Math Semester 1-converted

MRSM

Kubang Pasu

My Semester 1 Revision Book

Name: Amsyar
Zafri Bin Azmin
Class: 104 (Al-
Farabi)

MATH SEM 1 KuPa

Content

No. Topic Subtopic Page Due Date
6 May 2020
1 Chapter 1 1.1Note/Mindmap 3 – 6
Page 1 of 84
Collins KSSM 1.2 Exercise 7 – 10

Textbook Textbook

Chapter 1.1- Chapter

1.5 2.1-2.2

2 Chapter 2 2.1Note/Mindmap 11 – 12

Collins KSSM 2.2 Exercise 13 – 16

Textbook Textbook

Chapter 4.1- Chapter 1.1-

4.5 1.2

3 Chapter 3 3.1Note/Mindmap 17 – 18

Collins KSSM 3.2 Exercise 19 – 21

Textbook Textbook

Chapter 2.1- Chapter 1.3-

2.2 1.4

+ Recurring

Decimal

4 Chapter 4 4.1Note/Mindmap 22 – 23

Collins KSSM 4.2 Exercise 24 – 28

Textbook Textbook

Chapter 3.1- Chapter 1.2-

3.5 1.4

5 Chapter 5 5.1Note/Mindmap 29 – 31

Collins KSSM 5.2 Exercise 32 – 36

Textbook Textbook

Chapter 8.1- _

8.3

6 Chapter 6 6.1Note/Mindmap 37 – 38

Collins KSSM 6.2 Exercise 39 – 42

Textbook Textbook

Chapter 5.1- Chapter 3.1-

5.2 3.2

MATH SEM 1 KuPa

7 Chapter 7 7.1Note/Mindmap 43 – 44

Collins KSSM 7.2 Exercise 45 – 51

Textbook Textbook

Chapter Chapter 5.1

11.1-11.2

8 Chapter 8 8.1Note/Mindmap 52 – 53

Collins KSSM 8.2 Exercise 54 – 57

Textbook Textbook

Chapter Chapter 5.2

12.1

9 Chapter 9 9.1Note/Mindmap 58 - 59

Collins KSSM 9.2 Exercise 56 - 66

Textbook Textbook

Chapter Chapter 6.1

13.1-13.2 Chapter 6.2-

Chapter 6.3

13.6

10 Chapter 10 10.1Note/Mindmap 67 – 68

Collins KSSM 10.2 Exercise 69 – 76

Textbook Textbook

Chapter Chapter 7.1-

13.7 7.2

11 Chapter 11 11.1Note/Mindmap 77 – 79

Collins KSSM 12.2 Exercise 80 – 84

Textbook Textbook

Chapter 7.1- Chapter 4.1-

7.2 4.5

Chapter 7.4-

7.6

Page 2 of 84

MATH SEM 1 KuPa
Page 3 of 84

MATH SEM 1 KuPa

Common multiples Lowest Common Multiples (LCM)

The common multiple of several The lowest common multiples (LCM) of
whole numbers is the number which is several whole numbers is the smallest
the multiple of all whole numbers. common multiple of these numbers.

MULTIPLE CHAPTER
A whole number multiplied by
another whole number. FACTORS
A factor of a whole num
SQUARE NUMBER number that divide into
A number when you multiply
any number by itself. Common factor
The common factor of tw
SQUARE ROOT whole numbers is the num
The square root of n is the is a factor of each whole
number whose square is in n.

Prime factor
The prime factors of a whole
number are also the factors of
whole number.

Rational numbers Irrational number

A number that can be A number that can’t be
written as a fraction. written as fractions.

R1 REAL NUMBER
Real number has integers and
decimals. There are 2 types of
real number.

mber is any whole PRIME NUMBER
it exactly.
A whole number that has only
2 factors = itself and 1.

wo or more Highest common factor (HCF)
mber which
number. The highest common factor (HCF) of
several whole numbers is the largest
common factor of these numbers.

Page 4 of 84

MATH SEM 1 KuPa CHAPTER 1
1.1 Note/Mindmap

MULTIPLE

5 X 7 = 35 which means that 35 is a multiple of 5 and it is also a multiple 7. Here are some
multiples of 5 and 7 .
Multiples of 5 are = 5, 10, 15, 20, 25, 30….
Multiples of 7 are = 7, 14, 21, 28, 35,42…

COMMON MULTIPLES

24 is a multiple of 6 and 12 respectively, thus 24 is a common multiple of 6 and 12.

LOWEST COMMON MULTIPLE (LCM)

Find the LCM of 4 and 6.
Method 1: Listing the multiples

Multiples of 4 : 4 ,8 ,12 ,16 ,20 ,24
Multiples of 6 : 6 ,12 ,18 ,24
Therefore, the (LCM) of 4 and 6 is 12.
Method 2: Repeated division
24 6
22 3
31 3

11

Therefore, the (LCM) of 4 and 6 is 2 × 2 × 3=12

FACTOR

List all the factor of 42
1,2,3,6,7,14,21,42

Determine whether.
a) 6 is a factor of 42.

