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# modul 4 add maths 07

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### modul 4 add maths 07

1. 1. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 1 BIMBINGAN EMaS TAHUN 2007 ADDITIONAL MATHEMATICS FORM 4 MODULE 4 STATISTICS CIRCULAR MEASURE PANEL EN. KAMARUL ZAMAN BIN LONG – SMK SULTAN SULAIMAN, K. TRG. EN. MOHD. ZULKIFLI BIN IBRAHIM – SMK KOMPLEKS MENGABANG TELIPOT, K. TRG EN. OBAIDILLAH BIN ABDULLAH – SM TEKNIK TERENGGANU, K. TRG PUAN NORUL HUDA BT. SULAIMAN – SM SAINS KUALA TERENGGANU, K. TRG. PUAN CHE ZAINON BT. CHE AWANG – SBP INTEGRASI BATU RAKIT, K. TRG. JABATAN PELAJARAN TERENGGANU
2. 2. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 2 7 STATISTICS  PAPER 1 1 The mean of a list of numbers x – 1, x + 3, 2x + 4, 2x – 3, x + 1 and x – 2 is 7. Find (a) the value of x, (b) the variance of the numbers. Answer: (a) x = .……………………… (b) …………………………… 2 The mean of a list of numbers 3k , 5k + 4, 3k + 4 , 7k – 2 and 6k + 6 is 12. Find (a) the value of k, (b) the median of the numbers. Answer: (a) k = .……………………… (b) …………………………… 3 Given a list of numbers 8, 9, 7, 10 and 6. Find the standard deviation of the numbers. Answer: ………………………….
3. 3. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 3 4 The set of positive numbers 3, 4, 7, 8,12, x, y has a mean 6 and median 7. Find the possible values of x and y. Answer: x = …………………………….. y = …………………………….. 5 The test marks of a group of students are 15, 43, 47, 53, 65, and 59. Determine (a) the range, (b) the interquartile range of the marks. Answer: (a) …………………………… (b) …………………………… 6 The mean of five numbers is q . The sum of the squares of the numbers is 120 and the standard deviation of the numbers is 4m. Express q in terms of m. Answer : ……………………………
4. 4. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 4 7 The sum of the 10 numbers is 170 and the sum of the squares of the numbers is 2930. Find the variance of the 10 numbers. Answer: ……………………………… 8 Score 0 1 2 3 4 Frequency 7 10 p 15 8 The table shows the scores obtained by a group of contestants in a quiz. If the median is 2, find the minimum value of p. Answer: ……………………………… 9 The numbers 3, 9, y , 15, 17 and 21 are arranged in ascending order. If the mean is equal to the median, determine the value of y. Answer : y = …………………………… 10 Number 41 – 45 46 – 50 51 – 55 56 – 60 61 – 65 Frequency 6 10 12 8 4 The table above shows the Additional Mathematics test marks of 40 candidates. Find the median of the distribution. Answer:............................................. Number of goals 1 2 3 4 5
5. 5. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 5 11 The table above shows the number of goals score in each match in a football tournament. Calculate the mean and the standard deviation of the data. Answer : mean = …………………………… standard deviation = ……………... 12 Given the set of positive numbers n, 5, 11. (a) Find the mean of the set of numbers in terms of n. (b) If the variance is 14, find the values of n. Answer: (a) …………………………… (b) n = ..……………………… 13 The mean and standard deviation for the numbers x1, x2, …, xn are 74 and 26 respectively. Find the (a) mean for the numbers 3x1 + 5 , 3x2 + 5, …, 3xn + 5, (b) variance for the numbers 4x1 + 2 , 4x2 + 2, …, 4xn + 2. Answer: (a) …………………………… (b) …………………………… Frequency 7 6 4 2 1
6. 6. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 6 14 The mean of the data 2, h, 3h, 11, 12 and 17 which has been arranged in an ascending order, is p. If each of the element of the data is reduced by 2, the new median is 8 9 p. Find the values of h and p. Answer: h = …………………………… p = …………………………… 15 The table above shows a set of numbers arranged in ascending order where p is a positive integer. (a) Express the median of the set of the of numbers in terms of p. (b) Find the possible values of p. Answer: (a) ………………………….. (b) p = …………………...….  PAPER 2 16 A set of examination marks x1, x2, x3, x4, x5, x6 has a mean of 7 and a standard deviation of 14. (a) Find (i) the sum of the marks, x. (ii) the sum of the squares of the marks, x2 . (b) Each mark is multiplied by 3 and then 4 is added to it. Find, for the new set of marks, (i) the mean, (ii) the variance. Number 2 p – 1 7 p + 4 10 12 Frequency 2 4 2 3 3 2
7. 7. MODUL BIMBINGAN EMaS 2007 ADDITIONAL MATHEMATICS FORM 4 2007 All Rights Reserved JABATAN PELAJARAN TERENGGANU 7 17 Length (mm) 16 – 19 20 – 23 24 – 27 28 – 31 32 – 35 36 – 39 Frequency 2 8 18 15 6 1 The table above shows the lengths of 50 leaves collected from a tree. (a) Calculate (i) the mean, (ii) the variance length of the leaves. (b) Without drawing an ogive, find the interquartile range length of the leaves. 18 Set R consists of 40 scores, y, for a certain game with the mean of 9 and standard deviation of 5. (a) Calculate y and y2 . (b) A number of scores totaling 200 with a mean of 10 and the sum of the squares of these scores of 2700, is taken out from set R. Calculate the mean and variance of the remaining scores in set R. 19 A set of data consists of 10 number. The sum of the numbers is 150 and the sum of the squares of the numbers is 2 472. (a) Find the mean and variance of the 10 numbers. (b) Another number is added to the set of data and the mean is increased by 1. Find (i) the value of this number, (ii) standard deviation of the set of 11 numbers. 20 The table shows the frequency distribution of the scores of the scores of a group of pupils in a game. Score Number of pupils 10 – 19 1 20 – 29 2 30 – 39 8 40 – 49 12 50 – 59 m 60 – 69 1 (a) It is given that the median score of the distribution is 42. Calculate the value of m. (b) Use the graph paper provided by the invigilator to answer this question. Using a scale of 2 cm to 10 scores on the horizontal axis and 2 cm to 2 pupils on the vertical axis, draw a histogram to represent the frequency distribution of the scores. Find the mode score. (c) What is the mode score if the score of each pupil is increased by 5?