALCULATORS ARE NOT TO BE USED FOR THIS PAPER
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• Use the fact that 28 x 49 1372 to write down
  the answers to the following
• (a) 2.8 x 4.9

13.72
(b) 14 x 490
6860
(1/2 x 13720)
(c) 137.2 49
2.8
2. Find the value of (a) 5³ x 2³,
(b) 28.6 12.73
5 x 5 x 5 x 2 x 2 x 2
2 8 . 6 0 - 12 . 7 3 1 5 . 8 7
10 x 10 x 10
1000
3

• 3. Toby travels to work by train. He buys either
  a 5 return ticket or a 3 single ticket.
• Over the past few months he bought x return
  tickets.
• Write down, in terms of x, the total cost (in
  pounds) of these return tickets.

5x
(b) The number of single tickets he bought was 9
more than the number of return tickets he bought.
Write down, in terms of x, how many single
tickets Toby bought.
x 9
(c) Write down, in terms of x, the total cost (in
pounds) of these single tickets.
3 ( x 9)
(d) Write down, in terms of x, the total cost (in
pounds) of all the tickets Toby has bought. You
must simplify your answer as far as possible.
8x 27
5x 3(x 9)
5x 3x 27
4
4. Write does the following numbers correct to 2
significant figures. (a) 0.063732
0.064
(b) 7934
7900
5

• 5. In a game, a player throws two fair dice, one
  coloured red the other blue.
• The score for the throw is the smaller of the two
  numbers showing. For example
• if the red dice shows 5, and the blue shows 2,
  the score for the throw is 2
• if the red dice shows 3 and the blue dice shows
  3, the score for the throw is 3.
• Complete the following table to show all the
  possible scores.

Red dice
Blue dice
6
Red dice
Blue dice
11 36
(b) (i) What is the probability that a player
scores 1?
25 36
(ii) What is the probability that a player scores
more than 1?
A player wins a prize by getting a score of 2 or
less. (c) William plays the game once. What is
the probability that he wins a prize?
20 36
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(d) (i) 360 people each play the game
once. Approximately how many would expect to win
a prize?
5 x 360 9
5 x 40
200
(ii) It costs 1 to play the game once. The prize
for winning is 1.50. If the 360 people each play
the game once, approximately how much profit do
you expect the game to make?
Cost of playing 360 x 1 360
Winnings 200 x 1.50 300
Profit 360 - 300
60
8
6. ABCD is a kite. Calculate the size of the
angle marked x.
Diagram not drawn to scale.
ABC 110 (symmetry)
110 74 110 x 360
294 x 360
x 360 - 294
x 66
66
X
9
(No Transcript)
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8 x 2 16cm²
4 x 3 12cm²
12cm
7 cm
10 x 6 60cm²
54 cm
8 2 5 4 7 6 10 12
(b) Calculate the area of the shape ABCDEFGH
stating clearly the units of your answer.
16 12 60
88cm²
11
150
202
x
C
(b) Another town, C, is due East of B and on a
bearing of 150 (S30E) from A. Plot, as
accurately as you can, the position of this town.
12
10. A shopkeeper buys video recorders at 160
each. At what price must the shopkeeper sell the
video recorders in order to make a profit of 30?
Profit 30 x 160 100
Or 10 16
3 x 16
30 3 x 16 48
48
Selling Price 160 48
Selling Price 160 48
208
208
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Often is too vague, no never mentioned. No time
interval given
(ii) Write a better version of the question.
How many times a year do you go to the dentist?
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12. Given that h 12(a 17) , find the value of
h when a9 and m - 4. m
h 12 ( 9 17) - 4
h 12 x 8 - 4
h 12 x 2
h 24
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13. (a) Express 700 as a product of prime numbers
in index form.
700
700 2 x 2 x 5 x 5 x 7
700 2² x 5² x 7
(b) Use your result in part (a) to write down the
smallest multiple of 700 which is a perfect
square.
(2 x 5 x 7) x (2 x 5 x 7)
70 x 70
4900
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14. Solve the following equations. (a) 5 x
8 36 2 x
(b) 16 x 5 3 ( 4 x 7)
5x 2x 36 - 8
16x 5 12x 21
7x 28
16x 12x 21 5
x 28 7
4x 26
x 4
x 26 4
x 6 2 4
x 6 ½
17
15.
x
x 6

• The sides of a regular octagon are x cm long.
  Each side of a regular pentagon is 6cm longer
  than each side of the octagon. The perimeter of
  the octagon is 3cm longer than the perimeter of
  the pentagon.
• Write down an equation that x satisfies.