Solution: 42÷6 = 7
Therefore, 6 is a factor of 42.

b) 8 is a factor of 52.
52÷8=6 remainder 4
8 cannot divide 52 exactly.
Therefore, 8 is not a factor 52.

Page 5 of 84

MATH SEM 1 KuPa

PRIME FACTOR

List all the factor of 42
1,2,3,6,7,14,21,42
Therefore, the prime factor of 42 is 2,3 and 7.

COMMON FACTOR

Determine whether
a) 8 is a common factor of 32 and 48

solution:
32: 32÷8 = 4
48: 48÷8 = 6
Therefore, 8 is a common factor of 32 and 48.

b) 9 is a common factor of 32 and 45
Solution:
32: 32÷9 = 3 remainder 5
45: 45÷9 = 5
Therefore,9 is not a common factor of 32 and 45.

HIGHEST COMMON FACTOR (HCF)

Method 1: Listing the factor
Find the (HCF) of 24 ,48 and 60.
Solution:
Factors of 24: 1,2,3,4,6,8,12,24
Factors of 48: 1,2,3,4,6,8,12,16,24
Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60

Therefore, the (HCF) of 24, 48 and 60 is 12.

Method 2: Repeated division

2 24 48 60
2 12 24 30
3 6 12 15

2 45

Therefore, the (HCF) of 24,48,60 is 2×2×3=12

Page 6 of 84

MATH SEM 1 KuPa

PRIME NUMBER:
The prime number up to 50 are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

SQUARE NUMBER:
12,22,32,42 = 1,4,9,16
The square of 5 is 5x5 = 52 = 25

SQUARE ROOT:
The square root of 9 is √9 = 3

REAL NUMBER = 0,1,2,3,4,5 ….
= -2, - 1 , 0 , 1, 2
Natural number = 0.1, 0.2,0.3
Integer = Rational/Irrational number
Decimals = Can be written as fraction
Real number = Cannot be written as fraction
Rational number
Irrational number

Page 7 of 84

MATH SEM 1 KuPa

CHAPTER 1

1.2 Exercise

1. Write out the first five multiples of:

a) 4 = 4,8,12,16,20
b) 6 = 6,12,18,24,30
c) 8 = 8,16,24,32,40
d) 12 = 12,24,36,48,60
e) 15 = 15,30,45,60,75

2. Use your calculator to see which of the numbers below are:

225 252 361 297 162 363 161 289 224 205 312 378 315 182 369

a) multiples of 7 = 161,182,224,252,315,378
b) multiples of 9 = 162,225,252,297,315,369,378
c) multiples of 12 = 252,312

3. Find the LCM of these pairs of numbers.

a) 3 and 4 =

2 34 LCM 3 and 4 is 2×2×3 = 12

2 32

3 31

11

b) 6 and 8 =

2 68 LCM 6 and 8 is 2×2×2×3 = 24

2 34

2 32

3 31

11

c) 9 and 12 =

2 9 12 LCM 6 and 8 is 2×2×3×3 = 36

29 6

39 3

33 1

11

Page 8 of 84

MATH SEM 1 KuPa

d) 10 and 12 LCM 10 and 12 is 2×2×3×5 = 60
2 10 12 LCM 14 and 21 is 2×7×3 = 42
25 6 LCM 20 and 24 is 2×2×3×3×5 = 180
35 3
55 1
11

e) 14 and 21
2 14 21
7 7 21
31 3
11

f) 20 and 24
2 20 24
2 10 12
35 6
35 3
55 1
11

4. Find the HCF of these pairs of numbers.

a) 16 and 24

2 16 24 HCF 16 and 24 is 2×2×2 = 8

2 8 12

24 6

23

b) 28 and 35

7 28 35 HCF 28 and 35 = 7

45

Page 9 of 84

MATH SEM 1 KuPa

c) 24 and 30 HCF 24 and 30 is 2×3 = 6
2 24 30 HCF 48 and 60 is 2×2×3 = 12
3 12 15 HCF 28 and 70 is 2×7 = 14
45
HCF 75 and 125 is 5×5 = 25
d) 48 and 60
2 48 60
2 24 30
3 12 15
45

e) 28 and 70
2 28 70
7 14 35
25

f) 75 and 125
5 75 125
5 15 25
35

5. Write down all the prime numbers less than 40.
= 2,3,5,11,13,17,19,23,29,31 and 37.

6. Which of these numbers are prime?
43 47 49 51 54 57 59 61 65 67
= 43,47,57,59,61,67.

7. Write down the first ten square numbers.
= 1,4,9,16,25,36,49,64,81 and 100.

Page 10 of 84

MATH SEM 1 KuPa

8. Write down the answer to each of the following. You will need to use your calculator.
a) 5² = 5×5 = 25
b) 15² = 15×15 = 225
c) 25² = 25×25 = 625
d) 35² = 35×35 = 1,225
e) 45² = 45×45 = 2,025
f) 55² = 55×55 = 3,025
g) 65² = 65×65 = 4,225
h) 75² = 75×75 = 5,625
i) 85² = 85×85 = 7,225
j) 95² = 95×95 = 9,025

9. State whether each of these numbers is an integer or not.

a) 36 ÷ 10 = 3.6 not integers

b) 4.2 × 5 = 21 integers

c) √49 =7 integers

d) 14.4 × 5.3 = 76.32 not integers

e) –23 = integers

f) –√81 = -9 integers

g) 121² = 14 641 integers

h) √105 = 10.2 integers

10. State whether each of these numbers is rational or not.

a) 7 = rational
11 = rational

b) √16

c) 129.52 = rational

d) √68 = irrational

e) π × 10 = irrational

f) 3.45 ÷ 6 = rational

g) 2 × √12 = irrational

h) √0.25 = rational

Page 11 of 84

MATH SEM 1 KuPa NEGATIVE NUMBER NUMBER LINE
Have negative and positive nu
POSITIVE NUMBER Numbers less than
Numbers greater than zero.
zero.

