# GCE N(A)-Level A Maths Help & Practice

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##### 1Linear Inequalities

##### 2Algebraic Expressions

##### 3Linear Functions

- 3.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 3.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 3.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 3.4Gradient intercept form: y = mx + b
- 3.5General form: Ax + By + C = 0
- 3.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 3.7Rate of change
- 3.8Graphing linear functions using table of values
- 3.9Graphing linear functions using x- and y-intercepts
- 3.10Graphing from slope-intercept form y=mx+b
- 3.11Graphing linear functions using a single point and gradient
- 3.12Word problems of graphing linear functions
- 3.13Applications of linear relations

- 3.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 4Simultaneous Equations

- 4.1Determining number of solutions to linear equations
- 4.2Solving simultaneous linear equations by graphing
- 4.3Solving simultaneous linear equations by elimination
- 4.4Solving simultaneous linear equations by substitution
- 4.5Money related questions in linear equations
- 4.6Unknown number related questions in linear equations
- 4.7Distance and time related questions in linear equations
- 4.8Rectangular shape related questions in linear equations

- 4.1Determining number of solutions to linear equations
##### 5Factorisation

- 5.1Factorise by taking out the greatest common factor
- 5.2Factorise by grouping
- 5.3Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 5.4Factorising difference of squares:
*x^2 - y^2* - 5.5Factorise trinomials
- 5.6Solving polynomials with unknown coefficients
- 5.7Solving polynomials with unknown constant terms
- 5.8Factorising difference of cubes: $a^3-b^3$
- 5.9Factorising sum of cubes: $a^3+b^3$

- 5.1Factorise by taking out the greatest common factor
##### 6Quadratic Functions

- 6.1Introduction to quadratic functions
- 6.2Transformations of quadratic functions
- 6.3Quadratic function in general form:
*y = ax^2 + bx + c* - 6.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 6.5Completing the square
- 6.6Converting from general to vertex form by completing the square
- 6.7Shortcut: Vertex formula
- 6.8Graphing quadratic functions: General form VS. Vertex form
- 6.9Finding the quadratic functions for given parabolas
- 6.10Applications of quadratic functions

- 6.1Introduction to quadratic functions
##### 7Quadratic Equations and Inequalities

##### 8Surds

##### 9Solving Simultaneous Equations

- 9.1System of linear equations
- 9.2System of linear-quadratic equations
- 9.3System of quadratic-quadratic equations
- 9.4Solving 3 variable systems of equations by substitution
- 9.5Solving 3 variable systems of equations by elimination
- 9.6Solving 3 variable systems of equations with no solution, infinite solutions
- 9.7Word problems relating 3 variable systems of equations

- 9.1System of linear equations
##### 10Laws of Indices

##### 11Algebraic Fractions

##### 12Exponential Functions

##### 13Binomial expansions

##### 14Geometry and Measurement

##### 15Congruent Triangles

##### 16Angles, Lines, and Transversals

##### 17Circles

##### 18Surface Area and Volume

##### 19Conics

##### 20Trigonometric Ratios and Angle Measure

- 20.1Angle in standard position
- 20.2Coterminal angles
- 20.3Reference angle
- 20.4Find the exact value of trigonometric ratios
- 20.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 20.6Unit circle
- 20.7Converting between degrees and radians
- 20.8Trigonometric ratios of angles in radians
- 20.9Radian measure and arc length

- 20.1Angle in standard position
##### 21Sine Rule and Cosine Rule

##### 22Bearings

##### 23Graphing Trigonometric Functions

##### 24Applications of Trigonometric Functions

##### 25Trigonometric Identities

##### 26Solving Trigonometric Equations

- 26.1Solving first degree trigonometric equations
- 26.2Determining non-permissible values for trig expressions
- 26.3Solving second degree trigonometric equations
- 26.4Solving trigonometric equations involving multiple angles
- 26.5Solving trigonometric equations using pythagorean identities
- 26.6Solving trigonometric equations using sum and difference identities
- 26.7Solving trigonometric equations using double-angle identities

- 26.1Solving first degree trigonometric equations
##### 27Inverse Trigonometric Functions

##### 28Data and Graphs

##### 29Representing Data

##### 30Statistics

##### 31Probability

##### 32Differentiation

##### 33Integration