(ANSWER) ASSESSMENT 2 MAT183 (DEC 2021)

FSKM/ MATEMATIK/UiTM Pahang



ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

UNIVERSITI TEKNOLOGI
MARA PAHANG

MAT183
ONLINE ASSESSMENT 2

2:45 pm – 4:15 pm (90 minutes) – Answer time
4:15 pm – 4:45 pm (30 minutes) – Submission time

Name : ________________________________________________
UiTM ID : ________________________________________________
Group : ________________________________________________
Lecturer : ________________________________________________

Instructions to candidates

• This question paper consists of Part A (Question 1) and Part B (Question 2, 3, 4 and 5)
• Answer ALL Questions.
• You are advised to take 90 minutes to complete a written exam and 30 minutes to

save in pdf format and upload your answers.
• Write your answer CLEARLY using a BLUE or BLACK pen. It is your responsibility

that the copy is legible.
• This assessment is an Open Book Test but not an Open Discussion Test. So you are

not allowed to share your answers with others.
• Any LATE submission will NOT BE EVALUATED.
• Upload all your answers in single file in pdf format in folder ‘ASSESSMENT 2

MAT183’ in google classroom.
• It is your responsibility to make sure that your file is openable. So please recheck after

the submission.

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

PART A : QUIZ 2 (15 marks)

Question 1
Differentiate the following functions with respect to and simplify your answer.

a) = (3 2 + 1)3 ( 2 ) (5 marks)

(2 + 1) (5 marks)
b) =

√ 2 − 2

c) = ( ( (3 )) (5 marks)

PART B : TEST 2 (30 marks) (8 marks)

Question 2


Use implicit differentiation to find for a function
√ − (2 ) = +2

Question 3 (8 marks)
Use differential to estimate √15.98 − (15.98)23 + 5 correct to 4 d. p.

Question 4
A cylindrical jar with radius 5 cm is being filled with water at a rate of 30 cm3 −1. How
fast is the water level in the jar rising ?

(6 marks)

© Universiti Teknologi MARA Pahang CONFIDENTIAL
1

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

5. A 5-m ladder leans against a house on flat ground. The house is to the left of the

ladder. The base of the ladder starts to slide away from the house at 2 m/s. At what

rate is the angle between the ladder and the ground changing when the the angle is

radians ?
6

(8 marks)

END OF QUESTION PAPER
ALL THE BESTT

© Universiti Teknologi MARA Pahang CONFIDENTIAL
2

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

PART A : QUIZ 2 (15 marks) (5 marks)
1. Differentiate the following:

a) = (3 2 + 1)3 ( 2 )

= (3 2 + 1)3 = ( 2 ) M1
′ = 2( 2 ) ∙ 2 ∙ 2
′ = 3(3 2 + 1)2(6 )
′ = 2 2 2( 2 )
M1

′ = 18 (3 2 + 1)2

M1

= ′ + ′


= 18 (3 2 + 1)2 ( 2 ) + 2(3 2 + 1)3 2 2( 2 ) M1 A1


= 2(3 2 + 1)2[9 ( 2 ) + (3 2 + 1) 2 2( 2 )] #

5

(2 + 1) (5 marks)
1. b) =

√ 2 − 2

= (2 + 1) 1

= √ 2 − 2 = ( 2 − 2)2

′ = (2 + 1) (2 + 1) ∙ 2 ′ 1 ( 2 2)−12 M1
2
= − ∙ 2

M1 ′ = 2 (2 + 1) (2 + 1) ′ = M1
√ 2 − 2

′ − ′ M1
= 2

2 √ 2 − 2 (2 + 1) (2 + 1) − (2 + 1)
= √ 2 − 2

2

(√ 2 − 2)

