Microsoft Word - Revision 3
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MATHEMATICS FORM 5 – REVISION 3
Answer all the questions. 1.
The data shows the marks of a Mathematics test for 32 students. 99 49 72 81
71 74 66 71
30 46 46 72
82 68 39 98
37 87 48 34
41 51 41 36
46 52 75 94
44 53 86 91
(a) Using the data above and a class interval of 5 marks, complete the table in the answer space. [4 marks] (b) Based on the table in (a), (i) state the modal class, (ii) calculate the mean mark for the test and give your answer correct to two decimal places. [4 marks] (c)
By using a scale of 2 cm to 10 marks on the x-axis and 2 cm to 1 student on the yaxis, draw a histogram for the data. [4 marks]
Answer: (a)
Marks 30 − 39 40 − 49
Midpoint 34.5
Frequency
(b) (i) (ii)
(c) Please refer to the provided graph paper.
1
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
2.
40 85 54 79 38
33 77 70 39 68
85 54 74 76 37
66 54 62 74 86
86 69 63 50 34
58 50 60 98 31
33 50 66 48 90
86 86 77 56 98
The data above shows the marks of 40 students in a Mathematics test. (a) Construct a frequency table with intervals class of 10 marks, that is 30 − 39, 40 − 49, and so on. [3 marks] (b) Based on the table in (a), (i) determine the midpoint and frequency of each of the class interval in the table, (ii) state the modal class, (iii) calculate the mean mark for the test and give your answer correct to two decimal places. [4 marks] (c) By using a scale of 2 cm to 10 marks on the x-axis and 2 cm to 1 students on the y-axis, draw a frequency polygon for the data. [5 marks] Answer: (a)
Marks 30 − 39 40 − 49
Midpoint
Frequency
(b) (i) (ii) (iii)
(c) Please refer to the provided graph paper.
2
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
3.
The table shows the frequency distribution of the mass, in kg, of a group of 80 students. Mass (kg) 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64
Frequency 5 13 16 23 14 7 2
(a) (i) State the modal class. (ii) Calculate the estimated mean of the mass of the group of students. [4 marks] (b) Based on the table above, complete the table in the answer space to show the cumulative frequency distribution of the masses. [3 marks] (c) By using the scale of 1 cm to 5 kg on the horizontal axis and 1 cm to 10 students on the vertical axis, draw an ogive for the data. [4 marks] (d) 80% of all the students in the group have a mass of less than m kg. These students will be supplied with nutritional food. Using the ogive you had drawn in (c), find the value of m. [1 mark]
Answer: (a) (i) (ii)
3
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
(b) Upper Boundary (kg) Cumulative Frequency 29.5 0 34.5
(c) Please refer to the provided graph paper. (d)
4
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
Answers: 1 (a) Marks Midpoint Frequency 34.5 5 30 − 39 44.5 8 40 − 49 54.5 3 50 − 59 64.5 2 60 − 69 74.5 6 70 − 79 84.5 4 80 − 89 94.5 4 90 − 99 (b) (i) 40 − 49 (ii) (34.5 × 5) + (44.5 × 8) + (54.5 × 3) + (64.5 × 2) + (74.5 × 6) + (84.5 × 4) + Mean = (94.5 × 4) 32 = 62 (c)
5
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
Answers: 2 (a) Marks Midpoint Frequency 34.5 7 30 − 39 44.5 2 40 − 49 54.5 8 50 − 59 64.5 7 60 − 69 74.5 7 70 − 79 84.5 6 80 − 89 94.5 3 90 − 99 (b) (i) refer (a) (ii) 50 − 59 (iii) 63.25 (c)
6
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
Answers: 3(a) (i) Modal class is (45 - 49) kg. (ii)
(b)
(32 × 5) + (37 × 13) + (42 × 16) + (47 × 23) + (52 × 14) + (57 × 7) Mean = + (62 × 2) 80 3645 = 80 = 45.56 kg
Upper Boundary (kg) Cumulative Frequency 29.5 0 34.5 0+5=5 39.5 5 + 13 = 18 44.5 18 + 16 = 34 49.5 34 + 23 = 57 54.5 57 + 14 = 71 59.5 71 + 7 = 78 64.4 78 + 2 = 80
(c)
(d)
80 × 80 = 64 100 Therefore, p = 51.5 kg.
7
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
8
DES : CHAPTER 6 FORM 4
Answer all the questions. 1.
