TPF SESI 202223.docx A-F

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SM015
Mathematics 1
Semester 1
Session 2022/2023












JOHOR MATRICULATION ENGINEERING COLLEGE
___________________________________________________________________________
ASSIGNMENT 1
MATHEMATICS 1
INDIVIDUALASSIGNMENT
___________________________________________________________________________
INSTRUCTIONS TO STUDENTS
1. Answer all questions.
2. Your assignment should be answered by yourself. You should not copy other’s assignment.
3. Please take note that penalty will be imposed on late submission of this assignment.

EVALUATION
QUESTIONS MARKS MODERATION REMARKS
1

2


3

4


TOTAL
(15%)
NUMERACY LECTURER:
SKILLS (5%)
TOTAL
(20%)





Prepared by, Checked by,




_______________________


KHAIRUNAJIHA BINTI KASNAN ABIRAMY A/P SUBRAMANIAM



_______________________

SITI NOR WAZNA BINTI ABDUL HADI

SM015
Mathematics 1
Semester 1
Session 2022/2023

NUMERACY SKILLS EVALUATION
CRITERIA OF MARKS BASED ON
NUMERACY RUBRIC REMARKS
SKILLS
1

2


3

4


TOTAL LECTURER:

SM015
Mathematics 1
Semester 1
Session 2022/2023

TOPIC 3 : SEQUENCES AND SERIES (2 QUESTIONS)


1. A trading company made a profit of RM 50 000 in 2005 (Year 1). [Numeracy Skills]

A model for future trading predicts that profits will increase year by year as stated in
TABLE below :


Year Profit




2005 RM50 000



2006 RM50 000r



2007 RM50 000r 2






(a) Write down an expression for the predicted profit in Year n. [1 mark]



(b) The model predicts that in Year n, the profit made will exceed RM200 000.


log 4
Show that n   1. [3 marks]
log r


(c) Hence, using the model with r  1.09 ,


i. find the year in which the profit made will first exceed RM200 000.

[3 marks]
ii. find the total of the profits that will be made by the company from Year 1 to

Year 10, giving your answer to the nearest RM10 000.

[3 marks]

SM015
Mathematics 1
Semester 1
Session 2022/2023

1
1 1  3x   2 1
2. (a) If   1  , find the expansion of up to the term x . State
2
4 3x 2  4  4 3x


the value of x for which the expansion is valid. [4 marks]
(b) Hence, estimate the value of 7 correct to 3 decimal places. [3 marks]

(c) If x   2, find 10 using the expansion in 2(a). Comment your answer. [3 marks]



TOPIC 4 : MATRICES & SYSTEM OF LINEAR EQUATIONS (2 QUESTIONS)



x  2  1 x 2 x

 
3. (a) Show that the determinant of the matrix A =  1 3 1  is 2x  10x  6.
2
  2x 0  2  
Find the value of x if |A| = 22 and x > 0. Hence find the adjoint and inverse of

matrix A. [10 marks]




(b) Given a singular matrix E = Find the values of c.


[4 marks]


4. The following table shows the number of different types of cakes bought by a customer at
shop P, Q and R together with the total expenditure.

Banana Chocolate Vanilla Total Expenditure (RM)

P 5 8 5 36
Q 4 6 6 30

R 5 9 7 40



Let the price of each banana, chocolate and vanilla cakes bought from each shop be x, y

and z respectively. By using Cramer’s Rule in matrices, determine the values of x, y and z.
[11 Marks]




END OF QUESTION PAPER
TOTAL : 45 MARKS

SM015
Mathematics 1
Semester 1
Session 2022/2023

SUGGESTED ANSWER SCHEME INDIVIDUAL ASSIGNMENT

No Solution Marks
1(a) T  50000 T  50000r 0
1
1
T  50000r T  50000r 1
2
2
Therefore,

T  50000r n 1 , n  3 , 2 , 1 ,... B1 (State Tn)
n
1(b) T  50000r n 1  200000
n
K1
50000r n 1  200000
r n 1  4 (correct inequality)

log r n 1  log 4

n  1 log r  log 4 K1
log 4 (apply log)
n  1
log r

log 4 J1
n   1 - shown -
log r (correct simplification)




(c) Substitute r  1.09

i. log 4 K1
n   1
log1.09 (substitute r)

n  17.08
 n  18 K1

Therefore, the first year the profit will exceed RM200 000 is in
2005 + 17 (because inclusive) which is in 2022. J1

