Maths Sem 1 Revision Book

MURDE
MAT

EROUS
THS

STRIVE FOR MATHEMATICS A+

ALL THINGS ARE
DIFFICULT

BEFORE THEY ARE

EASY

WELCOME
TO MY

SEMESTER 1
REVISION BOOK

Chapter 1

1. Write Out the first five multiples of:
a4 b6 c 8 d 12 e 15

REMEMBER: The first multiple is the number itself.

a: 4,8,12,16,20
b: 6,12,18,24,30
c: 8,16,24,32,40
d: 12,24,36,48,60

2. Use your calculator to see which of the numbers below are: 182
a multiples of 7 b multiples of 9 c multiples of 12

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

a: 252,224,378,315,182,161
b: 225,252,297,162,378,315,369
c: 252,312

3. Find the LCM of these pairs of numbers.
a 3 and 4 b 6 and 8 c 9 and 12

d 10 and 12 e 14 and 21 f 20 and 24

a: 3|3,4 b: 2|6,8 c: 3|9,12
4|1,1 3|3,4 3|3,4
4|1,1 4|1,1

3 x 4 = 12 2 x 3 x 4 = 24 3 x 3 x 4 = 36

d: 2|10,12 e: 7|14,21 f: 2|20,24
5|5,6 2|2,3 2|10,12
6|1,1 3|1,1 5|5,6
6|1,1
2 x 5 x 6 = 60 7 x 2 x 3 = 42
2 x 2 x 5 x 6 = 120

4. Find the HCF of these pairs of numbers.
a 16 and 24 b 28 and 35 c 24 and 30

d 48 and 60 e 28 and 70 f 75 and 125

a: 4|16,24 b: 7|28,35 c: 6|24,30
2|4,6 4,5 3|12,15
2,3 4,5
=7
4 x 2 x 2 = 16 6 x 3 = 18

d: 4|12,15 e: 7|28,70 f: 5|75,125
3|4,5 2|4,10 5|15,25
2,5
4 x 3 = 12 3|3,6
7 x 2 = 14 1,2

5 x 5 x 3 = 30

5. Write down all the prime numbers less than 40.
Prime numbers that less than 40 are:
2,3,5,7,11,13,17,19,23,29,31,37.

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

Prime Numbers are:
43,47,59,61,67

7. Down the first ten square numbers.
1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25
6 x 6 = 36 7 x 7 = 49 8 x 8 = 64 9 x 9 = 81 10 x 10 = 100

8. Write down the answer to each of the following. You will need to use calculator.
a 52 b 152 c 252 d 352 e 452

f 552 g 652 h 752 I 852 j 952

a 25 b 225 c 625 d 1225 e 2025
f 3025 g 4225 h 5625 I 7225 j 9025

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

a 36 ÷ 10 b 4.2 x 5 c √49 d 14.4 x 5.3

e -23 f -√81 g 1212 h √105

a Not an integer number
b An integer number
c An integer number
d Not an integer number
e An integer number
f An integer number
g An integer number
h Not an integer number

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

a7 b √16 c 129.52 d √68

11

e π x 10 f 3.45 ÷ 6 g 2 x √12 h √0.25

a Rational number
b Rational number
c Rational number
d Irrational number
e Irrational number
f Irrational number
g Irrational number
h Rational number

