Master Year 10 Maths Step by Step

Understanding the number systems

Prime factorisation

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Ratios

Rates

Proportions

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

Metric systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Upper and lower bound

Understanding of squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Cartesian plane

Draw on coordinate planes

Introduction to transformations

Horizontal and vertical distances

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

Introduction to volume

Volume of prisms

Volume of cylinders

Word problems relating volume of prisms and cylinders

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

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

Compound inequalities

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Function notation (Advanced)

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inequalities of combined functions

Inverse functions

One to one functions

Difference quotient: applications of functions

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 gradient-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Parallel and perpendicular lines in linear functions

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous 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

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Standard form

Convert between radicals and rational exponents

Solving for indices

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

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

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

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

Exponents: Negative exponents

Exponents: Zero exponent: <i>a^0 = 1</i>

Exponents: Rational exponents

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Characteristics of polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials

Multiplying polynomials by monomials

Dividing polynomials by monomials

Common factors of polynomials

Factorising polynomials by grouping

Solving polynomials with the unknown "b" from <i>x^2 + bx + c</i>

Solving polynomials with the unknown "c" from <i>x^2 + bx + c</i>

Factorising polynomials: <i>x^2 + bx + c</i>

Applications of polynomials: <i>x^2 + bx + c</i>

Solving polynomials with the unknown "b" from \(ax^2 + bx + c\)

Factorising polynomials: \(ax^2 + bx + c\)

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

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

Evaluating polynomials

Using algebra tiles to factorise polynomials

Solving polynomial equations

Word problems of polynomials

Square and square roots

Cubic and cube roots

Evaluating and simplifying surds

Operations with surds

Conversion between entire surds and mixed surds

Adding and subtracting surds

Multiplying surds

Solving surd equations

Rationalize the denominator

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

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Median and mode

Mean

Range and outliers

Application of averages

Influencing factors in data collection

Data collection

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

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

Direct variation

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions