Quick Notes Math Form 2

Quick Notes






Mathematics Form 2






Chapter 1 - 4

Chapter 1:Patterns and Sequences


1.1 Patterns Patterns are list of numbers or objects 1.2 Sequence Sequence is a set of numbers
arranged based on a rule or design. or objects which follows a
certain patterns.
Patterns of various set of numbers
(i) Even numbers and odd numbers Pattern: Add 4
- Even numbers are referring to the numbers that are Therefore, the set of
divisible by 2 number is a sequence
Example:
2,4,6,8,10,12,14,....2,4,6,8,10,12,14,....
- Odd numbers are referring to the numbers that are not 1.3 Patterns and Sequence
divisible by 2. The pattern of a sequence is the rule or design of the sequence
Example: Patterns of a sequences
1,3,7,9,11,13,15,...1,3,7,9,11,13,15,...
(i)Numbers – Example 3, 6, 9,12, 15,……. Pattern: Addition
of 3
(ii)Pascal's Triangle (ii) Words – Example 1,9,17,25,33,...
• To build Pascal's Triangle, Therefore, the pattern for the above sequence is add 8 to
always start with 1 at the top. the previous number
• All rows will start 1 and end (iii) Algebraic expressions - It is an expression which has a
with 1.
• The number on the next row is combination of basic mathematical operations on
determined by adding the numbers, variables or other mathematical entities.
numbers on the previous row. 3,6,9,12,15,...
It is written as 3n where n=1,2,3,…
Terms of a sequence
th
The n term is a number sequence and is written as Tn
(iii) Fibonacci Numbers whereby T is the term and n is the position of the term.
• It is a pattern of numbers in a th
sequence. T = n term
n
• The sequence starts with Example
4,8,12,16
0,1,10,1,1. T1 = 4 Tn= a+(n-1)d
• The next term is obtained by T2 = 8 or Where,
adding the two previous terms. a – first term
T3 = 12 n – number of term
T4 =16 d - pattern

Chapter 2: Factorisation and Algebraic Fractions



Expansion of algebraic expression is 3. Using Cross Multiplication
2.1 Expansion the product of multiplication Algebraic expressions of ax + bx + c , where a ≠ 0 and a, b, c
2
of one or two expressions in brackets. are integer that can be factorised

1. Expansion on Two Algebraic Expressions Example : m2 -2m -8
• When doing an expansion of algebraic expressions, every m 2 2m
term within the bracket needs to be multiplied with the term (x) (x) (+)
outside the bracket. m -4 4m
- Example: a(x+y) = (a×x)+(a×y) m 2 -8 -2m
= ax+ay. Hence, (m+2)(m-2)
4. using common factor involving 4 algebraic terms
'B =Brackets 2. Combined Operations including
O=Order Expansion
D=Division Combine operations for algebraic 1 : Group 2px + 6qy – 4py – 3qx
st
terms with
M=Multiplication terms must be solved by following the
nd
A =Addition BODMAS' rule. common = (2px – 4py) – (3qx + 6qy) 2 : Find
= 2p(x-2y) -3q(x-2y)
Common
S=Subtraction Examples: factors in = (x-2y)(2p – 3q) factors
a bracket
a. (m+n)(x+y)=mx+my+nx+ny.
b. y(x+z) = yx+yz
2.2 Factorisation A process of determining the factors of 2.3 Algebraic Expression and Basic Arithmetic Operations
an algebraic expression or algebraic
terms and when multiplied together will Addition and Subtraction Multiplication and Division
(i)Factor form the original expressions. of Algebraic Expressions 2. Factorise expressions before
A number or quantity that Also known as the reverse process of division or multiplication
RULES!!
when multiplied with expansion. 1. Before adding or when it is necessary
another produces a given 7 7x + 35 subtracting two algebraic
number or expression. 1. Using HCF x + 5 HCf: 7 fractions, check the
(ii)Common factor Factorise 7x + 35 denominators first.
2. If they are not the same,
The factor of an algebra 2. Using difference of squares of two terms you need to express all 3.
term that divides two or This method can only be used if the two fractions in terms of common
more other terms exactly. algebraic terms are perfect squares denominators
2
2
(iii)Highest Common a – b 9m – 100
2
2
Factor (HCF) = (a) – (b) 2 = (3m) – (10) 2 1.
2
The largest of those = (a+b)(a-b) = (3m+10) (3m–10)
common factors.

Chapter 3 : Algebraic Formulae



3.1 Algebraic Formulae



Definition



It is written in the form of an equation that combines an algebraic expression using addition, subtraction,
multiplication or division.




1. Forming Formula 2. Changing the subject of the 3. Determining the value of the
Examples formula variable
• The value of a variable in the
1. • The subject of the formula is subject of the formula can be
represented by a letter.
• The subject of the formula should obtained when the value of
other variables is given.
be on the left side of the equation.
2.




3.




4.


• y,w,l and a are subjects of formula.
• A variable in formula can be
represented by letters a to z.

Chapter 4 : Polygon











4.1 Regular Polygon 4.2 Interior Angles and
Exterior Angels od Polygon

•Regular polygons are polygons for which all sides
are equal and all interior angles are of the same size.
•It also has congruent angles.
•Irregular polygons are polygons with irregular sides.

Polygon Number of sides Number of sides
(n)
od symmetry

Pentagon 5 5


Hexagon 6 6 Interior Angles Exterior Angles


•It is an angle that is formed
Heptagon 7 7 •It is an angle that is shaped when one side of the
by two adjacent sides of a polygon is extended.
polygon. •It is also known as a
Octagon 8 8 •Angle a,b and c are complement to an interior
interior angles angle of the polygon.
•Interior angle = (n-2) x 180 0 •Exterior angle = 360 0
Nonagon 9 9 n n
• Total sum of interior angles • Total sum of exterior
of a polygon = (n-2) x 180 0 angles = 360 0
Decagon 10 19 • Number of sides, n =
360 0
exterior angle
•