Mathematics M - MS2

Marking Scheme Term 2 Assessment 2021

No. Marks
M1 A1
1a. Mean = 39 = 3.9 kg M1 A1
10 M1 A1
B1
σ= 163.18 − 3. 92 = 1.05 kg B1
10
M1
b. Median = 1 (4. 0 + 4. 3) = 4. 15 kg A1
2
M1
c. Change : Mean, Median A1

Unchanged : Standard deviation M1 M1

2. A : winning the first challenge A1
M1
B : winning the second challenge A1
M1
Given P(A) = 2 , P(B) = 13 A1
3 24 M1 (correct
function)
a. P(B|A) = 5 A1
8 B1
M1
( ∩ ) = 5
( ) 8

( ∩ ) = 5 × 2 = 5
8 3 12

b. P(A|B) = ( ∩ )
( )

5

= 12
13

24

= 10
13

c. P(A|B’) = ( ∩ ')
( ')

= ( )− ( ∩ )
1− ( )

=2 − 5
3 12

11

24

= 6
11

d. P(A) = 2
3

P(A|B) = 10 ≠ P(A)
13

Not independent

3 a. F(2) = 1

1 [2(2) − ] = 1
3

= 1

b. P (X ≥ 1 ) = 1 − ( < 1 )
2 2

( )= 1 − 1 12
3 2

= 11
12

c. F(b) = 0.5

1 [2 − 1] = 0. 5
3

b = 1.25

median = 1.25

A1

4a. Scatter diagram on graph paper D1 D1
Linear relationship B1
Positive relationship B0
B1
b. B1
∑ = 427, ∑ = 145. 5, n = 8

∑ 2 = 23481, ∑ 2 = 2822. 75, ∑ = 8077 M1

= 8077− (427)(145.5) A1 (at least
8 2dp)

( )( )23481−4272 145.52 M1 A1
8 2822.75− 8 B1
M1 A1
= 0.8912

c. 2 = 0. 7942

79.42% of the variation in annual savings is explained by annual income.

5a. 2900+800+300 ×100 = 75. 47
3000+1500+800

( )b.1 2900 + 800 + 300 ×100 = 62. 50 M1 A1
3 3000 1500 800

c. This is because the selling price of Omega is smaller compared to others so B1

that it has a smaller impact on the total price. However, the changes in

price for Omega is larger than the others, giving a larger impact on the

ratios in simple average price relatives index.

6a. Present : Seasonal, trend B1 B1

Absent : Cyclic, irregular B1 B1

b. Additive model because amplitude of the fluctuation constant. B2

Section B

7a. 0.9+ +1.6 = 1. 20 M1
3

k = 1.1 A1

b.

Year Jan Intake October
- May 0.8738
2017 1.028 1.1000 0.8738
2018 0.9091 1.1215 0.7965
2019 0.9167 1.2727
2020 1.3333 -

Average 0.9513 1.2069 0.8480
Adj. Factor 0.9979 0.9979 0.9979
Adj. S. Index 0.95 1.20 0.85

M1 A1

M1
M1
A1

c.

Year Intake S. Index Seasonally adj. time series
2017 Jan 0.95 1.05
2018 May 1.20 0.92
2019 October 0.85 1.06
2020 Jan 0.95 1.16
May 1.20 1.00
October 0.85 1.06
Jan 0.95 1.05
May 1.20 1.17
October 0.85 1.06
Jan 0.95 1.16
May 1.20 1.33
October 0.85 1.06

M1 A1

d. = 87.27− (78)(13.08) = 0. 015734 M1
12
M1
650 − 782 A1
12

=( ) 13.08 − 78
12 0. 015734 12 = 0. 987729

= 0. 9877 + 0. 0157

e. = 13 M1
M1
= 0. 9877 + 0. 0157(13) = 1. 1918
A1
= 1. 1918×0. 95



= 1132 students

8a) X : number of bruised apple B1
~ (100, 0. 10)

μ = 100(0. 10) = 10 > 5

= 100(0. 90) = 90 > 5

σ2 = 100(0. 10)(0. 90) = 9

X~N (10, 9) M1 A1

P( a box rejected) = P(X > 12) B1

= P (X > 12.5) M1

= ( > 12.5−10 ) M1
3

= P ( Z > 0.8333)

= 0.20233 A1

b. Mean = 5 × 0.20233 = 1.01165 M1 A1

c. X ~ B(20, 0.10) B1

P(a box rejected) = P(X > 3)

=

1 − 20 (0. 10)0(0. 90)20 − 20 (0. 10)1(0. 90)19 − 20 (0. 10)2(0. 90)18 − 20 (0. 10)3(0. 90)17

0123

M1 M1

= 0.13295 A1

d. Mean = 25 × 0.13295 = 3.32375 M1 A1