Master O-Level Maths Step by Step

Place value

Comparing and ordering numbers

Rounding numbers

Divisibility Rules

Determining Common Factors

Determining Common Multiples

Introduction to exponents

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Adding and subtracting decimals

Multiplying decimals

Dividing decimals

Order of operations (BEDMAS)

Using models to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Ratios

Rates

Proportions

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

Solving linear equations using multiplication and division

Solving two-step linear equations: <i>ax + b = c</i>, <i>x/a + b = c</i>

Solving linear equations using distributive property: <i>a(x + b) = c</i>

Solving linear equations with variables on both sides

Solving literal equations

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Metric systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Understanding the number systems

Prime factorisation

Highest common factors (HCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting surds

Multiplying and dividing surds

Rationalize the denominator

Direct variation

Equivalent algebraic expressions

Adding and subtracting algebraic expressions

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

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

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

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

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Factorise by taking out the greatest common factor

Factorise by grouping

Factorising perfect square trinomials:&nbsp;<i>(a + b)^2 = a^2 + 2ab + b^2</i> or <i>(a - b)^2 = a^2 - 2ab + b^2</i>

Factorising difference of squares: <i>(a - b)(a + b) = (a^2 - b^2)</i>

Factorising trinomials

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Introduction to quadratic functions

Transformations of quadratic functions

Quadratic function in general form: <i>y = ax^2 + bx + c</i>

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

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

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

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

Indices: Product rule <i>(a^x)(a^y) = a^(x+y)</i>

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

Indices: Power rule <i>(a^x)^y = a^(x * y)</i>

Negative indices

Zero index: <i>a^0 = 1</i>

Rational indices

Solving exponential equations using laws of indices

Graphing exponential functions

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

Notation of matrices

Adding and subtracting matrices

Multiplying a matrix by a scalar

Multiplying a matrix by another matrix

Parallel and perpendicular line segments

Perpendicular bisectors

Angle bisectors

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

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

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

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 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

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

Converting between degrees and radians

Radian measure and arc length

Sine rule

Cosine rule

Sine rule and cosine rule word problems

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

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

Advantages and disadvantages of different graphs

Misleading graphs

Critiquing data presentation

Median and mode

Mean

Range and outliers

Application of averages

Standard deviation and variance

Z-score, quartiles, and percentiles

Determining probabilities using tree diagrams and tables

Probability of independent events

Frequency distribution and histograms

Addition rule for "OR"

Multiplication rule for "AND"