COMPILATION FINAL EXAM TBM1063

TABLE OF CONTENTS i
ii
Table of Contents iii
List of Formula 1
Important Notes 19
Linear Function and Graph
Linear Programming 25
Simple Interest 32
Compound Interest 39
Annuity

i

LIST OF FORMULA

1. m = y2 − y1
x2 − x1

2. y = mx + c

3. S = P(1+ rt)

4. I = Pr t , S =P+I

5. S = P(1 + i)n

6. r = 1 + k m −1
 m

7. S = R  (1 + i)n − 1
 i 
 

8. A = R1 − (1 + i)−n 
 i 


ii

IMPORTANT NOTES

CHAPTER 4: LINEAR FUNCTION AND GRAPH

• Graphing a linear equation involves 3 steps:
1. We need to find the two points which satisfy the equation,
2. Plot these points in the graph
3. Joint the 2 points

• Linear Function Formula

• How to find the linear equation that passes through 2 points:
1. Find the slope,
2. Find the y-intercept by substitute m, x and y (choose only 1 point) into linear
equation.
3. Substitute the y-intercept, (c) and slope, (m) into slope intercept form of the line

iii

• How to check the intersection point by using calculator.
Note:
- Clear all the previous data – [Shift, CLR, ALL (3), mode, mode, mode, EQN (1),
UNKNOWNS (2)
- Enter the coefficient value
Example:

iv

CHAPTER 5: LINEAR PROGRAMMING

MAXIMIZING PROBLEMS
Constraints: Use the symbol:- ≤
The feasible region: The area of the graph showing all the possible points that satisfy
all inequalities.
The optimum point (Corner point/Vertex): 1, 2 and 3

MINIMIZING PROBLEMS
Constraints: Use the symbol:- ≥
The feasible region: The area of the graph showing all the possible points that satisfy
all inequalities.
The minimum point (Corner point / Vertex): 1, 2 and 3

v

LINEAR FUNCTION AND GRAPH

JULY 2022
QUESTION 1

Identify the slope and y-intercept of a straight line

[1 point]

QUESTION 2

Convert the linear equation into a general form and identify its constants (A, B
[2 points]
and C). .

QUESTION 3

Find the equation of the straight line that passes through (-3, 1) and has a slope of 10.
[2 points]

1

QUESTION 4

Find the equation of the straight line which is passing through point (2, -6) and (-1, 9).
[3 points]

QUESTION 5

Find the intersection point between line and .

[4 points]

QUESTION 6

Suppose that a manufacturer will produce 4,000 units of scientific calculator when the price
is RM40 and 3,000 units when the price is RM45. If the relationship between price, p and
quantity, q sold is linear, determine the demand function.

[5 points]

2

QUESTION 7

Given the supply and demand equations of a certain product where p is the price per unit
and q is the quantity.

Determine the equilibrium price and quantity of the product.

[4 points]

NOVEMBER 2021 .
QUESTION 1

Identify the slope and y-intercept of a straight line

[1 point]

QUESTION 2

Convert the linear equation into a general form and identify its constants (A, B
[2 points]
and C). .

3

QUESTION 3
Find the equation of a straight line that passing through the points (1, -2) and (3, 5).

[3 points]

QUESTION 4 and .
Find the intersection point between line [4 points]

4

QUESTION 5

Let p represent the price per unit and q is the quantity demanded. The demand and supply
equations for a certain product are estimated below:

Determine the equilibrium price and quantity of the product.

[4 points]

QUESTION 6

The demand per week for selling frozen ‘Karipap Pusing’ is 3,000 unit when the price is RM10
per pack and 1,000 unit when the price is RM15. By assuming the price p and the quantity q
have a linear relationship, determine the demand function.

[5 points]

5

JULY 2021 .
QUESTION 1 [1 point]
Write the values of a and b of a general linear equation

QUESTION 2

Convert the linear equation into a slope intercept form and identify its slope and y-
[2 points]
intercept. .

QUESTION 3

Find the equation of a straight line that having slope -1 and passes through a point (9, 2).
[2 points]

QUESTION 4
Find the equation of a straight line that passing the points (2, -1) and (-4, 3).

[3 points]

6

QUESTION 5 and . Find the intersection point of A and
[4 points]
Given two lines
B.

