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GCE O-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

Factorising Quadratic Functions

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

Factorising trinomials

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

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

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

Partial fraction decomposition

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

Simultaneous linear equations

Simultaneous linear-quadratic equations

Simultaneous quadratic-quadratic equations

Inequalities in Two Variables

Graphing linear inequalities in two variables

Graphing systems of linear inequalities

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Applications of inequalities

What is linear programming?

Linear programming word problems

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

Polynomial Functions

Polynomial long division

Polynomial synthetic division

Remainder theorem

Factor theorem

Binomial expansions

Factorial notation

Binomial theorem

Exponential Functions

Solving exponential equations using laws of indices

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Logarithms

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Modulus Functions

Modulus functions

Solving modulus equations

Vectors

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

Scalar multiplication

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

Word problems on vectors

Matrices

Notation of matrices

Adding and subtracting matrices

Multiplying a matrix by a scalar

Multiplying a matrix by another matrix

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

Angles, Lines, and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Congruent Triangles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS 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

Set Theory

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

Data and Graphs

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Reading and drawing Venn diagrams

Frequency tables and dot diagrams

Pie charts

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

Derivative of trigonometric functions

Derivative of exponential functions

Product rule

Quotient rule

Derivative of logarithmic functions

Higher order derivatives

Rectilinear Motion: Derivative

Critical number & maximum and minimum values

Integration

Antiderivatives

Definite integral

Integration by parts

Trigonometric substitution

Integration of rational functions by partial fractions

Areas between curves

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