Chapter 2

a 3℃
b 2℃
c -4℃
d -6℃
e -5℃

a5
b2
c4
d -5

8 levels

a -11℃,-9℃,-8℃
b -11℃ - (-8℃) = -3℃

a 2<6 b -1 > -7 c -5 < 1 d 5<9
d -8 < 2 f -14 < -10 g -11 < 0 h -9 > -12

-8℃,-1℃,3℃,4℃

a -18 b -20 c -19 d -8
e 28 f 21 g -19 h -20

1. 9 + ( -1) = 8 2. 13 + (-5) = 8

a -3 x 4 b 8 ÷ -1 c -2 x (-3) d -4 x -9
-12 -8 5 36

e -5 x -3 f  5 x(3) g -3 x -4 h -3 x 3
15 12 -9
3

5

Chapter 3

a 12 3  4  5  6

4 8 12 16 20 24

b 2  4  6  8  10  12

3 6 9 12 15 18

c 4  8  12  16  20  24

5 10 15 20 25 30

d 3  6  9  12  15  18

10 20 30 40 50 60

a 4 2 2 b 3 3 1 c 5 5 1 d 6 3 3

10 5 12 4 25 5 15 5

e 8 4 2 f 10 10  1 g 12  2  6  2  3

12 3 30 3 20 10 5

i 30 10  3 j 42  7  6

50 5 49 7

a 1,1,1 b 3,3,1 c 7 ,5,2 d 3 ,2,1

432 842 12 6 3 10 5 4

a 0.3  3 b 0.8  4 c 0.9  9 d 0.07  7

10 5 10 100

e 0.08  8  4  2 f 0.15  3 h 0.48  12 i 0.32  8

100 25 20 25 25

j 0.27  27

100

a 1  1 4  0.25

4

b 2  2  5  0.4

5

c 7  7 10  0.7

10

d 9  9  20  0.45

20

e 7  7  8  0.875

8

a 0.2,0.3,0.4 b 0.6,0.7,0.8 c 0.2,0.4,0.25

3,5,3
485
5,5
12 11

9. Convert 0.5 to a fraction

0.5x1  1
2

10. Convert 3 to a decimal

11
3  3 11  0.273
11

When you multiply any whole number by 01 23 4 5
another whole number, the answer is called a
multiple of either of those numbers.

For example, 5 x 7 = 35, which means that
35 is a multiple of 5 and it is also a
multiple 0f 7. Here are some other multiples
of 5 and 7.

Multiples of 5 are 5 10 15 20 …..
Multiples of 7 are 7 14 21 28 …..

Less than 40;
2,3,5,7,11,13,17,19,23,29,31,37

Less than 100;
2,3,5,7,11,13,17,19,23,29,31,37,
41,43,47,53,59,61,67,71,73,79,83,8
9 and 97.

Integers consist of whole numbers
with a positive or negative sign and
including zero.

Representing integers on a number
line:

-4 -3 -2 -1 0 1 2 3

6 7 8 9 10 The lowest common multiple [ LCM ]
Of two numbers is the smallest number
That appears in the multiplication
tables of both numbers.

Example;

3 and 4

3 3, 4

4 1,1

3 x 4 = 12

The LCM of 3 and 4 is 12.

The Highest Common Multiple
[ HCF ] of two numbers is the
biggest number that divides exactly
into both of them.

Example;

16 and 24

4 16, 24

2 4, 6
2, 3

4x2=8
The HCF of 16 and 24 is 8

DEFINITION OF DIRECTED NUMBERS WHAT ARE THE RULES FOR DIRECTED NUM
Rule 1: If the signs are the same then add the numbers a
The numbers which have a direction and a size are original sign. Rule 2: If the signs are different then substra
called directed numbers. Once a direction is chosen minus small number. Keep the sign of the big number.
as positive (+), the opposite direction is taken as
negative (-). For example:…. For example:-15, 8,
100,-100, -3.5,0.33,-0.75 are directed numbers.
In the above example -15, 8, 100,-100 are called
integers.

HOW DOYOU ADD DIRECTED NUMBERS

TWO SIGNS
ü When adding positive numbers, count to the

right
ü When adding negative numbers, count to the

left
ü When substracting positive numbers, count

to the left
ü When substracting negative numbers, count to the

right.

MBERS

and keep the
act : Big number

WHAT IS A DENOMINATOR IN MATH ?? WHAT IS DECIMAL FRACTION??
In math, a denominator can be
defined as the bottom number in a Decimal Fraction.
fraction that shows the number of A fraction where the denominator (the
equal parts an item is divided into. It is bottom number) is a power of ten (such
the divisor of a fraction. as 10, 100, 1000, etc).You can
write decimal fractions with
What is the mixed number?? a decimal point (and no denominator),
A mixed number is a whole number, which make it easier to do calculations
and a proper fraction represented like addition and multiplication
together. ... It is thus, a mixed number. on fractions.
Some other examples of mixed
numbers are. Parts of a mixed number. CAN A FRACTION HAVE A DECIMAL??
A mixed number is formed by combining
three parts: a whole number, a numerator, You can absolutely make
and a denominator. a fraction with decimals! It's just that
it's not considered to be in standard form.
Just like you can absolutely have
fractions with a radical in the
denominator, but that's not considered to
be in standard form. Basically, if it's a
number, you can make a fraction with
it.

