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GCE N(A)-Level A Maths Topics

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form:

y - y_1 = m (x - x_1)

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Applications of linear relations

Simultaneous Equations

Determining number of solutions to linear equations

Solving simultaneous linear equations by graphing

Solving simultaneous linear equations by elimination

Solving simultaneous linear equations by substitution

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Factorisation

Factorise by taking out the greatest common factor

Factorise by grouping

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factorising difference of squares: x^2 - y^2

Factorise trinomials

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factorising difference of cubes:

a^3-b^3

Factorising sum of cubes:

a^3+b^3

Quadratic Functions

Introduction to quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic Equations and Inequalities

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Surds

Square and square roots

Cubic and cube roots

Operations with surds

Conversion between entire radicals and mixed radicals

Adding and subtracting surds

Multiplying surds

Rationalize the denominator

Solving equations with surds

Solving Simultaneous Equations

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Solving 3 variable systems of equations with no solution, infinite solutions

Word problems relating 3 variable systems of equations

Laws of Indices

Indices: Product rule (a^x)(a^y) = a^(x+y)

Indices: Division rule (a^x / a^y) = a^(x-y)

Indices: Power rule (a^x)^y = a^(x * y)

Negative indices

Zero index: a^0 = 1

Rational indices

Standard form

Algebraic Fractions

Simplifying algebraic fractions and restrictions

Adding and subtracting algebraic fractions

Multiplying algebraic fractions

Dividing algebraic fractions

Solving equations with algebraic fractions

Applications of equations with algebraic fractions

Simplifying complex fractions

Exponential Functions

Solving exponential equations using laws of indices

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Binomial expansions

Factorial notation

Binomial theorem

Geometry and Measurement

Parallel and perpendicular line segments

Perpendicular bisectors

Angle bisectors

Congruent Triangles

Classifying Triangles

Congruence and Congruent Triangles

Triangles Congruent by SSS Proofs

Triangles Congruent by SAS and HL Proofs

Triangles Congruent by ASA and AAS Proofs

Isosceles and Equilateral Triangles

Angles, Lines, and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Circles

Angles in a circle

Chord properties

Tangent properties

Circle and circumference

Arcs of a circle

Areas and sectors of circles

Inscribed quadrilaterals in circles

Central and inscribed angles in circles

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Conics

Conics - Parabola

Conics - Circle

Trigonometric Ratios and Angle Measure

Angle in standard position

Coterminal angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Sine Rule and Cosine Rule

Sine rule

Cosine rule

Sine rule and cosine rule word problems

Bearings

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Graphing Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Applications of Trigonometric Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Solving Trigonometric Equations

Solving first degree trigonometric equations

Determining non-permissible values for trig expressions

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Inverse Trigonometric Functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Inverse reciprocal trigonometric function: finding the exact value

Data and Graphs

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Reading and drawing stem-and-leaf diagrams

Reading and drawing Venn diagrams

Frequency tables and dot diagrams

Pie charts

Representing Data

Advantages and disadvantages of different graphs

Misleading graphs

Critiquing data presentation

Statistics

Median and mode

Mean

Range and outliers

Application of averages

Standard deviation, and variance

Z-score, quartiles, and percentiles

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Frequency distribution and histograms

Addition rule for "OR"

Multiplication rule for "AND"

Differentiation

Power rule

Slope and equation of tangent line

Chain rule

Product rule

Quotient rule

Higher order derivatives

Critical number & maximum and minimum values

Integration

Antiderivatives

Definite integral

Integration by parts

Integration of rational functions by partial fractions

Areas between curves

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