# GCE O-Level A Maths Help & Practice

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##### 1Solving Linear Equations

##### 2Linear Inequalities

##### 3Measuring Systems

##### 4Number Systems

##### 5Direct and Inverse Proportion

##### 6Algebraic Expressions

##### 7Surds

##### 8Linear Functions

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 8.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 8.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 8.4Gradient intercept form: y = mx + b
- 8.5General form: Ax + By + C = 0
- 8.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 8.7Rate of change
- 8.8Graphing linear functions using table of values
- 8.9Graphing linear functions using x- and y-intercepts
- 8.10Graphing from slope-intercept form y=mx+b
- 8.11Graphing linear functions using a single point and gradient
- 8.12Word problems of graphing linear functions
- 8.13Applications of linear relations

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 9Factorising Quadratic Functions

- 9.1Factorise by taking out the greatest common factor
- 9.2Factorise by grouping
- 9.3Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 9.4Factorising difference of squares:
*x^2 - y^2* - 9.5Factorising trinomials
- 9.6Solving polynomials with unknown coefficients
- 9.7Solving polynomials with unknown constant terms

- 9.1Factorise by taking out the greatest common factor
##### 10Quadratic Functions

- 10.1Introduction to quadratic functions
- 10.2Transformations of quadratic functions
- 10.3Quadratic function in general form:
*y = ax^2 + bx + c* - 10.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 10.5Completing the square
- 10.6Converting from general to vertex form by completing the square
- 10.7Shortcut: Vertex formula
- 10.8Graphing quadratic functions: General form VS. Vertex form
- 10.9Finding the quadratic functions for given parabolas
- 10.10Applications of quadratic functions

- 10.1Introduction to quadratic functions
##### 11Quadratic Equations and Inequalities

##### 12Algebraic Fractions

- 12.1Simplifying algebraic fractions and restrictions
- 12.2Adding and subtracting algebraic fractions
- 12.3Multiplying algebraic fractions
- 12.4Dividing algebraic fractions
- 12.5Solving equations with algebraic fractions
- 12.6Applications of equations with algebraic fractions
- 12.7Simplifying complex fractions
- 12.8Partial fraction decomposition

- 12.1Simplifying algebraic fractions and restrictions
##### 13Simultaneous Equations

- 13.1Determining number of solutions to linear equations
- 13.2Solving simultaneous linear equations by graphing
- 13.3Solving simultaneous linear equations by elimination
- 13.4Solving simultaneous linear equations by substitution
- 13.5Money related questions in linear equations
- 13.6Unknown number related questions in linear equations
- 13.7Distance and time related questions in linear equations
- 13.8Rectangular shape related questions in linear equations
- 13.9Simultaneous linear equations
- 13.10Simultaneous linear-quadratic equations
- 13.11Simultaneous quadratic-quadratic equations

- 13.1Determining number of solutions to linear equations
##### 14Inequalities in Two Variables

##### 15Laws of Indices

##### 16Polynomial Functions

##### 17Binomial expansions

##### 18Exponential Functions

##### 19Logarithms

- 19.1What is a logarithm?
- 19.2Converting from logarithmic form to exponential form
- 19.3Evaluating logarithms without a calculator
- 19.4Common logarithms
- 19.5Natural log: ln
- 19.6Evaluating logarithms using change-of-base formula
- 19.7Converting from exponential form to logarithmic form
- 19.8Solving exponential equations with logarithms
- 19.9Product rule of logarithms
- 19.10Quotient rule of logarithms
- 19.11Combining product rule and quotient rule in logarithms
- 19.12Evaluating logarithms using logarithm rules
- 19.13Solving logarithmic equations
- 19.14Graphing logarithmic functions
- 19.15Finding a logarithmic function given its graph

- 19.1What is a logarithm?
##### 20Modulus Functions

##### 21Vectors

##### 22Matrices

##### 23Trigonometric Ratios and Angle Measure

- 23.1Angle in standard position
- 23.2Coterminal angles
- 23.3Reference angle
- 23.4Find the exact value of trigonometric ratios
- 23.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 23.6Unit circle
- 23.7Converting between degrees and radians
- 23.8Trigonometric ratios of angles in radians
- 23.9Radian measure and arc length

- 23.1Angle in standard position
##### 24Sine Rule and Cosine Rule

##### 25Bearings

##### 26Graphing Trigonometric Functions

##### 27Applications of Trigonometric Functions

##### 28Trigonometric Identities

##### 29Solving Trigonometric Equations

- 29.1Solving first degree trigonometric equations
- 29.2Determining non-permissible values for trig expressions
- 29.3Solving second degree trigonometric equations
- 29.4Solving trigonometric equations involving multiple angles
- 29.5Solving trigonometric equations using pythagorean identities
- 29.6Solving trigonometric equations using sum and difference identities
- 29.7Solving trigonometric equations using double-angle identities

- 29.1Solving first degree trigonometric equations
##### 30Inverse Trigonometric Functions

##### 31Angles, Lines, and Transversals

##### 32Scale Factors and Similarity

##### 33Congruent Triangles

##### 34Circles

##### 35Surface Area and Volume

##### 36Conics

##### 37Set Theory

##### 38Data and Graphs

##### 39Statistics

##### 40Probability

##### 41Differentiation

- 41.1Power rule
- 41.2Slope and equation of tangent line
- 41.3Chain rule
- 41.4Derivative of trigonometric functions
- 41.5Derivative of exponential functions
- 41.6Product rule
- 41.7Quotient rule
- 41.8Derivative of logarithmic functions
- 41.9Higher order derivatives
- 41.10Rectilinear Motion: Derivative
- 41.11Critical number & maximum and minimum values

- 41.1Power rule
##### 42Integration