HOW DOYOU SIMPLFY A DECIMAL FRACTION??

Step 1:Write down the decimal divided by 1, like
this: decimal 1. Step 2: Multiply both top and
bottom by 10 for every number after
the decimal point. (For example, if there are two
numbers after the decimal point, then use 100, if
there are three then use 1000, etc.) Step
3: Simplify (or reduce) the fraction.

PERCENTAGE??
If you mean “percentage of the sum,
for each number” then by definition
the mean percentage is 100%
divided by the number of elements in

the list.

How do you calculate what percentage one number is of another?
Learning how to calculate the percentage of one
number vs. another number is easy. If you want to know
what percent A is of B, you simple divide A by B, then take
that number and move the decimal place two spaces to the
right.That's your percentage!

Chapter 4

a 3 x 6 = 18 b 12 ÷ 6 = 2 c 10 ÷ 5 = 2
d 4+5=9 e 3x3=9 f 5 + 8 = 13

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

1000 ÷ 25 = 40
40 x 85p = 3400p
3400p ÷ 100 = ＄34
No, she does not have enough.

Solution 1;
＄110 x 10% = ＄11

＄110 + 11 = ＄121 is the price that suitable for them to give rent.

Solution 2;
＄3.50 x 40 = ＄140

Yes, the shop cover its coasts.

a 1 x800  ＄200 b 2 x60  40 kilograms

4 3

c 3 x200  150 metres d 3 x48  18 litres

4 8

e 4 x30  24 minutes f 7 x120  84 kilometres

5 10

1 x60  15 1 x36  12
4 3

a 1 x40  20 b 1 x50  10

2 5
1 1

4 5

2 x15  10 5 x72  45
3 8

c 3 x12  9 d 5 x60  50

4 6
3 5

4 6

31 4 35  8 51  6

a8 8 8 b 10 10 10 c 12 12 12

44 1 8 2 4 6 6 1
82 10 5 12 2
936
d 541 52  3
e 10 10 10
88 8 f 99 9
6 2 3
10 5 3 3 1
93

3 x8* 3 x5 1 x5* 2 x2 7 * 3 x2

a5 8 b2 5 d 84

24  15  39 549 761
40 40 40 10 10 10 88 8
4 x2* 1 x5
3 x2* 3 5 * 2 x2
d5 2 5 10 63

85  3 e 639 f 541
10 10 10
10 10 10 66 6
1 2 9  3 9 (2 1)  1  1 1

10 10 66

a 1x 2= 1 b 3 x 23 c 3x1 3

23 3 4 5 10 5 2 10

d 3x22 1 1* 3  3*
58
73 7 e 53
f 3x88
42* 1x3  3
53 51 5 53 5
48* 85 13
g 4x36
h 79 5
52 5
65 11 4x9  9
7 8 14
5

1; 2; 1; 2;
1 1 x1 2 *
25  5 * b 5 x11 * 5 11 *
a 43 12 6 33
25 x 6  30 83 5x3  5
5 x 5  25 12 5 12 5x45 34 4
4 3 12 30 12  2 1 83 3 54 11

2 4

1; 2;

c 2 1 x11 * 10  3 1 *
33
23 10 x 3  1
5 x 4  10 3 10
23 3

Chapter 5

a 30 b 70 c 20 d 50 e 60
f 10 g 100 h 120 i 110 j 130

a 200 b 400 c 400 d 800 e 900
f 100 g 600 h 300 i 1000 j 1200

a 2000 b 4000 c 7000 d 4000 e 1000
f 7000 g 6000 h 9000 i 2000 j 10 000

a 4.6 b 0.09 c 5.716 d 4.56 e 2.10
f 0.763 g 7.1 h 8.91 i 23.781 j 1.0

a 3.7 b 8.7 c 5.3 d 18.8 e 0.4
f 26.3 g 3.8 h 10.1 i 11.1 j 12.0

a 6.72 b 4.46 c 1.97 d 3.49 e 5.81
f 2.56 g 21.80 h 12.99 i 2.30 j 5.56

a7 b9 c3 d8 e8
f3 g2 h2 i5 j4

a 50 000 b 60 000 c 30 000 d 90 000 e 10 000
f 50 g 90 h 30 i 100 j 200
k 0.5 l 0.3 m 0.006 n 0.05 o 0.0009
p 10 q 90 r 90 s 200 t 100

a 6700 b 36 000 c 69 000 e 27 000
f 7000 g 2200 h 960 j 330

a 50 000 b 6200 c 89.7 d 220
e8 f 1.1 g 730 h 6000
i 67 j6 k8 i 9.75
m 26 n3 o 870 p 40
q 0.085 r 0.0099 s 0.08 t 0.0620