(c) a  50000 ,

 
ii. 50000 1.09   1  K1
10
S  1.09 1 (substitute in correct
10

 759646.49 formula)
 RM 760 000 (nearest 10000) K1J1

TOTAL 10 MARKS

SM015
Mathematics 1
Semester 1
Session 2022/2023

2(a)  1
1  1  1   3   x 2
4  3x 2  4 

    1    1    K1

1   1  3   2  2 1   3  2  (correct formula)
 1       x    x  ...
2   2  4  ! 2  4  
  

1  3  3  9 2  
  1 x     x   ...  K1J1
2  8  8  16  

1 3 27 4 4 B1
  x  x 2  ... valid for   x 
2 16 256 3 3 (validity)



2(b) Substitute x = -1, into LHS and RHS: B1

1  1  3   1  27   1 2  ...

  1
4 3  2 16 256 K1
1  0.41797 (substitute)
7
 7  2.393 (correct to 3 d.p) J1

2(c) 1  1  1  3   2  27   2  2 ... K1
  2
4  3  10 2 16 256
1  35
10 64
10  . 1 8286 J1

The answer is incorrect because x is out of the validity range. B1
TOTAL 10 MARKS

3(a) 1 1 x  1 2 x
2

A   x  3  0
2x  2 2x  2 K1 (method)
( 2 2 ) 3( 2x  
2
x

= x   x   2 2 4x  2 ) K1 (simplify)
2
=2x  10x  6 (shown ) J1 (answer)
2
22 = 2x  10x  6 K1 (equate to 22)
2
2x  10x  28 0

2

x  5x  14 0
(x  7)(x  2) 0 J1

0
x
x  7 or - 2 , x    7 (choose the correct x)

SM015
Mathematics 1
Semester 1
Session 2022/2023



 50 7  5
A   1 3 1 


 14 0  2


K1 (3 correct)
  6 16  42
A
cof ( )   14  30 98  K1 (all correct)


 55 143 
 22   K1 (transpose)
  6 14 22 
A
Adj ( )   16  30  55 


 42 98 143 
  
 3 7 
  11 11 1  K1 (method)
  6 14 22   

1

A  1  16  30  55   8  15  5 
22    11 11 2  J1


  42 98 143   21 49 13 
  


 11 11 2 
TOTAL 10 MARKS
3(b)
E =

nd
By using 2 Row Expansion:


K1 (equate to 0)
K1 (method to solve)






J1 J1




TOTAL 4 MARKS

4 [Cramer’s Rule Method]

B1
A = (identify matrix A)

SM015
Mathematics 1
Semester 1
Session 2022/2023




K1





J1
Det (changing 1 column):
st





K1

= - 42

Det (changing 2nd column):




K1


= - 28

Det (changing 3rd column):

K1





= - 14
J1
Therefore, (all three correct)


K1



J1J1J1
TOTAL 11 MARKS

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INSTRUMEN





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BORANG MODERASI


LAPORAN MODERASI

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D1.3:













INSTRUMEN




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BORANG MTP

PB/MTP
CONTINUOUS ASSESSMENT FEEDBACK
MINISTRY OF EDUCATION MALAYSIA MATRICULATION PROGRAMME

Task
Details
Assignment (Individual) Assignment (Group)


Attribute’s strength Able to understand and analyse the Able to solve basic numerical problem
problem in the questions


Attribute that can be improved None None




Others Keep up the hard work Good job




Examiner Name & Signature
ABIRAMY A/P SUBRAMANIAM
Date 15/11/2022 15/11/2022

Student’s confirmation
I declare that I understand the feedback given by the lecturer.


Note (follow-up session if necessary) - -





Student’s Name & Signature B1T1(B)
MUHAMMAD AIMAN BIN MOHD ASRI



Date 15/11/2022 15/11/2022

PB/MTP
CONTINUOUS ASSESSMENT FEEDBACK
MINISTRY OF EDUCATION MALAYSIA MATRICULATION PROGRAMME

Task
Details
Assignment (Individual) Assignment (Group)


Attribute’s strength Able to understand and analyse the Able to solve basic numerical problem
problem in the questions


Attribute that can be improved None None




Others Keep up the hard work Good job




Examiner Name & Signature
ABIRAMY A/P SUBRAMANIAM
Date 15/11/2022 15/11/2022

Student’s confirmation
I declare that I understand the feedback given by the lecturer.


Note (follow-up session if necessary) - -





Student’s Name & Signature B1T1(B)
NUR AINA HAURA BINTI ROMANUS



Date 15/11/2022 15/11/2022

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