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APPLICATION
OF NUMBER - LEVEL 3
Time
allowed 1 hour 30 minutes, including reading time.
There
are two parts to the examination:
Part
1: Short answer questions
Part 2: Extended answer questions
Part
1 Short answer questions
EXAMPLES
1. Jess
has to quickly work out an estimate of {specific equation
given} in her head. Show a method she could use.
Use it to give an estimate for the
value of the calculation. [2 marks]
2. The
population of Kenya has been increasing by 4.5% per year,
(a) After how many years could you
expect its population to have doubled? [2 marks]
(b) Give two factors which could
affect your forecast in part (a). [1 mark]
5. A
store has a cafeteria that bakes its own cakes. The recipe
for a fruitcake mixture is:
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INGREDIENTS
|
PARTS
BY WEIGHT
|
|
butter
|
3
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|
sugar
|
3
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|
flour
|
3
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dried
fruit
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4
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powdered
egg
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4
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milk
|
2.75
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salt
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Trace
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baking
powder
|
0.25
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(a)
Find the actual weight in grams of flour and baking powder
used for 3 kg of the cake mixture. [2 marks]
(b)
The baking time for a cake depends on its weight and this
is shown in a graph.

Estimate
the baking time for the 3 kg cake. [1 mark]
Part
2: Extended Answer Question
People
are becoming aware of possible connections between "Body
Mass Index" and fitness. A person's Body Mass Index (BMI)
gives a rough measure of how under- or over-weight the person
might be.
Eleven
people volunteered to take part in an experiment to measure
their relative fitness and then compare the results with
their BMI. The people were in two groups, group A and group
B.
In the
fitness test, each person relaxed for 10 minutes (to establish
their resting pulse rate PR) and then undertook a specified
number of step-ups over a four minute period. The person's
pulse rate was measured immediately after finishing the
step-ups (Po), and again after 6 minutes of rest (P6).
A person's
fitness can be estimated by how quickly their heart rate
recovers after a period of strenuous exercises measure of
fitness, H, can be calculated using the formula.
{Specific
equation given here}
The
results are given in Table 1.
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Table
1
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|
Person
|
PR
beats/min
|
P0
beats/min
|
P6
Beats/min
|
Height
(m)
|
Weight
(kg)
|
H
|
| Group
A |
G
|
86
|
144
|
88
|
1.62
|
46
|
0.97
|
|
H
|
90
|
134
|
97
|
1.57
|
64
|
0.84
|
|
J
|
76
|
129
|
77
|
1.74
|
78
|
0.98
|
|
K
|
82
|
146
|
83
|
1.79
|
73
|
0.98
|
|
L
|
75
|
135
|
79
|
1.76
|
82
|
0.93
|
| Group
B |
M
|
72
|
100
|
76
|
1.58
|
48
|
|
|
N
|
78
|
95
|
78
|
1.64
|
54
|
|
|
P
|
68
|
120
|
80
|
1.78
|
54
|
|
|
Q
|
72
|
116
|
72
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1.74
|
58
|
|
|
R
|
80
|
112
|
80
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1.80
|
72
|
|
|
S
|
68
|
120
|
78
|
1.54
|
64
|
|
|
Table
2
Body Mass Index
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|
ht/m
|
1.50
|
1.52
|
1.54
|
1.56
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1.58