Chapter 6

a 64  8,8 b 25  5,5 c 49  7,7 d 81  9,9
e 16  4,4
f 26  5,6 g 100  10,10 h 121  11,11

a 15 b 17 c 21 d 25

e 33 f 37 g 56 h 78

10,2 2, 20,3 2

5  40  7

square root of 40 lies between 5 and 7.

1252 = 15 625 tiles

a 4 x 4 x 4 = 64
b 9 x 9 x 9 = 729
c 11 x 11 x 11 = 1331
d 2.4 x 2.4 x 2.4 = 13.824
e -5 x -5 x -5 = -125
f -2.5 x -2.5 x -2.5 = -15.625
g -7.7 x -7.7 x -7.7 = -456.533
h 75 x 75 x 75 = 421 875

a 3 82 b 3 64  4 c 3 125  5 d 3 1000  10
c 3 27000  30 f 3  27  3 g 3 1  1 h 3  216  6
i 3  8000  20 j 3  343  7 k 3 0.729  0.9 l 3 10.648  2.2

13 = 1
23 = 8
73 = 343
93 = 729

a 3 216, 64,6 2, 4 3 b 3 1000000, 12100, 112,53

13 = 1
43 = 64
93 = 729
163 = 4096
253 = 15 625

Rule of Four

The “Rule of Four” is a way to think about math both at the entry point of a task and in the representation of math
thinking. Showing our thinking through multiple representations helps us have a stronger and deeper understanding of th
mathematics. It also allows us to see connections across concepts and topics in mathematics.

Why use the “Rule of Four”?
When we strive to represent our understand using the “Rule of Four,” we are asking ourselves to find deeper connections bot
within and across concepts. In addition, it validates multiple perspectives in mathematics.

When to use the “Rule of Four”
The “Rule of Four” is appropriate for most math work. How much it is emphasized depends on the context.

How to use the “Rule of Four”
Student may not be familiar and/or fluent with representing their work in a variety of ways. Explicit modeling from the
teacher and giving students many opportunities to practice representing their work in multiple ways is an effective way to
teach students to think about their math work in this fashion. It is equally important that students make connections
among the representations.These connections lead to a deeper understanding over time.

THE 4 RULES
OF

The meaning Of Four Agreements are: What is the golden rule for solving equations?

The four basic mathematical operations-- How do we apply the Golden Rule? First it
should be stated, that when solving for an
he addition, subtraction, multiplication, and division- unknown variable in an equation, you must
-have application even in the most advanced try to get 0 on the side with the unknown
variable in addition/subtraction (and get 1 in
mathematical theories. Thus, mastering them is one multiplication/division).

of the keys to progressing in an understanding What are the 4 basic operations of arithmetic?

of math and, specifically, of algebra. The basic arithmetic operations
are addition, subtraction, multiplicatio
th n and division, although this subject also
includes more advanced operations, such as
What are the math rules? manipulations of percentages, square
roots, exponentiation,
Rules of Ordering in Mathematics - BODMAS logarithmic functions, and even
Brackets (parts of a calculation inside brackets trigonometric functions, in the same vein as
always come first). Orders (numbers involving logarithms ( ...
powers or square
o roots). Division. Multiplication.

What are the four order of operations?

Order of Operations Four: Students play a
generalized version of connect four, gaining the
chance to place a piece on the board by
answering order of operations questions
(addition/subtraction, multiplication/division,
exponents, and parentheses).

F
GUN SAFETY

CHAPTER 4
THE FOUR RULES

ACCURANCY What d
& PRECISION
degree
CHAPTER 5 measure
ESTIMATION & LIMITS actual,
affected
OF ACCURACY designa

What is an appropriate
maths?

In maths “to an appro
accuracy” means it wan
answer in the same form
lest accurate measure i
A triangle has side meas
integer, 4.1256cm and
perimeter.