The data shows the marks of a Mathematics test for 32 students. 99 49 72 81
71 74 66 71
30 46 46 72
82 68 39 98
37 87 48 34
41 51 41 36
46 52 75 94
44 53 86 91
(a) Using the data above and a class interval of 5 marks, complete the table in the answer space. [4 marks] (b) Based on the table in (a), (i) state the modal class, (ii) calculate the mean mark for the test and give your answer correct to two decimal places. [4 marks] (c)
By using a scale of 2 cm to 10 marks on the x-axis and 2 cm to 1 student on the yaxis, draw a histogram for the data. [4 marks]
Answer: (a)
Marks 30 − 39 40 − 49
Midpoint 34.5
Frequency
(b) (i) (ii)
(c) Please refer to the provided graph paper.
1
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
2.
40 85 54 79 38
33 77 70 39 68
85 54 74 76 37
66 54 62 74 86
86 69 63 50 34
58 50 60 98 31
33 50 66 48 90
86 86 77 56 98
The data above shows the marks of 40 students in a Mathematics test. (a) Construct a frequency table with intervals class of 10 marks, that is 30 − 39, 40 − 49, and so on. [3 marks] (b) Based on the table in (a), (i) determine the midpoint and frequency of each of the class interval in the table, (ii) state the modal class, (iii) calculate the mean mark for the test and give your answer correct to two decimal places. [4 marks] (c) By using a scale of 2 cm to 10 marks on the x-axis and 2 cm to 1 students on the y-axis, draw a frequency polygon for the data. [5 marks] Answer: (a)
Marks 30 − 39 40 − 49
Midpoint
Frequency
(b) (i) (ii) (iii)
(c) Please refer to the provided graph paper.
2
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
3.
The table shows the frequency distribution of the mass, in kg, of a group of 80 students. Mass (kg) 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64
Frequency 5 13 16 23 14 7 2
(a) (i) State the modal class. (ii) Calculate the estimated mean of the mass of the group of students. [4 marks] (b) Based on the table above, complete the table in the answer space to show the cumulative frequency distribution of the masses. [3 marks] (c) By using the scale of 1 cm to 5 kg on the horizontal axis and 1 cm to 10 students on the vertical axis, draw an ogive for the data. [4 marks] (d) 80% of all the students in the group have a mass of less than m kg. These students will be supplied with nutritional food. Using the ogive you had drawn in (c), find the value of m. [1 mark]
Answer: (a) (i) (ii)
3
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
(b) Upper Boundary (kg) Cumulative Frequency 29.5 0 34.5
(c) Please refer to the provided graph paper. (d)
4
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
Answers: 1 (a) Marks Midpoint Frequency 34.5 5 30 − 39 44.5 8 40 − 49 54.5 3 50 − 59 64.5 2 60 − 69 74.5 6 70 − 79 84.5 4 80 − 89 94.5 4 90 − 99 (b) (i) 40 − 49 (ii) (34.5 × 5) + (44.5 × 8) + (54.5 × 3) + (64.5 × 2) + (74.5 × 6) + (84.5 × 4) + Mean = (94.5 × 4) 32 = 62 (c)
5
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
Answers: 2 (a) Marks Midpoint Frequency 34.5 7 30 − 39 44.5 2 40 − 49 54.5 8 50 − 59 64.5 7 60 − 69 74.5 7 70 − 79 84.5 6 80 − 89 94.5 3 90 − 99 (b) (i) refer (a) (ii) 50 − 59 (iii) 63.25 (c)
6
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
Answers: 3(a) (i) Modal class is (45 - 49) kg. (ii)
(b)
(32 × 5) + (37 × 13) + (42 × 16) + (47 × 23) + (52 × 14) + (57 × 7) Mean = + (62 × 2) 80 3645 = 80 = 45.56 kg
Upper Boundary (kg) Cumulative Frequency 29.5 0 34.5 0+5=5 39.5 5 + 13 = 18 44.5 18 + 16 = 34 49.5 34 + 23 = 57 54.5 57 + 14 = 71 59.5 71 + 7 = 78 64.4 78 + 2 = 80
(c)
(d)
80 × 80 = 64 100 Therefore, p = 51.5 kg.
7
DES : CHAPTER 6 FORM 4
MATHEMATICS FORM 5 – REVISION 3
8
DES : CHAPTER 6 FORM 4
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