8x 5(x6) 3
(b) Solve the equation and hence find the length
of a side of the pentagon.
8x 5(x 6) 3
3x 33
x 33 3
8x 5x 30 3
8x 5x 33
x 11
Length of side of pentagon 11 6 17 cm
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• Jill and Alan invest some money and share any
  profit made in the ratio of 54.
• How much does Jill get when they make a profit of
  270?

5 4 9 parts
1 part 270 9
30
5 x 30
150
Jill gets 5 parts
(b) On another occasion, Alan received 136. How
much profit were they sharing?
Alan gets 4 parts 136
1 part 136 4
34
9 parts 34 x 9
306
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y
17. (a) Draw the image when the triangle ABC is
reflected in the line y-x.
5
A
4
3
B
2
1
1
-3
x
2
3
4
5
-1
-2
-4
-5
0
-1
-2
-3
C
y - x
-4
-5
20
y
(b) Draw the image when the triangle marked D is
rotated through 90 anticlockwise about the point
(1, -1).
5
4
3
D
2
1
1
-3
x
2
3
4
5
-1
-2
-4
-5
0
-1
-2
-3
-4
-5
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18. A sample of boys and girls at a school
yielded the following results for their eye
colour.
There are 930 boys and 720 girls at the school.
Use the results of the sample and these totals to
find an estimate for the total number of pupils
in the school with brown eyes.
40 x 930 30 x 720 100
80
4 x 93 30 x 9
372 270
642
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19. Solve the following simultaneous equations by
an algebraic (not graphical) method. Show all
your working. 3 x 4 y 22 2 x 3 y -
8
Multiply eqn 1 x 2 and eqn 2 x 3
Substitute y - 4 in equation 1
6x - 8y 44
3 x - 4 y 22
6x 9y - 24
3 x 4 x (-4) 22
- 8y - 9y 44 - - 24
3 x 16 22
-17y 68
3x 22 - 16
3x 6
y 68 -17
x 2
y - 4
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20. Factorise (a) 3xy² - 6xy,
3xy(y 2)
(b) x² 2x 8.
(Multiply -8 Add 2 / 4, -2)
(x 4) ( x 2)
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21. The times taken by 160 pupils to travel to
school were measured and the results are
summarised in the following table.

• Complete the following cumulative frequency table.

12
68
112
132
148
156
160
(b) On the graph paper, draw a cumulative
frequency diagram to show this information.
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(c) Use your cumulative frequency diagram to find
the interquartile range.
Upper Quartile
33 16 17 minutes
(d) Use your cumulative frequency diagram to
complete the following statement. 60 of the
pupils took less than minutes to travel to
school.
60
Lower Quartile
27 minutes
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A
22.
Diagram not drawn to scale.
6cm
9cm
B
C
3cm
D
E
7.2cm
In the diagram, BC is parallel to DE, and the
triangles ABC and ADE are similar. Showing all
your working, find the length of AB9cm, AC6cm,
BD3cm and DE 7.2cm. (a) BC
BC 9 x 7.2 12
BC 9 7.2 12
BC 5.4cm
AE 12 x 6 9
AE 8cm
AE 12 6 9
(b) AE.
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23. In each of the following formulae, every
letter stands for the measurement of a length. By
considering the dimensions implied by each
formula, write down, for each case, whether the
formula could be for a length, an area, a volume
or none of these. The first one has been done for
you.
Volume
Length
Volume
Area
28
24. (a) Rearrange the inequality 35 3n gt 2n 7
into the form n lt some number.
35 7 gt 2n 3n
28 gt 5n
5n lt 28
n lt 5 3 5
n lt 28 5
(b) Given that n also satisfies the inequality
3ngt1 , write down all the integer values of n
that satisfy both inequalities.
and
n lt 5 3 5
n gt 1 3
n 1, 2, 3, 4, 5