QUESTION 6

Let p represent the price per unit and q is the quantity demanded. The demand and supply
equations for a certain product are estimated below:

Determine the equilibrium price and quantity of the product.

[4 points]

7

QUESTION 7

A manufacturer will supply 1,200 units of air fryer per month when the unit price is RM180 and
1,800 units per month when the unit price is RM240. Assume that the price p and the quantity
q are linearly related. Determine the supply equation.

[5 points]

NOVEMBER 2020
QUESTION 1
Write the equation of the line that has a gradient of -7 and y-intercept is 3.

[1 point]

QUESTION 2

Convert the linear equation into slope intercept form and identify its slope and
[2 points]
y-intercept. .

8

QUESTION 3
Find the equation of a straight line that having a slope of 3 and passes through the point
(-2, 7).

[2 points].

QUESTION 4
Find the equation of a straight line that passes through the point (2, 3) and (1, -4).

[3 points]

QUESTION 5 and . Find the intersection point of and
[5 points].
Given two lines
.

9

QUESTION 6

If the demand per week for selling chocolate brownies is 50 units when the price is RM40 each
and 100 units at RM35 each. Determine the demand equation, assuming it is linear.

[5 points]

QUESTION 7

Given the supply and demand equations for a certain product where p is the price per unit
and q is the quantity.

Determine the equilibrium point of the product.

[4 points]

10

JULY 2020
QUESTION 1

Write the equation of the line that has a gradient of and y-intercept at (0, 15).

[1 point]

QUESTION 2

Convert the linear equation of into a slope-intercept form and identify its slope
[2 point]
and y-intercept. .

QUESTION 3

Find the equation of a straight line that having a slope of 7 and passes through the point
(-5, 10).

[2 points]

QUESTION 4
Find the equation of a straight line that passing through the point (3, 9) and (-6, -36).

[3 points]

11

QUESTION 5 and . Find the intersection point between
[5 points].
Given two lines
and .

QUESTION 6
A wholesaler sells 380 kg of durians when the price is RM18 per kg and 320 kg of durians
when the price is RM27 per kg. by assuming that the relationship between quantity and price
are linear, determine the demand function.

[5 points]

12

QUESTION 7

Given the supply and demand equations of a certain product where p is the price per unit and
q is the quantity.

Determine the equilibrium point of the product.

[4 points]

NOVEMBER 2019 .
QUESTION 1
Write the constants (a and b) of a straight line

[1 point]

QUESTION 2

Convert the linear equation into slope intercept form and identify its slope and
[2 points]
y-intercept. .

13

QUESTION 3

Find the equation of a straight line that having a slope of 10 and passes through the point
(2, 15).

[2 points]

QUESTION 4
Find the equation of a straight line that passing through (-1,2) and (5, 14).

[3 points]

QUESTION 5 and . Find the intersection point of and .
Given two lines [5 points]

14

QUESTION 6

If a gadget is priced at RM36, supplier will produce 86 gadgets, but if the price is RM20,
supplier will only manage to produce 46 gadgets. Determine the supply equation.

[5 points]

QUESTION 7

Let p represent the price per package and q represent the quantity demanded. The demand
and supply equations for certain products are estimated below:

Determine the equilibrium price and quantity of the product.

[4 points]

15

JULY 2019 .
QUESTION 1

Identify the slope and y-intercept of a straight line

[1 point]

QUESTION 2 into general form and identify its constants (a, b and c).
[2 points]
Convert linear equation of
.

QUESTION 3 and passes through the point (-6, 5).
Find the equation of a straight line that has slope [2 points]

QUESTION 4

Find the equation of a straight line which is passing through point (1, -4) and (-2, -7).
[3 points]

16

QUESTION 5 and line .
Find the intersection point between line [4 points]

QUESTION 6

Suppose the demand per week for a musical baby toy is 150 sets when the price is RM32 per
set and 200 sets when the price is RM30 per set. Find the demand equation for the musical
baby toy assuming that it is linear for p, price and q, quantity.

[5 points]

17

QUESTION 7

Given the supply and demand equations of a certain product where p is the price per unit and
q is the quantity.

Determine the equilibrium price and quantity of the product.

[5 points]

18

LINEAR PROGRAMMING

JULY 2022

QUESTION 8

In Rosalinda’s Garden shop, she makes two kinds of mixtures for planting: gardening mixture
and potting mixture. The profit to produce per packet of Garden Mixture and Potting Mixture
is RM3 and RM5 respectively. The ingredients of the two mixtures are shown in Table 1.

