1. KOLEKSI SOALAN MATEMATIK SPM
SPM 2003
The data in Diagram 8 shows the donations in RM, of 40 families to their children’s school
welfare fund.
40 24 17 30 22 26 35 19
23 28 33 33 39 34 39 28
27 35 45 21 38 22 27 35
30 34 31 37 40 32 14 28
20 32 29 26 32 22 38 44
Diagram 8
a) Using the data in Diagram 8, and a class interval of RM 5, complete the following table.
Donation (RM) Frequency Cumulative Frequency
11 – 15
16 – 20
[4 marks]
b) By using a scale of 2 cm to RM5 on the x-axis and 2 cm to 5 families on the y-axis, draw
an ogive based on the data. [4 marks]
c) From your ogive in (b)
i. find the third quartile,
ii. hence, explain briefly the meaning of the third quartile.
[4 marks]

2. SPM JULAI 2004
The data in Diagram 2 shows the number of durian trees planted by 44 farmers.
52 33 48 22 34 42 57 51 51 65 41
66 54 66 53 53 34 46 52 65 75 52
25 68 48 63 62 43 52 56 59 49 58
43 58 36 72 68 54 62 40 73 38 63
Diagram 2
a) (i) Based on the data in Diagram 2 and by using a class interval of 10, complete Table 2
provided in the answer space.
(ii) Hence, state the modal class.
[6 marks]
Answer :
Class Interval Upper Boundary Frequency Cumulative Frequency
11 – 20 20.5 0 0
21 – 30
Table 3
b) For this part of the question, use the graph paper on page 41 .
By using a scale of 2 cm to 10 trees on the x-axis and 2 cm to 5 farmers on the y-axis, draw
an ogive for the data.
[4 marks]
c) Based on the ogive in (b), Ahmad concludes that 50% of the farmers planted less than 52
durian trees.
Determine whether the conclusion is correct or not and give a reason.
[2 marks]

3. SPM 2004
The data in Diagram 7 shows the masses, in kg, of suitcase for a group of tourists. Each tourist
has one suitcase.
27 10 22 28 21 14 29 25
29 18 22 13 20 21 24 27
27 25 16 19 16 24 26 27
29 19 33 25 23 24 26 31
a) Based on the data diagram and by using a class interval of 3, complete Table 3 provided
in the answer space. [4marks]
b) Based on the table in (a), calculate the estimated mean mass of the suitcase.
[3marks]
c) By using a scale of 2 cm to 3 kg on the x-axis and 2 cm to 1 suitcase on the y-axis, draw
the histogram for the data. [3marks]
d) State one information obtained based on the histogram in (c). [2marks]
a)
Class interval Frequency Midpoint
10 – 12
13 – 15
Table 3

4. SPM JULAI 2005
Diagram 4 is a frequency polygon which represents the heights, in cm, for a group of 80 pupils.
30
25
Number of Pupils
20
15
10
5
0
115 120 125 130 135 140 145 150
Height (in cm)
Diagram 4
a) Based on the information from the frequency polygon, complete Table 4 in the answer
space.
b) Hence, calculate the mean height, in cm, of the pupils. Give your answer correct
to 2 decimal places.
[6 marks]
Answer:
Upper Cumulative
Height (in cm) Midpoint Frequency
Boundary Frequency
118 – 122 122.5 120 2 2
123 – 127
128 – 132
133 – 137
138 – 142
143 – 147
Table 4

5. c) For this part of the question, use the graph paper. You may use a flexible curve rule.
By using a scale of 2 cm to a height of 5 cm on the horizontal axis and 2 cm to 10 pupils
on the vertical axis, draw an ogive for the data.
[5 marks]
d) Give one information that can be obtained from the ogive in (c).
[1 mark]

6. SPM 2005
The data in the diagram shows the marks for English language monthly test for 42 pupils.
51 20 45 31 26 40 30
25 32 37 41 21 36 38
46 38 28 37 39 23 39
33 35 42 29 38 31 23
42 34 26 35 43 28 22
25 47 31 48 44 34 54
a) Using data in diagram and a class interval of 5 marks, complete Table 2 in the answer space.
Marks Midpoint Frequency
20 – 24 22
25 – 29
Table 2
[4 marks]
b) Based on your table in (a),
i. state the modal class,
ii. calculate the mean for the English Language monthly test and give your answer
correct to decimal places.
[4 marks]
c) By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 pupil on the vertical
axis, draw a histogram for the data.
[4 marks]

7. SPM JULAI 2006
Table 6 shows the distribution of age for a group of 40 tourists who visited a museum in a
particular day.
Age (Year) 20–24 25–29 30–34 35–39 40–44 45–49 50–54
Frequency 2 6 9 10 7 4 2
Table 6a
a) Based on the distribution of age in Table 6a, complete Table 6b in the answer space.
[2marks]
Answer:
Age (Year) Midpoint Upper Boundary Cumulative Frequency
20 – 24 22
25 – 29 27
30 – 34 32
35 – 39 37
40 – 44 42
45 – 49 47
50 - 54 52
Table 6b
b) Calculate the estimated mean age of the tourists.
[3marks]
c) For this part of the question, use the graph paper.
By using the scale of 2 cm to 5 years on the horizontal axis and 2 cm to 5 tourists on the
vertical axis, draw an ogive for the data in Table 6b.
[5marks]
d) From your ogive constructed in (c),
(i) find the first quartile,
(ii) state one piece of information about the first quartile
[2marks]

