Elementary Mathematics SA2 Overall Revision Notes
Chapter: All Chapters in Secondary 1
Secondary 1 Important Information
Part 1.1: Significant Figures
Include 1 extra digit for consideration. Exclude it if less than 5, add 1 more to previous digit if more than 5.
All non-zero figures are significant. (45152461.1257129507124057104517205)
Zeros that lie between non-zero figures are significant. (9.900000000000000000000000000009)
Zeros occurring after the decimal point but not followed by a non-zero digit are significant.
Zeros which do not come after a non-zero figure are not significant.
Always leave your answer in 3 significant numbers in exam papers unless otherwise stated.
Part 1.2: Types of numbers
Integers: Whole numbers. Example: 1, 2, 3, -1, -2, -3, 0. Surds and Fractions are not whole numbers.
Zero is neither a positive or negative number.
Rational numbers: Numbers that can be expressed in the form of (a/b) (a fraction)
Prime Numbers: Numbers that only have 2 different factors, 1 and the number itself, is a prime number
The absolute number of a positive number is itself, absolute number of a negative number is its opposite number.
Part 1.3: Types of Angles
Acute angles < 90° (Right Angle) < Obtuse angle (91° and 179°) < Reflex angles (180° and 360°)
Angles that add up to 90° are complementary angles.
Angles that add up to 180° are supplementary angles.
Adjacent angles on a straight line add up to 180°.
Vertically Opposite angles exist where 2 straight lines intersect. Name of polygon No. of sides
Angles that have the same vertex are called angles at a point. They add up to 360° Triangle 3
Quadrilateral 4
Part 1.4: Polygons Pentagon 5
Polygons are figures joined by 3 or more plane figures. Hexagon 6
Sum of interior angles of a polygon with n-sides: (n-2) x 180°. Heptagon 7
Sum of exterior angles of a polygon is 360°. Octagon 8
A regular polygon is a polygon with all interior sides equal with sides of the same Nonagon 9
length. Decagon 10
The various types of polygons: n-sided gon n
Part 1.5: Area of 2D Figures
Figure Formula
Square / Rectangle bh
Triangle 1
bh
2
Circle  r2
Trapezium 1
( a  b) h
2
Parallelogram bh
Circum. Of circle d

Elementary Mathematics SA2 Overall Revision Notes
Chapter: All Chapters in Secondary 2
Secondary 2 Important Information
Chapter 2.1: Algebraic Manipulation Chapter 2.2: Direct and Inverse Proportion
and Simplification
In direct proportion, when 1 proportion increases, the other
quantity will also increase, likewise if one decreases, the other will
(a  b) 2  a 2  2ab  b 2 also decrease.
If y is directly proportional to x, then y  kx (Where k is a constant
(a  b) 2  a 2  2ab  b 2
number)
(a  b)( a  b)  a 2  b 2 In inverse proportion, when 1 quality increases, the other quantity
decreases. When 1 quantity decreases, the other quantity increases;
but the products of the 2 quantities are constant
Chapter 2.3: Pythagoras Theorem k
If y is inversely proportional to x, then y  (where k is constant)
c a b
2 2 2 x
c  a2  b2 Chapter 2.4: Calculating Interest
Simple Interest: P x I x N
a  c b
2 2
Compound Interest: p(1  n)t
Where P = Sum of Money, T = Time, N = Interest Rate
Chapter 2.5: Volume and Surface Area of Chapter 2.6: Set Notation
Simple Figures and Solids  : Element of
Cylinders  : Not a element of
Surface area 2 r 2  2 rh
n(a) : The number of elements in a Set
Volume  r 2h
 : A proper subset
1 2
Cones Volume r h  : A subset
3
Surface Area  r 2   rl or  r (1  r )  or {} : Empty Set
L is the slant length.  : Universal Set
1 A': Complement of a Set
 Base Area  h
Volume
Pyramids 3 : Union of 2 Sets (dont repeat element)
Height is straight height
Base Area x Total Area of : Intersection of sets
Surface Area
slant faces
4 3
Volume r Chapter 2.7: Probability
Spheres 3
Surface Area 4 r 2 P( E ) 
No. of favourable outcomes for Event E
2 3 Total number of outcomes
Volume r
3
FYI:
Hemisphere 3 r 2
Surface Area Curved surface area: There are 4 suits in a pack of 52 playing cards, hearts,
2 r 2
diamonds, clubs and spades.
 Each suit have 13 cards: Ace, 2…10, Jack, Queen, King.
 ALL Spades and Clubs are black, all hearts and diamonds
are red.
 Picture cards include Jack, Queen, Kings. Therefore there
are 3 x 4 = 12 picture cards.
 In a pack of 54 playing cards, there are 2 extra jokers.