Mixture Availability

Gardening (x) Potting (y) 16 kg
11 kg
Soils 2 kg 1 kg 15 kg
Peat Moss 1 kg 2 kg
Fertilizer 1 kg 3 kg
Profit RM3 RM5

Table 1

By using the linear programming model,

a. write the objective function, Z. (1 point)
b. write the problem constraints and non - negative constraints. (4 points)
c. graph the feasible region. (5 points)
d. what is the maximum profit and how many packet of each type of mixture should be

produced? (5 points)

19

NOVEMBER 2021

QUESTION 8

NurlyaHana Collection has two branches located at Kelantan and Terengganu. Each branch
produces three different of scarf, there are Teratai, Habibah and Talia. Each brand must
produce at least 8750, 1600 and 500 pieces weekly of these three types of scarf respectively.
The number of scarfs per week as shown in the Table 1 below:

Scarf Kelantan (x) Terengganu (y) Weekly requirement
Teratai 50 25 8750
Habibah 4 8 1600
Talia 1 4 500
Operating Cost
RM580 RM750
Table 1

The operating cost per week of running the branches at Kelantan and Terengganu are
respectively RM580 and RM750. By using the linear programming model,

a. state the objective function, Z. (1 point)
b. determine the problem constraints and non - negative constraints. (4 points)
c. draw the graph and shade the feasible region. (5 points)
d. what is the minimum cost? (5 points)

20

JULY 2021
QUESTION 8
a. Sketch the inequality x≥-1

(2 points)

b. With the start of school approaching, Gadget World is planning on having a sale on
online learning materials. They have 800 ring lights, 450 speakers and 2400
headphone in stock. They plan on packing it in two different packages as shown in the
table below:

Materials Package A Package B Available
Ring Lights 1 2 800

Speakers 1 1 450

Headphones 6 4 2400

Price RM145 RM115

By using the linear programming model,

i. state the objective function, P (1 point)
ii. determine the problem constraints and non-negative constraints. (4 points)
iii. draw the graph and shade the feasible region. (5 points)
iv. how many packages should they put together of each type to obtain the

maximum profit? (3 points)

21

NOVEMBER 2020
QUESTION 8
a. Sketch the inequality x≤-3.

(2 points)

b. A dietician wishes to mix two kinds of food X and Y in such a way that the mixture
contains of at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C.
Table 1 below shows the vitamin content of one kg of food produced.

Food X Food Y Requirement
10
Vitamin A 12 12
8
Vitamin B 22

Vitamin C 31

Cost (per kg) 16 20

Table 1

Using the linear programming model,

i. write the objective function, C. (1 point)
ii. write the problem constraints and the non-negative constraints. (4 points)
iii. graph the feasible region. (5 points)
iv. what is the minimum cost and how much of each kind of food should be

produced? (5 points)

22

JULY 2020
QUESTION 8
a. Sketch the inequality of x≤-6.

(2 points)

b. Bonda Delight Bakery produces two types of chocolate cakes, standard and premium.
Each of the chocolate cake requires three stages of production: mixing, baking, and
decorating. Table 1 shows their processing time required by each product at each
stage and the profit gained from each product.

Standard Premium Time available
20 hours
Mixing 1 hour 2 hours 22 hours
12 hours
Baking 2 hours 1 hour

Packaging 1 hour 1 hour

Profit RM18 RM25

Table 1
By using the linear programming model,

i. write the objective function, Z. (1 point)
ii. write the problem constraints and the non-negative constraints. (4 points)
iii. graph the feasible region. (5 points)
iv. What is the maximum profit and how many each of chocolate cake need to

produce? (5 points)

23

JULY 2019
QUESTION 8
a. Sketch the inequalities y≥10.

(2 points)

b. A workshop has three types of machines R, S and T. These machines can manufacture
two products. The following table gives the information requires processing time on the
machines for each product.