DIRECTED NUMBER

Have negative and positive
numbers.

LAW OF ARITHMETIC OPERATIONS
A) Commutative law

a+b=b+a

axb=bxa

b) Associative law CHAPTER

(a + b) + c = a + (b + c) ADDING/ADDITION

(a x b) x c = a x (b x c) Addition of two or more
integers is the process of
c) Distributive law finding the sum of the
integers.
a x (b + c) = a x b + a x c SUBTRACTING/SUBTRACTION

a x (b – c) = a x b – a x c Subtraction between two
integers is the process of
d) Identity law finding the difference
between the two integers.
a+0+a a + (-a) = 0

ax0=0 ax1=a

a x 1/a = 1

umbers.

INEQUALITY SIGNS:

< means ‘is less than’

˃ means ‘is greater than’ or
‘more than’

ORDER OF OPERATIONS
Bracket

× or ÷ from left to right
+ or - from left to right

R2 BASIC ARITHMETIC OPERATION
1.Adding/Addition
2.Subtracting/Subtraction
3.Multiplying/Multiplication
4.Dividing/Division

DIVIDING/DIVISION MULTIPLYING/MULTIPLICATION

The sign of the product of The sign of the product of
integers. integers.

• (+) ÷ (+) = (+) • (+) × (+) = (+)
• (+) ÷ (-) = (-) • (+) × (-) = (-)
• (-) ÷ (+) = (-) • (-) × (+) = (-)
• (-) ÷ (-) = (+) • (-) × (-) = (+)

Page 12 of 84

MATH SEM 1 KuPa CHAPTER 2
2.1 Note/Mindmap

DIRECTED NUMBER.
Positive number: 1, 2, 3, 4, 5…
Negative number: -1, -2, -3, -4, -5…

USE OF DIRECTED NUMBER
1.Profit
2.Loss
3.Price

NUMBER LINE
Inequality signs:
< means ’less than’
> means ‘more than’ or ‘greater than’
-1 < 3
3>2
5 > -5

ADDING AND SUBTRACTING DIRECTED NUMBERS
-2 + 3 = 1
3+2=5
-3 – 2 = -5
3–2=1

MULTIPYING AND DIVIDING DIRECTED NUMBERS
2x2=4
-5 x - 3 = -15
10 ÷ 2 = 5
-15 ÷ 3 = -5

Page 13 of 84

MATH SEM 1 KuPa CHAPTER 2
1.2 Exercise

1. Write down the temperatures for each thermometer.

a) 3
b) 2
c) -4
d) -6
e) -5

2. The diagram shows the layout of a hotel and the lift numbers for each floor.
a) How many floors is the third floor above the basement?

= 5 floors
b) How many floors is the lower ground floor below the first floor?

= 2 floors
c) How many floors is the basement below the second floor?

= 3 floors
d) The cellar basement is three floors below the basement. What number is used for the lift?

= -2 – 3 = -5

Page 14 of 84

MATH SEM 1 KuPa

3. A hotel has 11 levels numbered from basement (–1) to ninth floor (+9).
A man is in a lift on the third floor. He goes up four levels and then down to the basement.
How many levels does the lift travel while descending?

Ninth floor (9) 3 + 4 – (-1) = 7 +1
Eight floor (8) =8
Seventh floor (7)
Sixth floor (6)
Fifth floor (5)
Fourth floor (4)
Third floor (3)
Second floor (2)
First floor (1)
Ground floor (0)
Basement (-1)

4. The temperature on three days in Quebec in Canada was –9°C, –8°C and –11°C.
a) Put the temperatures in order starting with the coldest.

= –11°C, –9°C and –8°C.
b) What is the difference in temperature between the coldest and the warmest temperature?

–11°C – (–8°C) = 3°C.

5. Copy each of these and put the correct symbol (< or >) in the space.

a) 2 ... 6 = 2<6

b) –1... –7 = -1 > -7

c) –5 ... 1 = -5 > 1

d) 5 ... 9 = 5 < 9

e) –8 ... 2 = -8 < 2

f) –14 … –10 = -14 < -10

g) –11 ... 0 = -11 < 0

h) –9 ... –12 = -9 > -12

Page 15 of 84

MATH SEM 1 KuPa

6. Here are some temperatures.
3°C –8°C –1°C 4°C
Copy and complete the following weather report using these temperatures.
Temperatures fell to –8°C making Newcastle the coldest place in the country today, while in Yorkshire the
temperatures were also below freezing at –1°C. People on the south coast enjoyed warmer temperatures,
with Eastbourne being the warmest at 4°C and Brighton only slightly lower at 3°C.