What is an example of accuracy?
Accuracy and

Precision: Accuracy refers to the closeness of a measured value to a
standard or known value. For example, if in lab you obtain a weight
measurement of 3.2 kg for a given substance, but the actual or known
weight is 10 kg, then your measurement is not accurate. ... Precision is
independent of accuracy.

WHAT IS ESTIMATION & OF ACCURACY

To describe all the possible values that a rounded number
could be, we use limits of accuracy.The
lower limit is the smallest value that would round up to
the estimated value.The upper limit is the smallest
value that would round up to the next estimated value.

do you understand by the term degree of accuracy? How do you calculate precision?

e of accuracy. • the degree of accuracy is a To calculate precision using a range of
e of how close and correct a stated value. is to the values, start by sorting the data in numerical
, real value being described. • accuracy may be order so you can determine the highest and
d by rounding, the use of significant figures. or lowest measured values. Next, subtract the
ated units or ranges in measurement. lowest measured value from the highest
measured value, then report that answer as
degree of accuracy in the precision.

opriate degree of How do you calculate appropriate degree of accuracy?
nts you to present your
m as the Appropriate degree of accuracy
in the question. For example. e.g If two sides of a right angled triangle are 1.6cm and
sures 3cm to the nearest 1.1cm, then the hypotenuse can be calculated as √(1.62 +
6.856cm.Work out the 1.12) = √(3.77) = 1.941648…… An
acceptable degree of accuracy is 1.9 but 1.94 is not
acceptable (3 significant figures).

WHAT IS VULGAR MATHS??

A vulgar fraction, common fraction or fraction

is a fraction written in the usual way which is one

number (integer) above another (integer) separated by

a line. Examples of vulgar fraction are:

1 , 5 , 200

2 11 100

If the numerator is equal to the denominator, the

fraction is equal to untiy, 7 for instance.
7

WHAT IS DECIMAL FRACTION??

Decimal Fraction.A fraction where the
denominator (the bottom number) is a power of ten
(such as 10, 100, 1000, etc).You can
write decimal fractions with a decimal point
(and no denominator), which make it easier to do
calculations like addition and multiplication
on fractions.

PERCENTAGE??

If you mean “percentage of the sum, for
each number” then by definition the mean
percentage is 100% divided by the number
of elements in the list.

THE
MEAN
AND
VULGAR
BITS

CHAPTER 6

VULGAR AND
DECIMAL FRATIONS
AND PERCENTAGE

Chapter 7

a 4+x b 7- x c k+3
d t- 8 e x +y f 4x
im
g 5t h ab
2

x  5  27
x  27  5
x  22

22 years old

Frank: 2  p  2 p
Chloe: 3  p
Lizzie: 2 p  2 p

a 7x3=21 days

b 7xz=7z

a $30 ÷ 3=$10
b $r ÷ 4= $r

4
c $p ÷ q= $ p

q

a 4(3)+3=15 b 4(6)+3=27 c 4(11)+3=47

a 3(2)-1=5 b 3(5)-1=14 c 3(10)-1=29

A 14-3(4)=2 b 14-3(6)=  4 c 14-3(10)= 16

4(2)  7 4(5)  7 4(15)  7

2 2 2

a  87 b  20  7 c  53
2 2 2

1  13  53
2 2 2

 0.5  6.5  26.5

3((2)(1)  5) 3((2)(3)  5) 3((2)(5)  5)
a  3(2  5) b  3(6  5) c  3(10  5)

 (3)(7)  (3)(11)  (3)(15)
 21  33  45

Chapter 8

a 12t b 10y c 8y d 9w
e 4t2 f 6b2 g 3w2 h 12y2
i 5p2 j 128t2 k 20m2 i 24t2

a 7tm b 5yw c 8tq d 69tn

e 30q f 10f g 18k h 35r

a t3 b p3 c 5m3 d 3r2t
e 8n3 f 20r3 g r4 h k5

a 16n5 b 12t7 c 7a7 d 3k7
e k3 f 10y2 g 18d3 h -12p6
i 5mq2 k 12m2t i 10q2p2
j 12m2y

Solution 1; Solution 2;
4000  3.5%  140
71  7
22

7  3.5%
2

After 1 week 140 bees left.

a 123 b 123 c 12m2 d 12m3

c is not equivalent to 12m3.