8. SPM 2006
The data in Diagram 7 show the donation, in RM collected by 40 pupils.
49 26 38 39 41 45 45 43
22 30 33 39 45 43 39 31
27 24 32 40 43 40 38 35
34 34 25 34 46 23 35 37
40 37 48 25 47 30 29 28
Diagram 7
a) Based on the data in diagram and by using a class interval of 5, complete Table 2 in the
answer space.
[3 marks]
b) Based on Table 2 in (a), calculate the estimated mean of the donation collected by a pupil.
[3 marks]
c) By using a scale 2 cm to RM 5 on the horizontal axis and 2 cm to 1 pupil on the vertical axis,
draw a frequency polygon for the data.
[5 marks]
d) Based on the frequency polygon in c), state one piece of information about donations.
[1 mark]
a)
Class interval Midpoint Frequency
21 – 25
26 – 30

9. SPM JULAI 2007
Diagram 8 shows the mass, in kg, of newspapers collected over the period of 40 days.
79 70 75 79 83 74 66 58
65 85 84 76 56 80 64 57
78 67 52 59 72 58 57 75
69 76 55 75 60 73 83 63
74 65 78 58 73 64 75 59
Diagram 8
a) Based on the data in Diagram 8, complete Table 8 in the answer space.
b) Hence, calculate the estimated mean of the mass of the newspapers collected.
c) For the part of the question, use a graph paper and by using the scale of 2 cm to 5 kg
on the horizontal axis to 1 day on the vertical axis, draw a histogram for the data.
d) Based on your histogram in 8(c), give one information about the modal class of
the data.
Answer :
(a)
Mass (kg) Frequency Midpoint
52 – 56
57 – 61
Table 8

10. SPM 2007
Table 2 shows the frequency distribution of the mass, in kg, of a group of 80 students.
Mass ( kg) Frequency
30 - 34 5
35 - 39 8
40 - 44 11
45 - 49 21
50 - 54 22
55 - 59 10
60 - 64 3
Table 2
a) i) State a modal class.
ii) Calculate the estimated mean of the mass of the group of students.
[4 marks]
b) Based on Table 2, complete Table 3 in the answer space to show the cumulative frequency
distribution of the masses.
Upper Boundary Cumulative Frequency
29.5 0
34.5
Table 3
[2 marks]
c) For this part of the question, use the graph paper provided.
By using the scale of 2 cm to 5 kg on the horizontal axis and 2 cm to 10 students on the
vertical axis, draw an ogive for the data.
[4 marks]

11. d) 25% of all the students in the group have a mass of less than p kg. These students will be
supplied with nutritional food.
Using the ogive you had drawn in (c), find the value of p.
[2 marks]

12. SPM JULAI 2007
Data in Diagram 9 shows the number of books read by 40 students in a reading programme in a
particular class.
18 14 11 16 13 17 12 23
12 19 17 15 11 21 7 14
15 11 5 18 9 22 24 19
17 9 14 12 6 15 10 13
19 15 20 10 14 8 12 16
Diagram 9
a) Based on the data in Diagram 9 and by using a class interval of 3, complete Table 9 in the
answer space.
[3 marks]
b) Based on Table 9, calculate the estimated mean of the books read by a student.
[3 marks]
c) For this part of the question, use the graph paper provided on page 31.
By using the scale of 2 cm to 3 books on the horizontal axis and 2 cm to one student on the
vertical axis, draw the frequency polygon for this data.
[4 marks]
d) Based on the frequency polygon 14(c), give one information about this reading programme.
[1 mark]

13. Answer:
(a)
Class interval Frequency Midpoint
5–7
8 – 10
Table 9

14. SPM 2008
The data below shows the payment, in RM, by 40 drivers at a toll booth.
38 34 41 25 19 32 28 42
32 25 32 27 42 23 18 46
21 42 36 30 33 37 43 25
24 18 26 35 47 22 38 33
30 23 37 48 39 34 41 27
a) Based on the data, complete Table 14 in the answer space.
[3 marks]
Class interval Midpoint Frequency
15-19 17
Table 14
b) Based on Table 14 in (a), calculate the estimated mean of the toll paid by a driver.
[3 marks]
c) For this part of the question, use the graph paper provided.
By using the scale of 2cm to RM5 on the horizontal axis and 2 cm to 1 driver on the vertical
axis, draw a frequency polygon for the data.
[5 marks]
d) Based on the frequency polygon in 14 (c), state the number of drivers who paid more than
RM34 for the toll.
[1 mark]