7. Write down the answer to each of the following, and then check your answers on a calculator.
a) –13 – 5 = -18
b) –12 – 8 = -20
c) –25 + 6 = -19
d) 6 – 14 = -8
e) 25 – (–3) = 28
f) 13 – (–8) = 21
g) –4 + (–15) = -19
h) –13 + (–7) = -20

8. Two numbers have a sum of 8. One of the numbers is negative. The other number is odd. What could the
numbers be? Give two different answers.
a) 11 + (-3) = 8
b) -5 + 13 = 8

9. Write down the answers to the following.
a) –2 × 4 = -8
b) –3 × 6 = -18
c) –5 × 7 = -35
d) –3 × (– 4) = 12
e) –8 × (–2) = 16
f) –14 ÷ (–2) = 7
g) –16 ÷ (–4) = 4
h) 25 ÷ (–5) = -5

Page 16 of 84

MATH SEM 1 KuPa
10. Work out each of these. Remember: First work out the bracket.
a) –3 × (–2 + 6) = -3 × 4
= -12
b) 8 ÷ (–3 + 2) = 8 ÷ (-1)
= -8
c) (6 – 8) × (–3) = (-2) × (-3)
= -6
d) –4 × (–6 – 3) = -4 × (-9)
= 36
e) –5 × (–6 ÷ 2) = -5 × (-3)
= 15
f) (–5 + 3) × (–3) = -2 × (-3)
=6
g) (6 – 9) × (–4) = -3 × (-4)
= 12
h) (2 – 5) × (5 – 2) = -3 × 3
= -9

Page 17 of 84

MATH SEM 1 KuPa

EQUIVALENT FRACTION REUCRRING DECIMALS IMPRO

Two or more fractions that Decimals representation of a A fracti
represent the same part of a number whose digits are (top nu
whole. periodic and the infinitely denom
repeated portion.

SIMPLEST TERMS/LOWEST FORM CHAPTER

The only number that is factor of
both the numerator and
denominator is 1.

MIXED NUMBER POSITIV
Made up of a whole number
and proper fraction. Represe
the sam
POSITIVE/NEGATIVE FRACTION
Representing the positive and negative fractions on number is the
same as integers.

OPER FRACTION PROPER FRACTIONS

ion with the numerator A fraction with the numerator (top number)
umber) is bigger than
minator (bottom number) is smaller than denominator (bottom
number)

R3 DECIMAL INTO A FRACTION.
A decimal can be changed into
VE/NEGATIVE DECIMALS fraction by using a place value
enting the decimals on a number line is table
me as integers
FRACTION INTO DECIMAL
A fraction can be changed into
decimals by dividing the
numerator by the
denominator.

Page 18 of 84

MATH SEM 1 KuPa CHAPTER 3

3.1 Note/Mindmap
FRACTION.
Equivalent fraction.

3 12

4 is equivalent to 16

Mixed number

1

12
Proper fraction

2
4

Improper fraction

5
4

Simplest terms/Lowest form

=



Fraction into decimal

1 = 0.5

2

Decimal into fraction

0.5 = 1

2

Positive/Negative fraction.

5
10

−5

10

Positive/Negative decimal
0.5

−0.5
Recurring decimal
0.555555555555 = 0. 5̇

Page 19 of 84

MATH SEM 1 KuPa CHAPTER 3
3.2 Exercise

1. Complete each of these statements.

a) 1 = 2 = = 4 = = 6 = 1 = 2 = = 4 = = 6
4 8 24 =
12 20 = 4 8 12 20 24
=
b) 2 = 4 = = = 10 = 12 2 = 4 = = = 10 = 12
3 6
12 18 3 6 12 18

c) 4 = = 12 = = = 4 = = 12 = = =
5
10 20 30 5 10 20 30

d) 3 = == = = 18 3 = = = = = 18
10
30 50 10 30 50

2. Cancel each of these fractions to its simplest form.

a) 4 =
10

b) 3 =
12

c) 5 =
25

d) 6 =
15

e) 8 = 4 =
12 6

f) 10 =
30

g) 12 = 6 =
20 10

h) 16 = 8 =
12
24

i) 30 =
50

j) 42 =
49

Page 20 of 84

MATH SEM 1 KuPa

3. Put the following fractions in order with the smallest first.

a) 1 , 1 , 1 = 3,6,4 = , ,
3 2 4
12 12 12

b) 3 , 3 , 1 = 6 , 3 , 4 = , ,
4 8 2 8 8 8

c) 5,2, 7 = 10 , 8 , 7 = , ,

6 3 12 12 12 12

d) 2 , 3 , 1 = 8,6,5 = , ,
5 10 4
20 20 20

4. Change each of these decimals to fractions in its simplest form.



a) 0.3 =

b) 0.8 = 8 =
10



c) 0.9 =



d) 0.07 =

e) 0.08 = 8 =
100

f) 0.15 = 15 =
100

g) 0.75 = 75 =
100

48 =

h) 0.48 = 100

i) 0.32 = 32 =
100



j) 0.27 =

5. Change each of these fractions to decimals.

1

a) 4 = 0.25

2

b) 5 = 0.4

c) 7 = 0.7
10

Page 21 of 84

MATH SEM 1 KuPa

d) 9 = 0.45
20

7

e) 8 = 0.875

6. Put each of the following sets of numbers in order with the smallest first. It is easier to change the
fractions into decimals first.