2 √ 2 − 2 (2 + 1) (2 + 1) − (2 + 1)
= √ 2 − 2
#
2 − 2

2 ( 2 − 2) (2 + 1) (2 + 1) − (2 + 1)
()
√ 2 − 2
= 2 − 2 A1

2 ( 2 − 2) (2 + 1) (2 + 1) − (2 + 1) 1 5
= ( ) ∙ ( 2 − 2)
√ 2 − 2

2 ( 2 − 2) (2 + 1) (2 + 1) − (2 + 1) 1
= #
3

( 2 − 2)2

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

1. c) = ( ( (3 )) (5 marks)

= ( ( (3 )) 5

M1 M1 M1 M1

= − 2( ( (3 )) ∙ ( (3 ) ∙ ( (3 ) ∙ 1 ∙ 3
3

1 ( (3 ) 2( ( (3 )) ( (3 ) # A1
= −

2

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

PART B : TEST 2 (30 marks) (8 marks)


2. Use implicit differentiation to find for a function
√ − (2 ) = +2

Solution :

= = (2 )

11 ′ = 1 ′ = − (2 ) ∙ 2 = +2
= √ = 2 = 2

1 1 = (2 ) ′ = +2 ∙ + 0)
2 (
′ = ∙ ′ = ′ + ′

′ 1 ′ = +2
2
= ′ = (2 ) − 2 (2 )

M1

M1 M1 M1 M1

√ − (2 ) = +2
− =

Differentiate : ′ − ′ = ′

1 − ( (2 ) − 2 (2 ) = +2 M1
2 )

1 − (2 ) + 2 (2 ) = +2
2

(2 ) 1 − (2 ) (2 ) + (2 )2 (2 ) = (2 ) +2
2

1 − 2 (2 ) + 4 2 (2 ) = 2 +2


1 − 2 (2 ) = 2 +2 − 4 2 (2 ) M1


81 − 2 (2 ) = (2 +2 − 4 2 (2 ))


1 − 2 (2 ) A1
= 2 +2 − 4 2 (2 ) #

3

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

3. Use differential to estimate √15.98 − (15.98)23 + 5 correct to 4 d. p (8 marks)

Solution :

= 15.98, 0 = 16, ∆ = −0.02 M1

( ) = √ − 3 + 5 M1

2

( 0) = (16) = √16 − (16)23 + 3 = 4 − 64 + 5 = −55 M1

( ) = √ − 3 + 5 = 1 − 3 + 5

2 2 2

′( ) = 1 −12 − 3 1 = 1 − 3√ M1
2 2 2√ 2
2

′( 0) = ′(16) = 1 − 3√16 = 1 − 3(4) M1
2√16 2 2(4) 2

1 47 M1
=8−6=− 8

√15.98 − (15.98)32 + 5 ≈ ( 0) + ∆ ∙ ′( 0) M1
47

≈ −55 + (−0.02) (− 8 )

≈ −54.8825 # (4 . ) A1 8

4

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

4. A cylindrical jar with radius 5 cm is being filled with water at a rate of 30 cm3 −1.
How fast is the water level in the jar rising ?
(6 marks)

Solution :
= 5

ℎ

= 30 3 −1, = 5


ℎ M1
=? M1
M1
V = 2ℎ
V = (5)2ℎ

V = 25 ℎ

Differentiate implicitly wrt t

= 25 ∙ ℎ M1


30 = 25 ∙ ℎ M1 6


ℎ = 30 = 0.382 cm −1 # A1
25

5

ONLINE ASSESSMENT 2/MAT183/DEC 2021 (ODL)

5. A 5-m ladder leans against a house on flat ground. The house is to the left of the

ladder. The base of the ladder starts to slide away from the house at 2 m/s. At what

rate is the angle between the ladder and the ground changing when the the angle is

radians ?
6

(8 marks)

Solution :

5 M1





M1
= 2 /


=? ℎ = 6

M1
= 5

= 5

Differentiate implicitly wrt t

= 5 (− ) ∙ M1 M1
M1
M1

= −5 ∙ A1


2 = −5 (6) ∙

1
2 = −5 (2) ∙


4 = −5

= 4 = −0.8 −1 # 8
−5

END OF ANSWER SCHEME
HAPPY MARKING

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