a combine like terms b combine like terms

 2y  5x  y  3x  4m  6 p  2m  4 p
 (5x  3x)  (2 y  y)  (4m  2m)  (6 p  4 p)
 8x  3y  2m 10 p
c combine like terms
d combine like terms
 3x  6  3x  2
 (3x  3x)  (6  2)  7 5x  2 8x
 6x  4  (8x  5x)  (7  2)
 3x  5
e combine like terms
f combine like terms
 5 p  2t  3 p  2t
 (5 p  3 p)  (2t  2t)  4 2x  4x 6
8p  (2x  4x)  (6  4)
 6x  2

a (4 p  2 p)  (4  2) b (4x  2x)  (5y  3y)
 2p 6  6x  2y

c (6t  3t)  ( p  5 p)  (4  3) d (4w  4w  2w)  (3k  k)
 3t  6 p  7  6w  4k

a (4x  3x)  (8 1) b (3y  5y)  (7  4) c (5a  a)  (3b  5b)
 x9  2y3  4a  2b

d (5c  3c)  (8d  4d ) e (7x)  (3y  5y)  (3  6) f (4n  4n)  (3b  b)
 2c  4d  7x 8y 3  2b

a (3x2-2x2)+(8-3)=x2+5 b (5a2-4a2)+(3b+2b)= a2+b
c (3k2+2k2)+(-3k+k)=5k2-2k d (3c2-3c2)+(4d-3d)= d
e (5x2-3x2)+(3y2+y2)=2x2+4y2 f (4y2-6y2)+(2z2-3z2)= -2y2-z2

Chapter 9

2x  7 1 2t  13  5 3x  17  5
a 2x  6 b 2t  8 c 3x  12

x3 t4 x4

4 y  27  7 2x  12  8 5t  27  3
d 4 y  20 e 2x  20 f 5t  30

y5 x  10 t6

1 x3363 1 p2232
2 3

g 1 3 h 1 1
2 3

2*(1)  2*3 3* 1  3*1
2 3

x6 p3

1 x3353  2k  3 13
2 k  2k  10

i 1 x 8 j x  28 k 5
2 x6

2* 1  2*8
2

x  16

 3z  0  6
l  3z  6

z2

x  4*3  4*3 y 4*5  2*5 z  4 *8  5*8
3 5 8

a x  4  12 b y  4  10 c z  4  40
y  10  4
x  12  4 z  40  4
y  14
x8 z  36

2x  2  8 3x  9  12 3t  6  9 2x 10  20
a 2x  8 2 b 3x  12  9 c 3t  9  6 d 2x  20 10

2x  6 3x  21 3t  3 2x  10
x3 x7 t 1 x5

4 y 10  14 6x  8  26 12t  4  20 2t 10  6
e 4 y  14 10 f 6x  26  8 g 12t  20  4 h 2t  6 10

4 y  24 6x  18 12t  24 2t  4
y6 x3 t2 t  2

2x 8  2 6y4 5 12k  4  11 10x 15  26
i 2x  28 j 6y 54 k 12k  11 4 l 10x  26 15

2x  6 6y 9 12k  15 10x  11
x  3 y  1.5 k  1.25 x  1.1

2x 1 x 3 3y  2  2y 6 5a  3  4a  4
a 13  x  2x b 6 2  2y 3y c  4  3  4a  5a

x2 y4 a7

5t  3  3t  9 7p 5  5p 3 6k  5  3k  20
d  9  3  3t  5t e 355p7p f  20  5  3k  6k

 2t  6  2 p  8  3k  15
t 3 p4 k 5

6m 1  m 11 5s 1  2s  7 4w  8  2w  8
g 111  m  6m h 7 1  2s  5s i 8  8  2w  4w

 5m  10  3s  6 w0
m2 s  2

5x  5  3x 10 5t 10  4t 1 4x 8  2x  2
j 10  5  3x  5x k 110  4t  5t l  28  2x  4x

 2x  5 t 9  2x  6
x  2.5 x  3

y  23  37
y  37  23
y  14
The girl is 14 years old.

x  4  6  26
4x  26  6
4x  20
x5

3x  2 y  12 3(2)  2 y  12
a 4x  y  5 2 y  12  6
2y  6
11x  22 y3
x2
4(7)  3y  37
4x  3y  37 3y  37  28
b 2x  y  17 3y  9
y3
 2x  14
x7 2(2)  3y  19
3y  19  4
2x  3y  19 3y  15
c 6x  2 y  22 y5