2

a) 0.3 , 0.2 , 5 = 0.3,0.2,0.4

= 0.2,0.3,0.4

7

b) 10 , 0.8 , 0.6 = 0.7 , 0,8 , 0.6

= 0.6 , 0.7, 0.8

1

c) 0.4 , 4 , 0.2 = 0.4 , 0.25 , 0.2

= 0.2 , 0.25 , 0.4

7. Which of the following can be written as terminating decimals:

2,3,4,5,5,3 ,3 = 0.6̇ , 0.75 , 0. 4̇ , 0.8333 , 0.625 , 0.428571 , 0.6

349687 5

= 3 , 5 ,3
4 8
5

8. Which of the following can be written as recurring decimals:

5,7,3,5,5,5 = 0.4166 , 0.28 , 0.214285 , 0.3125 , 0.15625 , 0.454545

12 25 14 16 32 11

= 5,3 ,5

12 14 11

9. Convert 0. 5̇ to a fraction.

= 5
9

10. Convert 3 to a decimal.
11

= 0.27272727

= 0. 27̈

Page 22 of 84

MATH SEM 1 KuPa ORDER OF OPERATIONS. SUBTACTING FRA

ADDITION OF INTEGERS. To work out 1 + 2 x 3 ,you When you subtra
Addition of two or more must work out x first. fractions with the
integers is the process of denominator, you
finding the sum of the the following:
integers.
A) a proper fractio
MULTIPLYING FRACTIONS. cannot be simplifi
To multiply fractions, you
multiply the numerators B) a proper fractio
together and you multiply the be simplified.
denominators together

FINDING A FRACTION OF A CHAPTER
QUANTITY.
CHOOSING THE CORRECT
To do this, you simply OPERATION.
multiply the fraction by the When a problem is given in
quantity. words you will need to decide
the correct operation to use
DIVIDING FRACTIONS.

To divide by a fraction, you
turn the fractions upsides
down (finding its reciprocal),
and thenBmAuSlItCipAlyR.ITHMETIC OPERATION

1.Adding/Addition

2.Subtracting/Subtraction

3.Multiplying/Multiplication

4.Dividing/Division

ACTION. DIVIDING/DIVISION ADDING FRACTIONS
act two
The sign of the product of When you add two fractions
same integers. with the same denominator,
u get one of you get one of the following:
on that • (+) ÷ (+) = (+)
ied • (+) ÷ (-) = (-) A) a proper fraction that
on that can • (-) ÷ (+) = (-) cannot be simplified
• (-) ÷ (-) = (+)
R4 B) a proper fraction that can
be simplified to its lowest
terms or simplest form.

C) an improper fraction that
cannot be simplified, so it is
converted to a mixed number.

D) an improper fraction that
can be simplified before it is
converted to a mixed number.

ADDING/ADDITION

Addition of two or more
integers is the process of
finding the sum of the
integers.

SUBTRACTING/SUBTRACTION MULTIPLYING/MULTIPLICATION

Subtraction between two The sign of the product of
integers is the process of integers.
finding the difference
between the two integers. • (+) × (+) = (+)
• (+) × (-) = (-)
• (-) × (+) = (-)
• (-) × (-) = (+)

Page 23 of 84

MATH SEM 1 KuPa CHAPTER 4
4.1 Note/Mindmap

Addition and subtraction of integers.

1) -1 + 4 =3
2) 2 + (-4) = -2
3) 3 – 5 = -2
4) – 6 – (-3) = -3

Multiplication and Division of integer

1) -4 x 2 = -8
2) 3 x 2 = 6
3) -10 ÷ 2 = -5
4) 20 ÷ 5 = 4

Fraction of a quantity

3 30 = 18
5

Adding and subtracting fraction
1+2=3

55 5

4−1=3

77 7

Page 24 of 84

MATH SEM 1 KuPa

CHAPTER 4
4.2 Exercise
1.Work out each of these. Remember: first work out the bracket.

a) 3 × (2 + 4) =
3 × 6 =

b) 12 ÷ (4 + 2) =

12 =
6

c) (4 + 6) ÷ 5 =

10 =

5

d) (10 − 6) + 5 =

4 + 5 =

e) 3 × (9 ÷ 3) =

3 × 3 =

f) 5 + (4 × 2 ) =

5 + 8 =

2.Copy each of these and then put in brackets to make each sum true.

a) 4 × 5 – 1 = 16 = 4 × (5 – 1) = 16
b) 8 ÷ 2 + 4 = 8 = (8÷ 2) + 4 = 8
c) 8 – 3 x 4 = 20 = (8 – 3) x 4 = 20
d) 12 – 5 x 2 = 2 = 12(-5 x 2) = 2
e) 3 x 3 + 2 = 15 = 3 x (3 + 2) = 15
f) 12 ÷ 2 + 1 = 4 = 12 ÷(2 + 1) = 4

Page 25 of 84

MATH SEM 1 KuPa

3. The organiser of a church fête needs 1000 balloons. She has a budget of $30.
Each packet contains 25 balloons and costs 85p. Does she have enough?

