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# Koleksi soalan matematik spm

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## Koleksi soalan matematik spmDocument Transcript

• KOLEKSI SOALAN MATEMATIK SPMSPM 2003The data in Diagram 8 shows the donations in RM, of 40 families to their children’s schoolwelfare 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]
• SPM JULAI 2004The 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 2a) (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 3b) 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]
• SPM 2004The data in Diagram 7 shows the masses, in kg, of suitcase for a group of tourists. Each touristhas 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
• SPM JULAI 2005Diagram 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
• 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]
• SPM 2005The 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 54a) 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]
• SPM JULAI 2006Table 6 shows the distribution of age for a group of 40 tourists who visited a museum in aparticular 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 6aa) 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 6bb) 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]
• SPM 2006The 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 7a) 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
• SPM JULAI 2007Diagram 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 8a) 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
• SPM 2007Table 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 2a) 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]
• 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]
• SPM JULAI 2007Data in Diagram 9 shows the number of books read by 40 students in a reading programme in aparticular 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 9a) 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]
• Answer: (a) Class interval Frequency Midpoint 5–7 8 – 10 Table 9
• SPM 2008The 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 27a) Based on the data, complete Table 14 in the answer space. [3 marks] Class interval Midpoint Frequency 15-19 17 Table 14b) 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]