Types of machine Product 1, x Product 2, y Available hours per week
120
R 32 45
80
S 11

T 12

Profit per unit RM40 RM30

Table 1
By using the linear programming model,

i. write the objective function, Z. (1 point)
ii. write the problem constraints and the non-negative constraints. (4 points)
iii. graph the feasible region. (5 points)
iv. what is the maximum profit and how many of each product should be

produced? (5 points)

24

SIMPLE INTEREST

JULY 2022
QUESTION 9
Kevin invested RM7,250 at a simple interest rate of 5% per annum for 6 years.
a. Find the amount of interest earned. (2 points)
b. Find the simple amount at the end of the investment period. (2 points)

QUESTION 10
Mr Lim invest RM10,200 in an investment fund for 7 years. At the end of the investment period,
the investment will be worth RM13,530. Find the simple rate that is offered.

(4 points)

25

NOVEMBER 2021
QUESTION 8
Mr. Thomas invested an amount of RM13,200 at the simple interest rate of 14% per annum.
a. Find the interest earned after 10 years. (2 points)
b. What is the amount of investment after 10 years? (1 point)

QUESTION 9
Isabella deposited RM7266 into a savings account at a local bank that earned a simple interest
rate of 5% per year. If the simple amount received was RM15,258.60, find period of savings,
t.

(3 points)

26

QUESTION 10
A business takes out a simple interest loan of RM300,000 at a rate of %. The total amount
the business will repay is RM770,590 for 8 years. Find the value of .

(3 points)

JULY 2021
QUESTION 9
Aisyah borrowed RM5,000 at a simple interest rate of 4% per annum. Find the amount paid at
the end of 9 years.

(3 points)

QUESTION 10
RM21,000 was invested in a bank that charged a simple interest rate of 11% per annum. If
the amount received was RM37,170, find period of investment, t.

(3 points)

27

NOVEMBER 2020
QUESTION 9
Siti invested RM5,000 at a simple interest rate of 3.5% per annum. She intends to withdraw
the money after 5 years.
a. Find the amount of interest earned. (1.5 points)
b Find the simple amount at the end of investment period. (1.5 points)

QUESTION 10
Amani deposited RM3,700 into a bank that offered 3% simple interest. After t years, the
accumulated amount is RM4,144. Find the value of t.

(4 points)

28

JULY 2020
QUESTION 9
On 5thMay 2020 Delisya borrowed RM7,500 from a bank which charged 3.5% simple interest.
Find the amount she needs to pay on 12th September 2020.

(4 points)

QUESTION 10
An investment of RM6,000 will be accumulated to RM8,400 in five years at r% simple interest.
Determine the simple interest rate offered.

(3 points)

29

NOVEMBER 2019
QUESTION 9
A RM9,500 loan was granted on 5 August 2017. It has to repaid on 10 January 2018. The
interest charged was 15% per annum at a simple interest rate. Find the amount that need to
be repaid on 10 January 2018.

(4 points)

QUESTION 10
How long should Ammar invest RM10,000 at a simple interest rate of 8% per annum if he
wants to earn an interest of RM1,200?

(3 points)

30

JULY 2019
QUESTION 9
How much should be invested to earn interest of RM250 at 5% simple interest rate per annum
for 20 months?

(3 points)

QUESTION 10
How long does it take for RM6,000 to accumulate to RM9,000 at a simple interest rate of 4%
per annum?

(4 points)

31

COMPOUND INTEREST

JULY 2022
QUESTION 11
A laptop is estimated to cost RM4,200 in three years’ time. Azlina wishes to buy this laptop in
three years’ time. How much must she save now in an account that pays 6% compounded
monthly?

(4 points)

QUESTION 12
Mahdi wishes to borrow some money to purchase a new motorbike. Bank Y charges him
4.15% compounded quarterly and Bank Z charges 3.25% compounded monthly. Which bank
offers a better deal?

(4 points)

32

NOVEMBER 2021

QUESTION 11

How much money should be deposited in a 6% saving account compounded quarterly to have
a total amount of RM85,060 after 5 years?

(3 points)

QUESTION 12

Lisa deposited RM4,400 in an account at a rate of 3.4% compounded semi-annually. How
much money will be in the account after 12 years?

(3 points)

QUESTION 13
Danial is going to buy a new car. He has received two different quotes:

Bank X: charges 7.8% compounded monthly.
Bank Y: charges 8% compounded semi-annually.

Which option should he choose?

(4 points)

33

JULY 2021
QUESTION 11
RMP is invested in an account earning 7.2% interest compounded monthly. If the amount at
the end of 6 years is RM13,290, find the value of P.