30 ÷ 0.85 = 35 Packets.
35 x 25 = 875 balloons

= not enough

4. A TV rental shop buys TVs for $110 each.
The shop needs to make a least 10 percent profit on each TV to cover its costs.
On average each TV is rented for 40 weeks at $3.50 per week.
Does the shop cover its costs?

10% of $110 = %11
$3.50 x 40 weeks = 140

= yes

5. Calculate each of these quantities.

a) 1 of $800
4

1 x $800 = $200
4

b) 2 of 60 Kilograms
3

2 x 60 Kilograms = 40 Kilograms
3

c) 3 of 200 meters
4

3 x 200 = 150 meters
4

d) 3 of 48 litres
8

3 x 48 litres = 18 litres
8

Page 26 of 84

MATH SEM 1 KuPa

e) 54of 30 minutes

4 x 30 minutes = 24 minutes
5

f) 170of 120 kilometres

7 x 120 kilometres = 84 kilometres
10

6) In each case, find out which is the smaller number.

a) 1 of 60 or 1 of 40 =
4 2

b) 1 of 36 or 1 of 50 =

35

c) 2 of 15 or 3 of 12 =

34

d) 5 of 72 or 5 of 60 =

86

7) Calculate each of these. Remember to cancel down.

a) 3+1 = 4 =

88 8

b) 3+5 = 8 =

10 10 10

c) 5+1 = 6 =

12 12 12

d) 5−4 =

88

e) 9−3 = 6 =

10 10 10

f) 5−2 = 3 =

99 9

8) Evaluate the following. Show your working.

a) 3 + 3 = 24 + 15 =

5 8 40 40

b) 1 + 2 = 5 + 4 =

2 5 10 10

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MATH SEM 1 KuPa

c) 7 − 3 = 7 − 6 =
8 4 8 8

d) 4−1= 8 − 5 = 3

5 2 10 10 10

e) 1 3 + 2 3 = 8 + 23 = 16 + 23 = 39 =
5 10 5 10 10 10 10

f) 2 5 − 1 2 = 17 − 5 = 17 − 10 = 7 =
6 3 63 6 6 6

g) 5 5 + 4 5 − 2 1 = 45 + 49 − 13 =
8 12 6 8 12 6

h) 4 7 − 1 1 + 2 2 = 67 − 4 + 12 = 67 − 20 + 36 = 83 =
15 3 5 15 3 5 15 15 15 15

9. Evaluate the following, leaving your answer in its simplest form

a) 1 x 2 = 2 =
2 3 6

b) 3 × 2 = 6 =

4 5 20

c) 3 × 1 =

5 2

d) 3 × 2 = 6 =

7 3 21

e) 1 ÷ 1 = 1 × 3 =

5 3 5 1

f) 3 ÷ 1 = 3 × 3 = 9 =
53 5 1 5

g) 4 ÷ 2 = 4 × 3 = 12 =
5 3 5 2 10

h) 4 ÷ 8 = 4 × 9 = 36 =
7 9 7 8 5

10. Evaluate the following, leaving your answer as a mixed number wherever possible.

a) 1 1 × 1 2 ÷5 = 5×5 ÷ 5 = 25 × 6 = 150 =
4 3 5 60
6 43 6 12

b) 5 × 1 1 ÷ 1 1 = 5 ×4 × 10 = 200 =
8 3 10 8
3 11 264

c) 2 1 × 1 1 ÷ 3 1 = 5 × 4 × 3 = 60 =
2 3 3 2 3 10 60

Page 28 of 84

MATH SEM 1 KuPa

ROUNDING WHOLE NUMBERS ROUNDING DECIMALS

If you want to round a number to the nearest a) Count along the dec
multiple of ten, you round it up if it end in 5 or decimal point and lo
above, you round it down if it ends in less than be removed.
5.
b) When the value of t
five, just remove th

c) When the value of t
add 1 onto the digit
place then remove

CHAPTER 5

cimal places from the ROUNDING TO SIGNIFICANT FIGURES
ook at the first digit to
a) From the left, count the digits. If you are
this digit is less than rounding to 2 sf, count two digits, for 3 sf
he unwanted place. count three digits, and so on. When the
this digits is 5 or more, original number is less than 1, start
t in the last decimal counting from the first non-zero digit.
the unwanted places.
b) Look at the next digit to the right. When
the digit you counted to the same.
However, if the value of this next digit is
equal to or greater than 5, add 1 to the
digit you counted to.

c) Ignore all the other digits, but put enough
zeros to keep the number the right
size(value)

Page 29 of 84

MATH SEM 1 KuPa CHAPTER 5

5.1 Note/Mindmap

Rounding whole number
To the nearest 10
12 = 10
25 = 30
21 = 20
To the nearest 100
151 = 200
149 = 100
321 = 300
To the nearest 1000
1234 = 1000
3252 = 3000
4263 = 4000

