O Level – Elementary Mathematics

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Arithmetic

1. Real numbers : {1,2,3,4,5,……..}
2. Whole numbers : {0,1,2,3,4,……..}
3. Integers : {……..-3,-2,-1,0,1,2,3,……..}
4. Negeative integers : {-1,-2,-3……..}
5. Postive integers : {1,2,3,4,5,……..}
6. Even numbers : {2,4,6,8,……..}
7. Odd numbers : {1,3,5,7,……..}
8. Prime numbers : {2,3,5,7,11,13,17,……..}

Prime numbers are natural numbers that have exactly two factors, 1 and itself

9. Rational numbers : {1/8, 1/2, 1,3,51/2,……..}

Rational numbers are numbers that can be written as a fraction, a/b where a and b are integers and b cannot be 0.

10. Irrational numbers : {root 2, root 5, pie……..}

Irrational numbers are numbers that cannot be expressed as exact fractions.

11. Perfect squares : {1,4,9,16,25,36,……..]

12. Real numbers are made up of rational and irrational numbers.

NOTE
ZERO is neither odd or even and is neither positive or negative.

From O-Level Elementary Mathematics Singapore Tutor

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Mensuration

Area of rectangle = Length x Breadth

Area of triangle = 1/2 x base x height

Area of parallelogram = base x height

Area of trapezium = 1/2 x ( sum of parallel sides ) x height

Area of rhombus = base x height

Area of cirle = 1/2 x pie x rrdius ^ 2

From O-Level Elementary Mathematics Singapore Tutor

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Coordinate Geometry

1) A (X1, Y1) and B (X2, Y2)

AB = Sq rt

2) Mid point M

3) Gradient = rise / run

4) Equation of straight line y = mx + c

From O-Level Elementary Mathematics Singapore Tutor

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Method of Proving Triangles are Congruent

1. All the corresponding sides are equal (SSS)
2. Two sides and the included angle are equal (SAS)
3. Two angles and a corresponding side ar equal (ASA)
4. Both triangles have a right angle , equal hypothenuse and another side is equal (RHS)

From O-Level Elementary Mathematics Singapore Tutor

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Investigative Problems

1+2+3+4+5………….+n = (1/2)(n)(n+1)

General Term = first term + (n-1)common different

Trianglular numbers
1, 3, 6, 10,………
1, 1+2, 1+2+3, 1+2+3+4,……….

From O-Level Elementary Mathematics Singapore Tutor

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Please be inform 2013 E Maths schedule has been posted on the class schedule.

From O-Level Elementary Mathematics Singapore Tutor

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Starting New Classes!

S3 E Math Class starting 5 Jan 2013 – Sat 11 am to 12.30 pm
S4 E Math Class starting 10 Jan 2013 – Thu 6 pm to 8 pm

From O-Level Elementary Mathematics Singapore Tutor

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Coordinate Geometry

Distance between two points A(x1,y1) and B(x2,y2)
AB = Sq rt (x2-x1)^2 + (y2-y1)^2

Midpoint M of the line joining two points A(x1,y1) and B(x2,y2)
Midpoint M = ( (x1+x2/2 , (y1+y2)/2 )

Gradient m of the line passing through two points A(x1,y1) and B(x2,y2)
m = (y2-y1)/(x2-x1)

When 3 points A B and C are collinear
Gradient of AB = Gradient BC

Equation of straight line
y = mx + c
or
y-y1 = m(x-x1)

From O-Level Elementary Mathematics Singapore Tutor

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Variations

Direct variation
If y is directly proportional to x^2
y = kx^2 where k is a constant

Inverse variation
If y is inversely proportional to x
y = k/x where k is a constant

Joint variation
if y is directly proportional to X^2 and inversely proportional to z
y = kz/x^2

From O-Level Elementary Mathematics Singapore Tutor

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Simple Interest

Interest, I = (PRT)/100
Where P = Principal
R = Interest Rate per yr in %
T = Time in yr

From O-Level Elementary Mathematics Singapore Tutor

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Significant figures

1. All non-zero digits are significant.
2. A zero (zeroes) between non-zero digits is (are) significant
3. In a whole number, zeros after the last non-zero digit may or may not be significant.
4. In a decimal, zeros before the first non-zero digit are NOT significant
5. In a decimal, zeros after the non-zero are significant

Examples
7006 = 7000 (1 sf)
7006 = 7000 (2 sf)
7006 = 7010 (3 sf)
7436 = 7000 (1 sf)
7436 = 7400 (2 sf)
7436 = 7440 (3 sf)

0.00609 = 0.006 (1 sf)
0.00609 = 0.0061 (2 sf)
6.009 = 6.01 (3 sf)

From O-Level Elementary Mathematics Singapore Tutor

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Units

Length
1 m = 100 cm
1 km = 1000 m

Area
1 m^2 = 100^2 cm^2
1 km^2 = 1000^2 m^2
1 hectare = 100^2 m^2
1 km^2 = 100 hectares

Volume
1 m^3 = 100^3 cm^3
1 litre = 1000 ml = 1000 cm^3

Mass
1 kg = 1000 g
1 g = 1000 mg
1 tonne = 1000 kg

From O-Level Elementary Mathematics Singapore Tutor

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Density

The density of a substance is the mass per unit volume of the substance

Density = Mass/Volume

Units are g/cm^3 or kg/m^3

Profit and Loss

Profit = Selling Price – Cost Price

Loss = Cost Price – Selling Price

Profit % = Profit/Cost Price x 100%

Loss % = Loss/Cost Price x 100%

From O-Level Elementary Mathematics Singapore Tutor

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Simple Interest

I = (PRT)/100

I = simple interest
P = principal amount
R = interest rate per annum
T = period of time in year

Compound Interest

Example
Mr Lim took a loan of $10,000 from a bank for 3 years at a rate of 8%. What is the compound interest?

First year, 1000*8/100 = $80
Second year, 1080*8/100 = $86.40
Third year, 1166.4*8/100 = $93.312

Compound interest = 80+86.40+93.312 = $259.712

From O-Level Elementary Mathematics Singapore Tutor

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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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