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GCE N(A)-Level 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

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

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

Properties and graphs of quadratic functions

Solving Quadratic Equations

Solving quadratic equations by factorising

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

The discriminant: Nature of roots of quadratic equations

Applications of quadratic equations

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 exponent rules

Graphing exponential functions

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 Angles and Proofs

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

Trigonometry

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Angle Measure in Radian

Converting between degrees and 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

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"

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