Rounding decimals
One decimal place
4.83 = 4.8
8.25 = 8.3
23.883 = 23.9
Two decimal places
5.783 = 5.78
6.007 = 6.01
33.085 = 33.09
Three decimal places
45.71593 = 45.716
6.90354 = 6.904
7.43627 = 7.436

Page 30 of 84

MATH SEM 1 KuPa
Rounding significant figures(sf)
One sf
94558 = 90000
30569 = 30000
9.9 = 10
Two sf
94558 = 95000
30569 = 31000
1.689 = 1.7
Three sf
89.67 = 89.7
54.87 = 54.9
32.876 = 32.9

Page 31 of 84

MATH SEM 1 KuPa CHAPTER 5
5.2 Exercise

1. Round each of these numbers to the nearest 10

a) 34 = 30
b) 67 = 70
c) 23 = 20
d) 49 = 50
e) 55 = 60
f) 11 = 11
g) 95 = 100
h) 123 = 120
i) 109 = 110
j) 125 = 130

2. Round each of these numbers to the nearest 100.

a) 231 = 200
b) 389 = 400
c) 410 = 400
d) 777 = 800
e) 850 = 900
f) 117 = 100
g) 585 = 600
h) 250 = 300
i) 975 = 1000
j) 1245 = 1200

3. Round each of these numbers to the nearest 1000.

a) 2176 = 2000
b) 3800 = 4000
c) 6760 = 7000
d) 4455 = 4000
e) 1204 = 1000
f) 6782 = 7000
g) 5500 = 6000
h) 8808 = 9000
i) 1500 = 2000
j) 9999 = 10 000

Page 32 of 84

MATH SEM 1 KuPa

4. Round each of the following to the number of decimal places indicated.

a) 4.572 (1 dp) = 4.6
b) 0.085 (2 dp) = 0.9
c) 5.7159 (3 dp) = 5.716
d) 4.558 (2 dp) = 4.56
e) 2.099 (2 dp) = 2.1
f) 0.7629 (3 dp) = 0.763
g) 7.124 (1 dp) = 7.1
h) 8.903 (2 dp) = 8.90
i) 23.7809 (3 dp) = 23.781
j) 0.99 (1 dp) = 1.00

5. Round each of the following numbers to one decimal place.
a) 3.73 = 3.7
b) 8.69 = 8.7
c) 5.34 = 5.3
d) 18.75 = 18.8
e) 0.423 = 0.4
f) 26.288 = 26.3
g) 3.755 = 3.8
h) 10.056 = 10.1
i) 11.08 = 11.1
j) 12.041 = 12

6. Round each of the following numbers to two decimal places.
a) 6.721 = 6.72
b) 4.457 = 4.46
c) 1.972 = 1.97
d) 3.485 = 3.49
e) 5.807 = 5.80
f) 2.564 = 2.56
g) 21.799 = 21.80
h) 12.985 = 12.99
i) 2.302 = 2.30
j) 5.555 = 5.56

Page 33 of 84

MATH SEM 1 KuPa

7. Round each of the following to the nearest whole number.

a) 6.7 = 7
b) 9.3 = 9
c) 2.8 = 3
d) 7.5 = 8
e) 8.38 = 8
f) 2.82 = 3
g) 2.18 = 2
h) 1.55 = 2
i) 5.252 = 5
j) 3.999 = 4

8. Round each of the following to one significant figure.

a) 51 203 = 50 000
b) 56 189 = 60 000
c) 33 261 = 30 000
d) 89 998 = 90 000
e) 94 999 = 90 000
f)53.71 = 50
g) 87.24 = 90
h) 31.06 = 30
i) 97.835 = 100
j) 184.23 = 200
k) 0.5124 = 0.5
l) 0.2765 = 0.3
m) 0.006 12 = 0.006
n) 0.049 21 = 0.05
o) 0.000 888 = 0.000 9
p) 9.7 = 10
q) 85.1 = 90
r) 91.86 = 90
s) 196 = 200
t) 987.65 = 1000

9. Round each of the following numbers to 2 significant figures.

a) 6725 = 6700
b) 35 724 = 36 000
c) 68 522 = 69 000
d) 41 689 = 42 000
e) 27 308 = 27 000
f) 6973 = 7000
g) 2174 = 2200
h)958 = 960

Page 34 of 84

MATH SEM 1 KuPa

i) 439 = 440
j) 327.6 = 330

10. Round each of the following to the number of significant figures (sf) indicated.
a) 46 302 (1 sf) = 50 000
b) 6177 (2 sf) = 6200
c) 89.67 (3 sf) =89.7
d) 216.7 (2 sf) = 220
e) 7.78 (1 sf) = 8
f) 1.087 (2 sf) = 1.1
g) 729.9 (3 sf) = 730
h) 5821 (1 sf) = 6000
i) 66.51 (2 sf) = 67
j) 5.986 (1 sf) = 6
k) 7.552 (1 sf) = 8
l) 9.7454 (3 sf) = 9.75
m) 25.76 (2 sf) = 26
n) 28.53 (1 sf) = 30
o) 869.89 (3 sf) = 870
p) 35.88 (1 sf) = 40
q) 0.084 71 (2 sf) = 0.085
r) 0.0099 (2 sf) = 0.01
s) 0.0809 (1 sf) = 0.08
t) 0.061 97 (3 sf) = 0.062

Page 35 of 84

MATH SEM 1 KuPa PERFECT CUBES

CUBES Are equivalent to the
Cube is equivalent to the number of unit blocks that
product of the length if the can form a cube.
3 sides of cube

CUBE NUMBERS CHAPTE
A cube of number is formed
when you multiply the number SQUARE ROOT
by itself and then by itself a number which produces a
again. specified quantity when
multiplied by itself.
RELATIONSHIP BETWEEN
CUBES AND CUBE ROOTS

CUBE

5 25

CUBE ROOT

t SQUARE
Square is equivalent to the
ER 6 product of the length of two
sides of a square.

