Mathematics

1
Mathematics Intermediate Tier Paper 2 Summer
2002 (2 hours)
2

• (a) Calculate 26 of 34.

26 x 34 100
8.84
3
(b) The total cost of 8 loaves and 12 baguettes
is 15.48 . One loaves cost 93p. Find the cost of
one baguette.
Cost of 8 loaves 8 x 93 7.44
Cost of baguettes 15.48 7.44
8.04
Cost of 1 baguette 8.04 12
0.67
67c
4
x 7 5
5

3. (a) Simplify 7a 5 3a 4.
7a 3a 5 4
4a - 9
6
(b) Find the value of 4x 3y when x - 6 and y
5.
4x -6 3 x 5
-24 15
-9
7
4. Draw, on the grid, an enlargement of the given
shape, using a scale factor of 4.
8
5. (a) A solid cuboid measures 6.4 cm by 4.8,cm
by 3.5cm, as shown in the diagram. Calculate its
volume, clearly stating the units of your answer.
3.5cm
4.8cm
6.4cm
Volume length x width x height
6.4 x 4.8 x 3.5
107.52cm³
9
Front and back 2 x 6.4 x 3.5
44.8cm²
Top and bottom 2 x 6.4 x 4.8
61.44cm²
Sides 2 x 4.8 x 3.5
33.6cm²
Total 44.8 61.44 33.6 139.84cm²
10
6. Eighty pupils were asked what they drank with
their breakfast. Of these pupils, 36 drank tea,
18 drank coffee, 16 drank milk and 10 drank other
drinks.

• What is the probability that a randomly chosen
  pupil

(i) drank coffee at breakfast?
18 80
(ii) did not drink tea at breakfast?
44 80
1 - 36 80
11
(b) Draw a pie chart to illustrate the different
drink that the pupils had with their
breakfast.You should show how you calculate the
angles of your pie chart.
1 drink 360 80 4.5
Tea 36 x 4.5 162
Coffee 18 x 4.5 81
Milk 16 x 4.5 72
Others 10 x 4.5 45
12
7. Mr and Mrs Gann received their electricity
bill.The details were as follows.
Present meter reading 54261 Previous meter
reading 52815
Charge per unit 6.52 pence per unit
VAT 5
Service charge 10.56
Showing all your working, find the total cost of
the electricity including VAT.
Units used 54261 - 52815
1446
Cost of units 1446 x 6.52
9427.92c
94.28
Cost including service charge 94.28 10.56
104.84
VAT 5 x 104.84 100
5.24
Total 104.84 5.24
110.08
13
8. ABCD and ADEF are two parallelograms in which
ADC130 and DEF60 . Find BAF
BAD 50
DAF 60
50
60
BAF 50 60 110
14
9. The weight of eighty eggs were measured and
the results are sumarised in the following table.
(a) On the graph paper, draw a grouped frequency
diagram for the data.
15
30
25
20
15
Frequency
10
5
70
80
100
90
60
50
Weight (grams)
(b) Write down the modal class.
70 - 80
16
10. Write down, in terms of n, the nth term of
each of the following sequences.
n
(n 2)

• 1 x 3 2 x 4 3 x 5 4 x 6
  .. x ..

7n - 4
(b) 3 10 17 24

7 7 7
17
11. A gardner is making a circular lawn of radius
6m

• Calculate the area of the lawn.