Elementary Mathematics SA2 Overall Revision Notes
Secondary 3 Chapters 1 – 5
Indices, Quadratic Equations, Coor. Geo and Linear Equalities
Part 3.1: The Law of Indices Part 3.2: Solving Quadratic Equations
Multiplication Laws a m  a n  a m  n
a m  bm  (ab)m
Cross x2  x  6
Method
Division Laws a m  a n  a mn x( x  1)  6
a x  6 or x  1  6
a m  bm  ( )m
b x5
Power Law (a )  a
m n mn Completing y  x 2  6 x  11
the Square
Zero a0  1 6 6 6
y  x 2  2 x( )  ( ) 2  11  ( ) 2
Negative Indices 1 2 2 2
an 
an y  ( x  3) 2  20
x Quadratic b  b 2  4ac
x(a  n ) 
an Formula
2a
Fractional Indices m
a n  n a m  ( n a )m
Part 3.3: Sketching Graphs of Quadratic Equations
y  ( x  h)2  k y  ( x  a)( x  b)
Identify shape of curve Look for sign in front of (x – h) to Look at the formula ax 2  bx  c . If a >1,
determine if it is U-shaped or not. it’s positive. Otherwise it’s negative.
Find turning point (h, k ) ab
, sub answer into equation. (a, b)
2
Find y-intercept Sub x = 0 into the equation. (0, y )
Line of symmetry, reflect x  h , reflect to get (2 x, y) x  a , reflect to get (2a, y)
Part 3.4: Coordinate Geometry Part 3.5: Linear Inequalities
Length of line 1.) If a < b and b < c, then a < c.
( y2  y1 )2  ( x2  x1 ) 2
segment 2.) If a < b, then for a real number c, a + c < b + c and
Gradient y2  y1 a–c<b–c
x2  x1 3.) If a and b are real numbers and c is a positive real
Note: Gradient of straight line = number, ac <bc and a/c < b/c
0, Gradient of vertical line is When dividing both sides of an inequality by a
undefined. positive number, the sign remains unchanged.
Equation of y  mx  c
4.) Let a and b be any real numbers. If a < b, for a
line m = gradient, c = y-intercept
negative real number c, ac >bc and a/c > b/c
When m is negative, graph is in
this shape: The inequality sign is reversed when both sides
are multiplied or divided by a negative number.
Alternatively, just swop the positions of the
numbers (recommended).

Elementary Mathematics SA2 Overall Revision Notes
Secondary 3 Chapters 6 – 9B
Congruency/Similarity, Area/Vol of Similar Objects, Trigonometry
Part 3.6: Corguency and Similarity
SSS (3 sides) All 3 sides are equal.
Congruency
SAS (Side – Angle – Side) 2 sides are equal, included angle equal.
(3 tests
AAS (Angle – Angle – Side) 2 angles equal, included side equal.
required)
RHS (Right – Angle Hyp. Side) Longest side of triangle equal, 1 angle equal.
Similarity (2 RRR (3 Sides) 3 sides equal proportions
tests AAA (3 Angles) 3 angles equal
required) RAR (Ratio – Angle – Ratio) 2 sides equal proportion, included angle equal.
Part 3.7: Area and Volume of Similar Figures and Solids
Use for area / surface area Use for volume / mass
If Area=A and Length=l , If Volume=V and Length=l ,
2 3
A1  l1  V1  l1 
   
