TRIAL STPM MATHEMATICS M (KEDAH) –SMK KhirJohari Section A [45 marks]

Answer all questions in this section.

1 Below is the data relating to the number of minutes, to the nearest minutes, that a

random sample of 65 trains from town A were late arriving at stop 3. Minutes late 0 2 3 3 3 4 4 4 4 5 5 5 5 5 5 0 6 6 6 7 7 8 8 8 9 1 0 0 0 2 2 3 3 4 4 4 5 1 6 6 7 7 8 8 8 9 9 2 1 2 2 3 3 3 3 4 2 6 3 3 4 4 5 3 6 8 4 1 3 4 7 7 9 5 2 4 Key : 0 | 2 means 2 minutes (a) Find the median and the quartiles of these times . [3 marks]

(b) Draw a boxplot to represent the data. [3 marks]

(c) Based on the boxplot, comment on the skewness of the distribution. [1 mark] 2 The table below shows the price for three different stationeries: pen, ruler and

eraser, sold by a dealer.

Price (RM per box of half a dozen) Stationeries

2001 2002 2003

Pen 2.20 2.35 2.64 Ruler 1.33 1.46 1.65 Eraser 0.91 0.99 1.08

By using year 2002 as the base year, calculate :

(i) the simple aggregate price index for the year 2001 and 2003. [4 marks]

(ii) the Laspeyres price index for the year 2001, if the quantity of pen, ruler and eraser sold in 2002 are 21 000 unit, 27 000 unit and 48 000 unit respectively.

[3 marks] 3 A teacher wishes to find an equation that can relate age, x, (in months) with

height, y, (in cm) of a student. The teacher randomly chooses ten students and the following data are obtained.

∑ ∑∑ ∑∑ ==== 454232,008189,746289,3701,6701 22 xyyxyx

(i) If the equation of the regression line of y on x is bxay += , determine the

values of a and b, correct to two decimal places. [6 marks]

(ii) Estimate the height of a 14-year old student. [2 marks]

(iii) Give a reason as to why this regression line is not suitable in predicting the height of a 30 year-old person. [1 mark]

4 The probabilities of two events A and B are given by P(A) = 0.3 and P(B) = 0.5

respectively.

(a) Calculate )( BAP ∪ if

(i) A and B are mutually exclusive, [2 marks]

(ii) A and B are independent. [2 marks]

(b) For the case A dan B are independent, calculate )( 'BAP ∩ [2 marks]

5 Bag A contains 2 blue balls and 3 white balls, while bag B contains 1 blue ball

and 5 white balls. A ball is drawn from each bag. Let X be the random variable representing the total number of blue balls selected.

(a) Find the probability distribution for X. [2 marks]

(b) Sketch a probability distribution graph. [2 marks]

(c) Verify that ∑=

==n

i

xXP1

1)( [2 marks]

6 The following table shows the quarterly sales (in 610 tins) of a certain food

produced by a company from the year 1999 to the year 2002.

Year Quarter 1 Jan – March

Quarter 2 Apr – June

Quarter 3 July – Sept

Quarter 4 Oct – Dec

1999 15 21 60 24 2000 18 30 64 26 2001 19 32 65 28 2002 21 33 68 32

Draw a graph for the above data. On the same axes, plot the moving averages to

eliminate seasonal variation. Calculate the seasonal variations. [10 marks]

Section B [15 marks]

Answer ONLY one question in this section. 7 The table below shows the length of pebbles from the bed of a river.

Length, x (mm) Frequency

0 5<≤ x 10

5 10<≤ x 8

10 20<≤ x 12

20 50<≤ x 25

50 100<≤ x 30

(a) Given that the frequency density for the class 0 5<≤ x is 10. Write down the

frequency densities for the other classes. [5 marks] (b) Represent the data in a histogram. [4 marks] (c) Use your histogram to estimate the mode length of a pebble. [2 marks] (d) Calculate (i) the mean length of a pebble. [2 marks] (ii) the median length of a pebble. [2 marks]

8 Two variables x and y are believed to be related by the equation xaby = where

a and b are constants. The table below records ten pairs of observation.

x 4 2 9 19 25 40 52 64 75 86

y 20 18 28 39 44 55 63 82 99 102

(a) Obtain the equation of the relevant linear regression line and determine the values of a and b. (b) Calculate the coefficient of determination between the variables in (b) and comment on the result. (c) Deduce the non-linear correlation curve between x and y. [15 marks] Prepared by : Firdaus bin Abdul Kareem Ketua Panitia Matematik PraU.