3.142 x 6 x 6
A pr²
113.097
113.1 m²
(b) The gardener wishes to put an edging around
the circumference of the lawn. Calculate the
length of edging needed.
C p d or C 2 p r
C 2 x 3.142 x 6
C 37.699
C 37.7 m
18
12. Beverley leaves home at 11.00 a.m. to go for
a drive in her car. She travels a certain
distance then stops for three quarters of an hour
before starting back for home at a speed of 40
m.p.h.
(a) Calculate the speed for the first part of her
journey.
68 2
34 m.p.h.
19
70
60
50
Distance (miles) from home
40
30
20
10
Time
1100
1400
1300
1500
1200
(b) On the graph paper, draw lines to
represent (ii) Her ¾ hour stop and
(ii) her return journey home.
20
13. (a) The population of a country increased
from 56 000 000 to 59 500 000. What percentage
increase is this?
Increase
59 500 000 56 000 000
3 500 000
Percentage increase 3 500 000 x 100
56 000 000
6.25
21
(b) What will be the amount if 5000 is invested
for 3 years at the rate of 4 compound interest
per annum?
200
Interest 1st year 4 x 5000 100
Amount in the bank 5000 200 5200
208
Interest 2nd year 4 x 5200 100
Amount in the bank 5000 208 5408
Interest 3rd year 4 x 5408 100
216.32
Amount in the bank 5408 216.32 5624.32
22
14. Solve the following equation.
15-4x 3 7
15 4x 3 x 7
15 4x 21
15 21 4x
-6 4x
- 6 x 4
- 3 x 2
-1 ½ x
x -1 ½
23
15. A solution to the equation x³ 5x 30
0 lies between 2 and 3.
Use the method of trial and improvement to find
this solution correct to one decimal place.
-1.875
Try x 2.5 2.5³ 5 x 2.5 30
Too small
Too big
Try x 2.6 2.6³ 5 x 2.6 30
0.576
-0.6686
Too small
Try x 2.55 2.55³ 5 x 2.55 30
Felly x 2.6 (1 ll.d.)
24
16. (a) The batting scores of 100 cricketers were
recorded and the results are summarised in the
following table.
On the graph paper, draw a frequency polygon for
the data.
25
(b) Find an estimate for the mean of the batting
scores.
35
3510 100
Sfx Sf
20x9.545x29.524x49.59x69.52x89.5
20452492
26
17. The diameter of a circle, AB is of length
8.7cm, BC has length 5.4cm and ACB 90 .
Calculate the length of AC.
Diagram not drawn to scale.
AB² AC² CB²
Neu / or AC² AB² - BC²
8.7² AC² 5.4²
AC² 8.7² - 5.4²
8.7² - 5.4² AC²
46.53 AC²
AC v 46.53
AC 6.82cm
27
18. ABCD is a rectangle.
B
C
D
A

• Draw the locus of all the points inside the
  rectangle whose distance from AB is the same as
  their distance from AD.

(b) Draw the locus of all the points inside the
rectangle which are 6cm from DC.
(c) Draw the locus of all the points inside the
rectangle whose distance from A is the same as
the length of AB.
28
19. Find, in standard form, the value of (a)
(7.4 x 10 -5) x (3.9 x 10 -4)
2.889 x 10 -8
(b) 59639 0.087
6.86 x 10 5 (3 sig.fig)
29
20 (a) Simplify the expression
(4x3y2) x (2x4y5)
8x7y7
(b) Expand and simplify (x 5) (x 6)
First Outside Inside Last
x² -6x 5x - 30
x² -x - 30
(c) Make d the subject of the following formula
h v t - d
h² t - d
d t - h²
30
21. Solve the following equation 4x 8
x 2 3 6
6 (4x 8) 6 x 6 x 2 multiply every term
by 6 3 6
2(4x 8) x 12 expand brackets
8x 16 x 12
8x - x 12 16 collect terms
7x 28
x 28 7
x 4
31
22. A vertical flagpole, BDC, stands on
horizontal ground ABE. It is supported by two
ropes AC and DE. The length of AC is 13.5m, and
the distance CD is 4.7m. The rope AC makes an
angle of 62 with the ground and the rope DE is
fixed to the ground at E such that BE is 8.4m.
Diagram not drawn to scale.
Sin 62 BC 13.5
BD 11.9 4.7 7.2m
13.5 Sin 62 BC
Tan BDE 8.4 7.2
BC 11.9m
Tan BDE 1.16667
BDE Tan-1 1.16667
Calculate the size of BDE.
BDE 49.4
32
23. Two bags contain some coloured balls, which
are identical except for their colour. One ball
is taken at random from each bag and their
colours noted. The probability of the selected
ball from the first bag being red is ¼ . The
probability of the selected ball from the second
bag NOT being red is ?.
(a) Complete the following tree diagram.
(b) Calculate the probability that both balls are
red.
?
P(red, red)
¼
1 x 1 4 3
1 12
?
¾
(c) Calculate the probability that only one ball
is red.
?
P (red, not red) P(not red, red)
1 x 2 3 x 1 4 3 4
3
2 3 12 12
5 12