14x  28 5(4)  2 y  14
x2  2 y  14  20
 2 y  6
5x  2 y  14 y3
d 3x  y  9

x4

a 4x  3y  $3.35
3x  y  $2.20

4x  3y  $3.35 4(0.65)  3y  $3.35
b 3x  y  $2.20 3y  $3.35  $2.6
3y  $0.75
 5x  $3.25 y  $0.25
x  $0.65
5 cups of tea and 4 biscuits cost $4.25
5 0.65  $3.25
4 0.25  $1

6x  5y  23 6(3)  5y  23
a 5x  3y  18 5y  23 18
5y  5
 7x  21 y 1
x3
3(7)  4 y  13
3x  4 y  13  4 y  13  21
b 2x  3y  20  4 y  8
y2
17x  119
x7 8(2.5)  2 y  14
 2 y  14  20
8x  2 y  14  2 y  6
c 6x  4 y  27 y3

22x  55 5(7)  2 y  33
x  2.5 2 y  33  35
2 y  2
5x  2 y  33 y  1
d 4x  5y  23

17x  119
x7

2x  3y  $28.50
a 3x  2 y  $31.50

2x  3y  $28.50 2(7.5)  3y  $28.50
b 3x  2 y  $31.50 3y  $28.50 15
3y  $13.5
 5x  $  37.5 y  4.5
x  $7.5

CHAP
ALGEBRAIC REPRESENT

❑ ALGEBRAIC EXPRESSION : mmm
o UNKNOWN mm m
o TERM WITH ONE UNKNOWN
5M Unknown
Cofficient

1. LIKETERM

6X AND 10X

2. UNLIKETERM

12P AND 12Q

PTER 7
TATIONS AND FORMULAE

❑ Example ;

5 + 7 + 3 = 7 + 5 + 3
= 7 + 8

−2 − 5 + 3 + 5 = −5 + 5 − 2 + 3
= 0 + 1
=

4 − 4 − 2 − 2 = 4 − 2 − 4 − 2
= 2 − 6

❑ SMAR

o When the ‘+’ sign which lies before the bracke
brackets remains unchanged

o When the ‘-’ sign which lies before the bracket
brackets changes from:

‘+ to –’ ;‘- to +’

✓ -(a + b) = -a – b
✓ -(a – b) = -a + b
✓ -(-a + b) = + a – b
✓ -(-a – b) = + a + b

.

❑ Examples ; = 5 + 3 + (2 + )
2 + 5 + + 3 = 8 + 3

4 + 6 − 2 + 4 = 4 − 2 + 6 + 4
= 2 + 10

3 + 6 + 3 − 2 = 3 + 3 + (6 − 2)
= 6 + 4

RT TIPS

ets is removed, the sign for each term in the
ts is removed, the sign for each term in the

ADD & SUBSTRACT

TWO OR MORE

ALGEBRAIC

EXPRESSION

CHAPTER 8
ALGEBRAIC MANIPULATION

❑ EXAMPLE
Solve the one va

2 + 1 = 7
2 = 7 − 1
2 = 6
= 3

✓ Substract 1
✓ Divide both

Solve the two va

4 + 2 =
5 + 3 =
4 + 2 =
4 + 2 −
4 = 8 − 2

✓ You can sol
✓ Subtstitute
✓ Subtitute -2

❑ EXAM
Solve the simult
❑ EXAMPLE

6x+5y=23
5x+3y=18
-7x= -21
X=3

✓ First make t
✓ Second subs
✓ Third divid
✓ Fourth sub

; CHAPTER9
ariables ;

SOLUTIONS OF EQUATIONS AND INEQUALITIES

7

1

1 from both sides. = 3 = −2
h sides by 2.

ariables ;

8
9
8
2 = 8 − 2
2

lve this system by elimination or substitution
−21y + 2 for x in 5 + 3 = 9
2 for y in x = −21y+2

MPLES ; + = ∗ = −
taneous equations ; ∗ =
; ∗ =

6(3)+5y=23
5y=23-18
5y=5
y=1

the ‘y’ has a same number. If the number different then multiply it till it have the same number.
stract both equations if the sign same. If the equations have different sign then add.
de if there has more then 1 value
the value to the next equation and so on so you will get the value of x and y