Mathematics M - QP2

Name : ………………………………………………… Class :

I.C Number : ……………………………........…………
………..…….…..

KOLEJ TINGKATAN ENAM SHAH ALAM
JALAN TIMUN 24/1

SHAH ALAM SELANGOR DARUL EHSAN
TERM TWO ASSESSMENT 2021

MATHEMATICS (M) 950/2

PAPER 2

DURATION ONE HOUR AND THIRTY MINUTES

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO.
Answer all questions in Section A.
Answer one question only in Section B.
All working should be shown.
Scientific calculators may be used. Programmable and graphic display calculators are
prohibited.

1

Section A [45 marks]

1 The weights, in kg, of 10 watermelons are recorded as follows :

4.8, 4.0, 5.2, 4.3, 2.8, 2.0, 2.8, 3.3, 4.8, 5.0

(a) Calculate the mean and standard deviation. [4]

(b) Find the median. [2]

(c) It is found that the weighing machine over-registers by x kg. State which of the

three measures that are changed and remains unchanged. [2]

2 In a game, all contestants are given two challenges. For each contestant, the

probability of passing the first challenge is 2 and the probability of passing the second
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challenge is 13 . It is known that of those who passes the first challenge, 5 of them also
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pass the second challenge. A contestant is chosen at random.

(a) Find the probability that the contestant passes both challenges. [2]

(b) Given that the contestant passes the second challenge, find the probability that the

contestant passes the first challenge. [2]

(c) Given that the contestant fails the second challenge, find the probability that the

contestant passes the first challenge. [3]

(d) Determine whether the events of “passing the first challenge” and “passing the

second challenge” are independent. [2]

3 A continuous random variable X has cumulative distribution function is given by

( ) = {0. ≤0 1 2, 0 < ≤1, 1 (2 − ), 1 < ≤2. 1. ≥2
3 3
[2]
(a) Show that m = 1. [2]
[3]
(b) Find ( ≥ 1 ).
2

(c) Find the median of X.

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4 A study was conducted on how the annual income, x, relates to the annual savings, y,
among young working professionals. A sample of x and y values in RM thousand are shown
in the table below.

x 55 67 65 48 39 44 50 59

y 15.5 22 25 18 10 13.5 19 22.5

(a) Construct a scatter diagram for the bivariate data. Comment on the relationship

between x and y. [3]

(b) Find the Pearson correlation coefficient. [4]

(c) Calculate the coefficient of determination and comment on your result. [3]

5 Three types of mobile phones are sold at a telecommunication centre. The selling

price, in RM, for the years 2017 and 2019 are shown in the table below.

Type of mobile phones Year 2017 Year 2019

Alpha 3000 2900

Beta 1500 800

Omega 800 300

Taking the year 2017 as the base year, calculate [2]
[2]
(a) the simple aggregate price index for the year 2019.
(b) the simple average price relatives index for the year 2019. [1]

Explain why there is a difference between the indices obtained in (a) and (b).

6 A time series graph is shown below.

(a) Identify the components of time series which are present and absent. [4]
(b) State, with a reason, the model that best describes the time series. [2]

3

Section B [15 marks]
You may answer all questions but, only the first answer will be marked.

7 The number of the new students registering for a business programme in a college for
three intakes and their moving averages from the year 2017 to the year 2020 are shown in the
table below.

Year Intake Number of new students Moving Average
(‘000)

2017 January 1.0 -
May 1.1 1.00

October 0.9 1.03

2018 January 1.1 1.07
May 1.2 1.07

October 0.9 1.03

2019 January 1.0 1.10
May 1.4 1.10

October 0.9 1.13

2020 January k 1.20
May 1.6 1.20

October 0.9 -

(a) Find the value of k, correct to one decimal place. [2]

(b) Using a multiplicative model, calculate the seasonal index for each intake, correct to

two decimal places. [5]

(c) Obtain a seasonally adjusted time series. [2]

(d) Using the least squares method and the following values,

∑ = 78, ∑ 2 = 650, ∑ = 13. 08, ∑ 2 = 14. 37, ∑ = 87. 27

Find the equation of the linear trend line for the seasonally adjusted time series, where

y is seasonally adjusted number of new students in intake t with t = 1 for the January

intake for the year 2017. [3]

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(e) Forecast the number of new students for January intake of the year 2021. [3]

8 A fruit seller received boxes containing 100 apples each from a supplier. The

probability that an apple is bruised is 0.10. All boxes are inspected and a box is rejected if it

contains more than 12 bruised apples. The fruit seller receives five boxes per week.

(a) Using a suitable approximate distribution, calculate the probability that a box chosen

at random is rejected. [7]

(b) Estimate the mean number of boxes rejected per week. [2]

The fruit seller also receives apples in 25 small boxes per week, each containing 20 apples
from another supplier. The probability that an apple is bruised is also 0.10. All boxes are
inspected and a box is rejected if it contains more than three bruised apples.

(c) Calculate the probability that a box chosen at random is rejected. [4]

(d) Estimate the mean number of boxes rejected per week. [2]

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