SQUARE NUMBERS
The product of a number
multiplied by itself

RELATIONSHIP BETWEEN
SQUARES AND SQUARE
ROOTS

SQUARE

5 25

SQUARE ROOT

PERFECT SQUARE

Are equivalent to the number
of square with measurement
of 1 unit x 1 unit that can form
a square.

Page 36 of 84

MATH SEM 1 KuPa CHAPTER 6

6.1 Note/Mindmap

Square number
6² = 6 x 6
5² = 5 x 5
7² = 7 x 7

Square root
√36 = 6
√25 = 5
√9 = 3

Cubes number
6³ = 6 x 6 x 6
5³ = 5 x 5 x 5
7³ = 7 x 7 x 7

Cubes root
3√8 = 2
3√1 = 1
3√1000 = 10

Page 37 of 84

MATH SEM 1 KuPa CHAPTER 6
6.2 Exercise

1. Write down the two square roots of each of these numbers.
a) 64 = 8
b) 25 = 5
c) 49 = 7
d) 81 = 9
e) 16 = 4
f) 36 = 6
g) 100 = 10
h) 121 = 11

2. Write down the answer to each of the following. You will need to use your calculator.
a) √225 = 15
b) √289 = 17
c) √441 = 21
d) √625 = 25
e) √1089 = 33
f) √1369 = 37
g) √3136 = 56
h) √6084 = 78

3. Put these in order starting with the smallest value.
2², √20 ,√10, 3² =
2² = 4, √20 = 4.47, √10 = 3.16, 3² = 9
= √10, 2², √20, 3²

Page 38 of 84

MATH SEM 1 KuPa

4. Between which two consecutive whole numbers does the square root of
40 lie?

= √40
= 6.32
= 6-7

5. A child has 125 square tiles which she is arranging into square patterns.
How many tiles will be in the biggest square she can make?
= 121

6. Find the following cubes:
a) 4³ = 64
b) 9³ = 729
c) 11³ = 1331
d) 2.4³ = 13.824
e) (–5)³ = -125
f) (–2.5)³ = -15.625
g) (–7.7)³ = -456.533
h) 75³ = 421 875

7. Write down the cube root of each of these.
a) 8 = 2
b) 64 = 4
c) 125 = 5
d) 1000 = 10
e) 27 000 = 30
f) –27 = -3
g) –1 = -1
h) –216 = -6
i) –8000 = -20
j) –343 = 7

Page 39 of 84

MATH SEM 1 KuPa
k) 0.729 = 0.9
l) 10.648 = 2.2

8. Use these four numbers to make a cube number:
1279
= 2197

9. Write these numbers in order, smallest first.
a) 3√216 6² 4³ √64 = 6, 36, 64, 4

= √ , √64, 6², 4³
b) 5³ 11² √12 100 √1 000 000 = 125, 121,110,100

= √ ,√12100,11²,5³

10. 36³ = 46 656. Work out 1³, 4³, 9³, 16³, 25³.

1³ = 1 x 1 x 1
=1

4³ = 4 x 4 x 4
= 64

9³ = 9 x 9 x 9
= 729

16³ = 16 x 16 x 16
= 4096

25³ = 25 x 25 x 25
= 15625

Page 40 of 84

MATH SEM 1 KuPa Variable
Fixed Variable Variable is a quantity
Always constant at any which value is not yet
time. known.

Varied value CHAPT
Changes over the time.

Unlike terms Algebraic term
Is a number or the
Terms which do not have product of a number with
the same variable with the one or more variables.
same powers.
Like terms
Terms which have the
same variable with the
same power.

Expressions Algebraic expression
This is any combination of Consist of one algebraic
letters and number. term or the combination
of two or more algebraic
TER 7 terms with addition or
subtraction.

Formula
These are like equations in
that they contain an equal
sign, but there is more
than ones variable and
they are rules for working
out amounts such as area
or the taxi fares.

Equation

An equation contains an
equals sign and at least
one variable.

Page 41 of 84

MATH SEM 1 KuPa CHAPTER 7
7.1 Note/Mindmap

Variable: 4x – 7 = 5
The letter x is the variable.

Expression: 2x + 4y

Equation: contains and equal sign and at least one variable.

Formula: C = 3 + 4m

Additions and subtraction of algebraic expressions:
(8m – 6n) + (7m + 2n - 3) = 5m – 4n

Like terms: 2x and 50x
Unlike terms:0.6xy and -98xy

Page 42 of 84