Excel in Year 10 Maths

Understanding the number systems

Prime factorisation

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Patterns

Combining like terms

Evaluating algebraic expressions

Solving one-step equations: x + a = b

Graphing linear relations

Model and solve one-step linear equations: <i>ax = b</i>, <i>x/a = b</i>

Solving two-step linear equations using addition and subtraction: <i>ax + b = c</i>

Solving two-step linear equations using multiplication and division: <i>x/a + b = c</i>

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

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

Representing patterns in linear relations

Reading linear relation graphs

Solving linear equations by graphing

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

Applications of linear relations

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

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: <i>y = f(-x)</i>

Reflection across the x-axis: <i>y = -f(x)</i>

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

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

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

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

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Finance: Compound interest

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

Characteristics of polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials

Multiplying polynomials by monomials

Dividing polynomials by monomials

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

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

Factorise by taking out the greatest common factor

Factorise by grouping

Factorising difference of squares: <i>x^2 - y^2</i>

Factorising trinomials

Factoring difference of cubes

Factoring sum of cubes

Characteristics of 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 parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

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 radicals

Multiplying and dividing radicals

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

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Classifying Triangles

Isosceles and Equilateral Triangles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

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

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

Circles and circumference

Angles in a circle

Arcs of a circle

Areas and sectors of circles

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

Standard angle

Coterminal angles

Reference angles

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Sine rule

Cosine rule

Applications of the sine rule and cosine rule

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

Introduction to probability

Organizing outcomes

Probability of independent events

Comparing experimental and theoretical probability

Median and mode

Mean

Range and outliers

Application of averages

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Pie charts

Reading and drawing Venn diagrams

Stem-and-leaf plots

Frequency tables and dot plots

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions