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 = R1 − (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