(3 points)

QUESTION 12
Khalish saved RM7,000 in an account for 8 years. The interest was charged at 8%
compounded quarterly. Calculate the accumulated amount at the end of 8 years.

(3 points)

34

NOVEMBER 2020
QUESTION 11
En Malek invested a sum of money in Bank S that offered interest 4% compounded quarterly.
After 6 years, the accumulated amount in the account is RM 13332.21. Find the amount of
money invested.

(3 points)

QUESTION 12
Tharmizi intends to borrow some money to expand his business. Bank A offers him 3.2%
compounded monthly and Bank B offers 4.25% compounded quarterly. Find the equivalent
effective rate of both banks to help Tharmizi decides which bank gives a better offer.

(4 points)

35

JULY 2020
QUESTION 11
Encik Zulkifli makes an investment at a bank which pays 4% interest compounded semi-
annually. After 4 years the money worth RM9,750. Find the money invested.

(4 points)

QUESTION 12
A loan of RM10,000 was made at 6% compounded monthly. Find the total payment after 36
months.

(3 points)

36

NOVEMBER 2019
QUESTION 11
Puan Ramlah wishes to invest some money into a bank. She has two options to choose:

Bank A: earn 4.5% compounded quarterly.
Bank B: earn 4.2% compounded monthly.

Which bank should she invest?

(4 points)

QUESTION 12
Chuah receives a loan of RM3,500 from a finance company which charges interest of 5.25%
compounded monthly. If Chuah settles the loan after 4 years, calculate the amount he must
repay.

(3 points)

37

JULY 2019
QUESTION 11
If Amjad invest RM3,600 at 6% compounded semi-annually for eight years, find the amount at
the end of eight years.

(3 points)

QUESTION 12
A trust fund for education is being set up so that at the end of 20 years there will be RM50,000.
If the fund earns interest of 7% compounded quarterly, how much money should be deposited
into the fund?

(4 points)

38

ANNUITY

JULY 2022
QUESTION 13
Serena wins an annuity that pays RM1,400 at the end of every 6 months for 7 years. If money
is worth 12% compounded semi-annually, what is the present value of this annuity?

(4 points)

QUESTION 14
RM315 is deposited every three months for 4 years 9 months at 13.5% compounded quarterly.
Find the future value of this annuity at the end of the investment period?

(4 points)

39

NOVEMBER 2021
QUESTION 14
RM 500 was invested every month in an account that pays 6.5% compounded monthly.
Calculate the amount in the account after 18 years.

(3 points)

QUESTION 15
A husband and wife made a loan of RM90,000 at 7% compounded monthly to purchase a
house. They agreed to repay the loan in monthly payments over a period of 15 years. Find the
monthly payment.

(4 points)

40

JULY 2021
QUESTION 13
Nabil has to pay RM840 every month for 9 years to settle a car loan at 5% compounded
monthly. Find the original value of the loan.

(4 points)

QUESTION 14
Find the accumulated amount of an annuity of RM450 at the end of every six months for seven
years if interest charged at 4% compounded semi-annually.

(4 points)

41

QUESTION 15
A businessman borrowed RM12,000 from a bank to expand his business which charged
interest of 4.5% compounded monthly. The loan is paid by monthly payment for 4 years. How
much his monthly payment.

(4 points)

NOVEMBER 2020
QUESTION 13
Balya is planning to go for a vacation 18 months from now. He needs RM10,000 to fulfill his
vacation’s planning. Find the amount that he has to save every month in a bank that offers 7%
compounded monthly.

(4 points)

42

QUESTION 14
Aisyah bought an apartment by taking a loan for 35 years with an interest rate of 4%
compounded monthly. She paid back RM980 every month to settle the loan. Find the amount
of the loan.

(3 points)

JULY 2020
QUESTION 13
Zuhayr paid RM650 every three months for 7 years for a loan he obtained that charged 5.5%
compounded quarterly. Find the loan he borrowed.

(3 points)

43

QUESTION 14
Find regular payment for an investment to be worth RM50,000 in 15 years at 6.25%
compounded monthly.

(4 points)

NOVEMBER 2019
QUESTION 13
Jasmin deposited RM565 at the end of every 6 months for 8 years in a savings account that
paid interest rate at 6.5% compounded semi-annually. Find the amount in the account just
after her last deposit.

(3 points)

44