A2  l2  V2  l2 
Remember to know the format for presentation! Refer to appendix 1 for more info.
Part 3.8: Trigonometry, Further Trigonometry, Applications of Trigonometry
Trigonometry Opposite BC Adjacent AB Opposite BC
Ratios (TOA CAH sin    cos    tan   
SOH) Hypotenuse AC Hypotenuse AC Adjacent AB
Trigo ratios for sin   sin(180   ) cos    cos(180   )
obtuse angles
1 1 1
Area of triangle ab sin C bc sin A ac sin B
2 2 2
a b c sin A sin B sin C
Sine Rule    
sin A sin B sin C a b c
a  b  c  2bc cos A
2 2 2
b  a  c  2bc cos B
2 2 2
c  b  a  2bc cos C
2 2 2
Cosine Rule b c a
2 2 2
a c b
2 2 2
a 2  b2  c2
cos A  cos B  cos C 
2bc 2bc 2bc
Angle of elevation is the angle between the line of sight and line when object is above the observer.
Angle of Elevation
Angle of depression is the angle between the horizontal line and the line of sight when object is
and Depression
below the observer.
A bearing is an angle that tells the direction of 1 place from another.
Bearings Bearings are always measured from the North, measured in clockwise and written as 3 digits. (Note:
For angles with 2 digits, write 0 in front). Remember to put degrees.

Elementary Mathematics SA2 Overall Revision Notes
Secondary 3 Chapter 10
Symmetry Properties of Circles
1. A chord is a line formed by joining 2 points on the circumference of a circle. (the red
line)
2. A chord divides a circle into 2 segments: A is the minor segment and B is the major
segment.
3. Arcs are part of a circumference of a circle.
4. The part of a circle’s area between the arc is known as a sector.
1. Perpendicular Bisecting 2. Equal chords are
Chord: equidistant from the centre
If OM is perpendicular to of circle:.
AB,
AM = MB. If AB = CD, then OX = OY.
Likewise, if OX = OY, AB =
CD.
Equal chords, equidistant from centre.
3. Tangent at a point: A 4. Tangents from an external point:
tangent (a line which Tangents drawn from an external point to a circle
touches the circle at 1 are equal in length.
point) is
perpendicular to the
 PA  PB
radius of the circle at Tangents subtend equal angles at centre,
the point of contact. POA  POB
Line OP bisects the angle between the tangents,
OB is perpendicular
to AC APO  BPO
OBA  OBC  90o (Tangent perpendicular to radius)
5. Angle at the Centre of a Circle: An
angle at the centre of a circle is twice
any angle at the circumference
subtended by the same arc.
 at circle =
2   at circumference
6. Angle at the 7. Angle in Semicircle: If AB is the 8.
Circumference of a diameter of the circle APB, then Opposite Angles of Cyclic Quadrilateral:
Circle: Angles in APB  90o The opposite angles add up to 180 degrees.
the same segment Opp s of quad
of a circle are
equal.  in a semicircle = 90 o
= s in opp. segment
If a line is extended to E
from DC, angle A = angle
BCE. (Exterior angle of a
cyclicquad
s in the
same segment

Elementary Mathematics SA2 Overall Revision Notes
Secondary 3 Chapter 11
Arc Length, Sector Area and Radian Measure
Chapter 11.1: Introduction Chapter 11.2: Radian Measure
1. Radian is another common unit to measure
angles.
2. A radian is a measure of the angle subtended at
the centre of a circle by an arc equal in length to
the radius of the
circle.
3. To convert radians to degrees and vice versa, use
these formulas:
 rad  180
1. Arcs are part of a circumference of a circle.
180
1rad 
2. The part of a circle’s area between the arc is known as a 
sector. 
1  rad
180
3. A chord is any line segment that joins 2 points on a circle.
4. Segments are formed when chords divide the circle into
different parts.
Chapter 11.3: Arc Length, Area of Sector and Area of Segment
Degree Measure Radian Measure

x
Length of arc Length of arc   2 r Length of arc, s  r
360
x 1
Area of sector Area of sector   r2 Area of sector  r 2
360 2
Area of segment APB
Area of segment APB  Area of sector OAPB  Area of OAB
Area of segment
 Area of sector OAPB  Area of OAB 1 1
= r 2  r 2 sin 
2 2