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1.60
|
1.62
|
1.64
|
1.66
|
1.68
|
1.70
|
1.72
|
1.74
|
1.76
|
1.78
|
1.80
|
|
wt(kg)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
40
|
18
|
17
|
17
|
16
|
16
|
16
|
15
|
15
|
15
|
14
|
14
|
14
|
13
|
13
|
13
|
12
|
|
42
|
19
|
18
|
18
|
17
|
17
|
16
|
16
|
16
|
15
|
15
|
15
|
14
|
14
|
14
|
13
|
13
|
|
44
|
20
|
19
|
19
|
18
|
18
|
17
|
17
|
16
|
16
|
16
|
15
|
15
|
15
|
14
|
14
|
14
|
|
46
|
20
|
20
|
19
|
19
|
18
|
18
|
18
|
17
|
17
|
16
|
16
|
16
|
15
|
15
|
15
|
14
|
|
48
|
21
|
21
|
20
|
20
|
19
|
19
|
18
|
18
|
17
|
17
|
17
|
16
|
16
|
15
|
15
|
15
|
|
50
|
22
|
22
|
21
|
21
|
20
|
20
|
19
|
19
|
18
|
18
|
17
|
17
|
17
|
16
|
16
|
15
|
|
52
|
23
|
23
|
22
|
21
|
21
|
20
|
20
|
19
|
19
|
18
|
18
|
18
|
17
|
17
|
16
|
16
|
|
54
|
24
|
23
|
23
|
22
|
22
|
21
|
21
|
20
|
20
|
19
|
19
|
18
|
18
|
17
|
17
|
17
|
|
56
|
25
|
24
|
24
|
23
|
22
|
22
|
21
|
21
|
20
|
20
|
19
|
19
|
18
|
18
|
18
|
17
|
|
58
|
26
|
25
|
24
|
24
|
23
|
23
|
22
|
22
|
21
|
21
|
20
|
20
|
19
|
19
|
18
|
18
|
|
60
|
27
|
26
|
25
|
25
|
24
|
23
|
23
|
22
|
22
|
21
|
21
|
20
|
20
|
19
|
19
|
19
|
|
62
|
28
|
27
|
26
|
25
|
25
|
24
|
24
|
23
|
22
|
22
|
21
|
21
|
20
|
20
|
20
|
19
|
|
64
|
28
|
28
|
27
|
26
|
26
|
25
|
24
|
24
|
23
|
23
|
22
|
22
|
21
|
21
|
20
|
20
|
|
66
|
29
|
29
|
28
|
27
|
26
|
26
|
25
|
25
|
24
|
23
|
23
|
22
|
22
|
21
|
21
|
20
|
|
68
|
30
|
29
|
29
|
28
|
27
|
27
|
26
|
25
|
25
|
24
|
24
|
23
|
22
|
22
|
21
|
21
|
|
70
|
31
|
30
|
30
|
29
|
28
|
27
|
27
|
26
|
25
|
25
|
24
|
24
|
23
|
23
|
22
|
22
|
|
72
|
32
|
31
|
30
|
30
|
29
|
28
|
27
|
27
|
26
|
26
|
25
|
24
|
24
|
23
|
23
|
22
|
|
74
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
26
|
26
|
25
|
24
|
24
|
23
|
23
|
|
76
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
26
|
26
|
25
|
25
|
24
|
23
|
|
78
|
35
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
26
|
26
|
25
|
25
|
24
|
|
80
|
36
|
35
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
26
|
26
|
25
|
25
|
|
82
|
36
|
35
|
35
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
26
|
26
|
25
|
|
84
|
37
|
36
|
35
|
35
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
27
|
26
|
|
86
|
38
|
37
|
36
|
35
|
34
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
27
|
|
88
|
39
|
38
|
37
|
36
|
35
|
34
|
34
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
|
27
|
|
90
|
40
|
39
|
38
|
37
|
36
|
35
|
34
|
33
|
33
|
32
|
31
|
30
|
30
|
29
|
28
|
28
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a) Use
the information in Table 1 to calculate the values for H
for the member in group B (the values of H for group A have
already been calculated).
Make
it clear how you calculated at least one
of the values of H. (4 marks)
b) Find
the range of H values for each group.
Choose,
then find an appropriate average (mean, median or mode)
for each of the two sets of values of H and
give a reason for your choice.
Show
clearly one of your calculations of average. (5 marks)
c) Use
your results from part a) and part b) to compare the levels
of fitness of the two groups.
Give at least two reasons to support your conclusions.
(2 marks)
d) Using
Table 2, find the Body Mass Index for each of the eleven
volunteers.
Present
the values for H and BMI in a suitable table. (4 marks)
e) Present
a suitable, clearly labelled graph showing H plotted against
BMI for the eleven volunteers (plot BMI across
the page and H upwards). (7 marks)
f) Describe
any ways in which BMI and H appear to be related. Comment
on the possibility of estimating an
individual's H value from their
Body Mass Index. (3 marks)
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