O Level – Elementary Mathematics

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Factorization

Some useful identities

a^2 + 2ab + b^2 = (a + b)^2

a^2 – 2ab + b^2 = (a – b)^2

a^2 – b^2 = (a+b)(a-b)

a^3 + b^3 = (a+b)(a^2-ab+b^2)

a^3 – b^3 = (a-b)(a^2+ab+b^2)

From O-Level Elementary Mathematics Singapore Tutor

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Investigative Problems & Number Patterns

Problem Solving

1. Reading and understanding the problem.

2. Choosing an appropriate strategy to solve the problem.

3. Apply the strategy.

4. Check the answer and looking back.

Some of the common strategies used in solving mathematics problems are:

1. Simplify the problem
2. Draw a diagram or table
3. pattern recognition
4. Trial and error
5. Use of algebra
6. Exhaustive listing
7. Use of models
8. Work backwards
9. Solve part of the problem
10. Eliminate the unlikely possibilities

From O-Level Elementary Mathematics Singapore Tutor

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Simple Probability

Definition
If an event A can happen in m ways of n equality likely ways, then the probability or chance of n happening denoted by P(A) is defined as
P(A) = m/n

Probability that event A occurs
=(number of outcomes favorable to the event of A)/(Total number of equality possible outcomes)

Properties of Probability
1. If A is an impossible event, then P(A)=0
2. If A is a sure event, then P(A)=1
3. if A is any events
P(A)smaller or equal to 1
P(A)greater or equal to 0

From O-Level Elementary Mathematics Singapore Tutor

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Investigation Problem

1+2+3+4………..+n =(1/2)(n)(n+1)

General term Tn = a + (n-1)d
a = first term
d= common difference

Triangular numbers
1
3 = 1+2
6 = 1+2+3
10 = 1+2+3+4

From O-Level Elementary Mathematics Singapore Tutor

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Greatest and Smaller Values

If X is between 2 and 10
If Y is between 1 and 15
Both X and Y are positive number

Max (X+Y) = 10+15 = 25
Min (X-Y) = 2-15 = – 13

Max (X-Y) = 10-1 = 9
Min (X-Y) = 2-1 = 1

Max (XY) = 10*15 = 150
Min (XY) = 2*1 = 2

Max (X/Y) = 10/1 = 10
Min (X/Y) = 2/15

From O-Level Elementary Mathematics Singapore Tutor

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Transformation Part 1

1. Reflection
A reflection is a transformation which reflects all points of a plane in a line (on the plane)called the mirror line.

2. Rotation
A rotation is a transformation which rotates all points on a plane about a fixed point (called the centre of rotation)through a given angle in anti-clockwise or clockwise direction. The angle through which the points are rotated is called the angle of rotation.

From O-Level Elementary Mathematics Singapore Tutor

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Transformation Part 2

1. Translation
A translation is a transformation which moves all points in a plane through the same distance in the same direction

2. Enlargement
An enlargement, centre O and scale factor k is a transformation which enlarges a given figure k times the original size.

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching Graphs of y = ax^n

S4 – Revising Bar Charts, Pie Charts, Pictogram and practice P1 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching Graphs of y = ax^n

S4 – Revising Bar Charts, Pie Charts, Pictogram and practice P1 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching geometrical properties of angles, angle properties of polygon and symmetry.

S4 – Revising frequency distribution, histograms, Mean, median and mode and practice P2 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching Similarity and Congruency, Area and Volumes of similar figures

S4 – Revising simple probability and practice P1 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching Geometrical Properties of Circles

S4 – Revising Vectors in Two Dimensions and practice P2 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching Trigonometry 1

S4 – Revising Probability and practice P2 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Teaching Trigonometry 2

S4 – Revising Statistics – Frequency Table, Bar Charts, Pie Charts, line graph, Pictograms, Dot diagrams, Stem and leaf diagrams,Histograms and practice P1 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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S3 – Practice exam questions focusing on simultaneous equations

S4 – Revising Statistics – Mean, Median,and Mode and practice P2 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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