SMJK Perempuan China Pulau Pinang Mid-Year Examination 2013 MATHEMATICS M Term 2 Upper Six Form
Time: 1 hour 30 minutes _________________________ _____________________________________ ________________________ _________________________ _________________________ _____________ _ Instructions: Answer all questions in Section A and any one question in Section B. Write the question numbers clearly and arrange them in the correct order. All necessary working must be shown clearly. A list of mathematical formulae, statistical tables and graph papers are provided. Section A [45 marks] Answer all questions in this section. 1
Two judges rank the eight paintings in a competition as follows: Paintings 1st judge 2nd judge
A 2 4
B 5 3
C 3 2
D 6 6
E 1 1
F 4 8
G 7 5
H 8 7
Calculate Spearman’s coefficient of rank correlation for the data and comment on the answer. 2
[4]
The marks of the students in a certain class in a History examination are as follows. 28 33 55 38 42 39 27 48 51 37 57 49 33 The marks of the students in a Physics examination are summarised as follows. Lower quartile: 28, Median: 39, Upper quartile: 67. The lowest mark was 17 and the highest mark was 74. a) Draw box-and-whisker plots in a single diagram on graph paper to illustrate the marks for History and Physics. b) State one difference, which can be seen from the diagram, between the marks for History and Physics.
3
[5] [1]
A hotel has 90 rooms. The table summarises information about the number of rooms occupied each day for a period of 200 days. Number of rooms occupied Frequency
1 – 20
21 – 40
41 – 50
51 – 60
61 – 70
71 – 90
10
32
62
50
28
18
a) Draw a cumulative frequency graph to illustrate this data. b) Estimate the number of days when over 30 rooms were occupied. c) On 75% of the days at most n rooms were occupied. Estimate the value of n.
[4] [2]
1
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[2] 4
The table below shows the prices of meat and the quantities of meat bought by a family for the months of January and October 2009.
Meat Chicken Beef Mutton Fish Rabbit
January Price Quantity (RM per kg) (kg) 6.00 20 10.00 10 8.00 10 12.00 15 5.00 5
October Price Quantity (RM per kg) (kg) 7.00 10 12.00 8 9 a 14.00 10 6.00 4
a) If the simple aggregate price index increase by 30% from January to October, determine the value of a. b) Calculate the Laspeyres price index, and comment on the family’s change in expenditure on meat. c) Calculate the Paasche quantity index, and comment on the family’s change in expenditure on meat. 5
[3] [3]
The table below shows the numbers of successful loans approved by a bank from years 2009 to 2012. Year 2009 2010 2011 2012
6
[2]
Q1 88 92 95 98
Number of successful loans Q2 Q3 128 108 125 110 123 106 118 104
Q4 75 82 88 92
a) Plot a time series, and discuss the overall trend, b) Calculate the seasonal indices using a multiplicative model.
[3] [5]
a) From the 300 Form Six students in a school, 100 of them read newspaper A and 80 read newspaper B. 40 of the students read both newspaper. i) Calculate the probability that a randomly chosen Form Six student of the school reads either newspaper A or B. ii) Find the probability that a randomly chosen Form Six student of the school from the group of students who reads newspaper B also reads newspaper A.
[3]
b) In a certain African village, 80% of the villagers are known to have a particular eye disorder. Twelve people are waiting waiting to see the nurse. i) What is the most likely number to have the eye disorder? ii) Find the probability that fewer than half have the eye disorder.
[2]
[3] [3]
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Section B [15 marks] Answer any one question in this section. 7
In a small town there are two chicken rice shops that operate next to each other. The number of customers patronizing one shop may affect the business of the other shop. The table below shows the records of the number of customers, in hundreds, who patronize two chicken rice shops over a ten-day period. It is believed that the number of customers that patronizes shop A, x (hundreds) and that of shop B, y (hundreds), fit the curve of the form , where a and b are constants.
No. Day of customers (x 100 people)
Shop A, x Shop B, y
1
2
3
4
5
6
7
8
9
10
2.4 4.2
3.4 5.2
3.1 4.8
2.5 4.1
2.1 3.2
2.9 4.7
3.6 4.8
2.5 3.6
2.3 3.0
2.4 4.2
a) Transform the equation to the appropriate linear form and determine the values of a and b. b) Calculate the coefficient of determination between the variables in (a) and comment on the result. c) Deduce a non-linear correlation curve between x and y. d) What is the estimated number of customers that patronizes shop B when 420 customers patronize shop A? Comment on the result.
[8] [3] [1] [3]
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8
a) A student finds that the average number of amoebas in 10 ml of pond water from a particular pond is four. Assuming that the number of amoebas follows a Poisson distribution, find the probability that i) there are exactly five amoebas in a 10 ml sample, ii) there are fewer than three amoebas in a 20 ml sample.
[2] [3]
b) the continuous random variable X has has probability density function f(x) where
, 2 0 2 2 40 ,, 01 i) ii) iii) iv)
[2] [3] [3] [2]
Find the value of the constant k . Sketch y = f(x) Find Find P(X>1)
1 11.
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