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Year 10 Maths Topics

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Number System and Radicals
Understanding the number systems
Prime factorisation
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Patterns and Solving Equations
Patterns
Combining like terms
Evaluating algebraic expressions
Solving one-step equations: x + a = b
Graphing linear relations
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Linear Equations (Basic)
Model and solve one-step linear equations: ax = b, x/a = b
Solving two-step linear equations using addition and subtraction: ax + b = c
Solving two-step linear equations using multiplication and division: x/a + b = c
Solving two-step linear equations using distributive property: a(x + b) = c
video
Solving Linear Equations
Solving linear equations using multiplication and division
Solving two-step linear equations: ax + b = c, x/a + b = c
Solving linear equations using distributive property: a(x + b) = c
Solving linear equations with variables on both sides
Solving literal equations
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Solving Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
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Introduction to Relations and Functions
Relationship between two variables
Understand relations between x- and y-intercepts
Domain and range of a function
Identifying functions
Function notation
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Linear Relations
Representing patterns in linear relations
Reading linear relation graphs
Solving linear equations by graphing
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Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
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
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Solving Simultaneous Equations
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
video
Transformations of Functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Combining transformations of functions
Even and odd functions
video
Exponents
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
video
Exponential Functions
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
Finance: Compound interest
video
Logarithmic Functions
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
video
Introduction to Polynomials
Characteristics of polynomials
Equivalent expressions of polynomials
Adding and subtracting polynomials
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Multiplying and Dividing Polynomials
Multiplying and dividing monomials
Multiplying polynomials by monomials
Dividing polynomials by monomials
video
Operations of Polynomials
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
video
Factorising Polynomial Expressions
Common factors of polynomials
Factorising polynomials by grouping
Solving polynomials with the unknown "b" from x^2 + bx + c
Solving polynomials with the unknown "c" from x^2 + bx + c
Factorising polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + cax2+bx+c
Factorising polynomials: ax2+bx+cax^2 + bx + cax2+bx+c
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Evaluating polynomials
Using algebra tiles to factorise polynomials
Solving polynomial equations
Word problems of polynomials
video
Factorising Polynomial (Advanced)
Factorise by taking out the greatest common factor
Factorise by grouping
Factorising difference of squares: x^2 - y^2
Factorising trinomials
Factoring difference of cubes
Factoring sum of cubes
video
Quadratic Functions
Characteristics of 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 parabolas for given quadratic functions
Finding the quadratic functions for given parabolas
Applications of quadratic functions
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Conics
Conics - Parabola
Conics - Ellipse
Conics - Circle
Conics - Hyperbola
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Radicals
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
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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
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Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
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Scale Factors and Similarity
Enlargements and reductions with scale factors
Scale diagrams
Similar triangles
Similar polygons
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Properties of Triangles
Classifying Triangles
Isosceles and Equilateral Triangles
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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
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Pythagorean Theorem
Squares and square roots
Pythagorean theorem
Estimating square roots
Using the pythagorean relationship
Applications of pythagorean theorem
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Introduction to Surface Area of 3D Shapes
Introduction to surface area of 3-dimensional shapes
Nets of 3-dimensional shapes
Surface area of prisms
Surface area of cylinders
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Introduction to Volume
Introduction to volume
Volume of prisms
Volume of cylinders
Word problems relating volume of prisms and cylinders
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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
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Circles
Circles and circumference
Angles in a circle
Arcs of a circle
Areas and sectors of circles
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Introduction to Trigonometry
Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a}ao​ )
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
video
Trigonometric Ratios and Angle Measure
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
video
Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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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
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Introduction to Probability
Introduction to probability
Organizing outcomes
Probability of independent events
Comparing experimental and theoretical probability
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Statistics
Median and mode
Mean
Range and outliers
Application of averages
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Data and Graphs
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
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Introduction to Matrices
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
video
Determinants and Inverses of Matrices
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

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