# GCE O-Level Maths Help & Practice

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##### 1Numbers and Relations

##### 2Number Theory

##### 3Adding and Subtracting Integers

##### 4Multiplying and Dividing Integers

##### 5Operations with decimals

##### 6Adding and Subtracting Fractions

##### 7Multiplying and Dividing Fractions

##### 8Ratios, Rates, and Proportions

##### 9Percents

##### 10Solving Linear Equations

##### 11Linear Inequalities

##### 12Measuring Systems

##### 13Number Systems

##### 14Surds

##### 15Direct and Inverse Proportion

##### 16Algebraic Expressions

##### 17Linear Functions

- 17.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 17.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 17.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 17.4Gradient intercept form: y = mx + b
- 17.5General form: Ax + By + C = 0
- 17.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 17.7Rate of change
- 17.8Graphing linear functions using table of values
- 17.9Graphing linear functions using x- and y-intercepts
- 17.10Graphing from slope-intercept form y=mx+b
- 17.11Graphing linear functions using a single point and gradient
- 17.12Word problems of graphing linear functions
- 17.13Applications of linear relations

- 17.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 18Simultaneous Equations

- 18.1Determining number of solutions to linear equations
- 18.2Solving simultaneous linear equations by graphing
- 18.3Solving simultaneous linear equations by elimination
- 18.4Solving simultaneous linear equations by substitution
- 18.5Money related questions in linear equations
- 18.6Unknown number related questions in linear equations
- 18.7Distance and time related questions in linear equations
- 18.8Rectangular shape related questions in linear equations

- 18.1Determining number of solutions to linear equations
##### 19Factorising Quadratic Functions

- 19.1Factorise by taking out the greatest common factor
- 19.2Factorise by grouping
- 19.3Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 19.4Factorising difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 19.5Factorising trinomials
- 19.6Solving polynomials with unknown coefficients
- 19.7Solving polynomials with unknown constant terms

- 19.1Factorise by taking out the greatest common factor
##### 20Quadratic Functions

- 20.1Introduction to quadratic functions
- 20.2Transformations of quadratic functions
- 20.3Quadratic function in general form:
*y = ax^2 + bx + c* - 20.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 20.5Completing the square
- 20.6Converting from general to vertex form by completing the square
- 20.7Shortcut: Vertex formula
- 20.8Graphing quadratic functions: General form VS. Vertex form
- 20.9Finding the quadratic functions for given parabolas
- 20.10Applications of quadratic functions

- 20.1Introduction to quadratic functions
##### 21Solving Quadratic Equations

##### 22Algeraic Fractions

- 22.1Simplifying algebraic fractions and restrictions
- 22.2Adding and subtracting algebraic fractions
- 22.3Multiplying algebraic fractions
- 22.4Dividing algebraic fractions
- 22.5Solving equations with algebraic fractions
- 22.6Applications of equations with algebraic fractions
- 22.7Simplifying complex fractions
- 22.8Partial fraction decomposition

- 22.1Simplifying algebraic fractions and restrictions
##### 23Laws of Indices

##### 24Exponential Functions

##### 25Vectors

##### 26Matrices

##### 27Geometry and Measurement

##### 28Scale Factors and Similarity

##### 29Congruent Triangles

##### 30Angles, Lines, and Transversals

##### 31Circles

##### 32Surface Area and Volume

##### 33Trigonometry

- 33.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 33.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 33.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 33.4Combination of SohCahToa questions
- 33.5Solving expressions using 45-45-90 special right triangles
- 33.6Solving expressions using 30-60-90 special right triangles
- 33.7Word problems relating ladder in trigonometry
- 33.8Word problems relating guy wire in trigonometry
- 33.9Other word problems relating angles in trigonometry

- 33.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 34Angle Measure in Radian

##### 35Sine Rule and Cosine Rule

##### 36Bearings

##### 37Set Theory

##### 38Data and Graphs

##### 39Representing Data

##### 40Statistics

##### 41Probability