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1. Adding and Subtracting Fractions

1.1 Using models to add and subtract fractions
1.2 Adding fractions with like denominators
1.3 Subtracting fractions with like denominators
1.4 Adding and subtracting fractions with unlike denominators
1.5 Adding and subtracting mixed numbers

2. Multiplying and Dividing Fractions

2.1 Multiplying fractions and whole numbers
2.2 Dividing fractions with whole numbers
2.3 Multiplying proper fractions
2.4 Multiplying improper fractions and mixed numbers
2.5 Dividing fractions and mixed numbers
2.6 Applications of fraction operations

3. Pythagorean Theorem

3.1 Squares and square roots
3.2 Pythagorean theorem
3.3 Estimating square roots
3.4 Using the pythagorean relationship
3.5 Applications of pythagorean theorem

4. Percents

4.1 Representing percents
4.2 Percents, fractions, and decimals
4.3 Percent of a number
4.4 Adding and multiplying percents
4.5 Taxes, discounts, tips and more
4.6 Simple interest

5. Surds

5.1 Square and square roots
5.2 Cubic and cube roots
5.3 Evaluating and simplifying surds
5.4 Converting radicals to mixed radicals
5.5 Converting radicals to entire radicals
5.6 Adding and subtracting surds
5.7 Multiplying and dividing surds
5.8 Rationalize the denominator

6. Algebraic Expressions

6.1 Equivalent algebraic expressions
6.2 Adding and subtracting algebraic expressions
6.3 Multiplying monomial by monomial
6.4 Multiplying monomial by binomial
6.5 Multiplying binomial by binomial
6.6 Multiplying polynomial by polynomial
6.7 Applications of polynomials

7. Introduction to Relations and Functions

7.1 Relationship between two variables
7.2 Understand relations between x- and y-intercepts
7.3 Domain and range of a function
7.4 Identifying functions
7.5 Function notation

8. Linear Functions

8.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
8.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
8.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
8.4 Gradient intercept form: y = mx + b
8.5 General form: Ax + By + C = 0
8.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
8.7 Rate of change
8.8 Graphing linear functions using table of values
8.9 Graphing linear functions using x- and y-intercepts
8.10 Graphing from slope-intercept form y=mx+b
8.11 Graphing linear functions using a single point and gradient
8.12 Word problems of graphing linear functions
8.13 Parallel and perpendicular lines in linear functions
8.14 Applications of linear relations
8.15 Perpendicular line equation

9. Simultaneous Equations

9.1 Determining number of solutions to linear equations
9.2 Solving simultaneous linear equations by graphing
9.3 Solving simultaneous linear equations by elimination
9.4 Solving simultaneous linear equations by substitution
9.5 Money related questions in linear equations
9.6 Unknown number related questions in linear equations
9.7 Distance and time related questions in linear equations
9.8 Rectangular shape related questions in linear equations
9.9 Simultaneous linear-quadratic equations
9.10 Simultaneous quadratic-quadratic equations
9.11 Solving 3 variable simultaneous equations by substitution
9.12 Solving 3 variable simultaneous equations by elimination
9.13 Solving 3 variable simultaneous equations with no solution, infinite solutions
9.14 Word problems relating 3 variable simultaneous equations

10. Factorisation

10.1 Factorise by taking out the greatest common factor
10.2 Factorise by grouping
10.3 Factorising difference of squares: x^2 - y^2
10.4 Factorising trinomials
10.5 Factoring difference of cubes
10.6 Factoring sum of cubes

11. Quadratic Functions

11.1 Introduction to quadratic functions
11.2 Transformations of quadratic functions
11.3 Quadratic function in general form: y = ax^2 + bx + c
11.4 Quadratic function in vertex form: y = a(x-p)^2 + q
11.5 Completing the square
11.6 Converting from general to vertex form by completing the square
11.7 Shortcut: Vertex formula
11.8 Graphing quadratic functions: General form VS. Vertex form
11.9 Finding the quadratic functions for given parabolas
11.10 Applications of quadratic functions

12. Solving Quadratic Equations

12.1 Solving quadratic equations by factorising
12.2 Solving quadratic equations by completing the square
12.3 Using quadratic formula to solve quadratic equations
12.4 Nature of roots of quadratic equations: The discriminant
12.5 Applications of quadratic equations

13. Inequalities

13.1 Express linear inequalities graphically and algebraically
13.2 Solving one-step linear inequalities
13.3 Solving multi-step linear inequalities
13.4 Compound inequalities
13.5 Solving absolute value inequalities
13.6 Graphing linear inequalities in two variables
13.7 Graphing simultaneous inequalities
13.8 Solving quadratic inequalities in one variable

14. Algebraic Fractions

14.1 Simplifying algebraic fractions and restrictions
14.2 Adding and subtracting algebraic fractions
14.3 Multiplying algebraic fractions
14.4 Dividing algebraic fractions
14.5 Solving equations with algebraic fractions
14.6 Applications of equations with algebraic fractions
14.7 Simplifying complex fractions
14.8 Partial fraction decomposition

15. Reciprocal Functions

15.1 Graphing reciprocals of linear functions
15.2 Graphing reciprocals of quadratic functions

16. Angles, Lines, and Transversals

16.1 Pairs of lines and angles
16.2 Parallel lines and transversals
16.3 Parallel line proofs
16.4 Perpendicular line proofs

17. Scale Factors and Similarity

17.1 Enlargements and reductions with scale factors
17.2 Scale diagrams
17.3 Similar triangles
17.4 Similar polygons

18. Properties of Triangles

18.1 Classifying Triangles
18.2 Isosceles and Equilateral Triangles

19. Congruent Triangles

19.1 Congruence and Congruent Triangles
19.2 Triangles Congruent by SSS Proofs
19.3 Triangles Congruent by SAS and HL Proofs
19.4 Triangles Congruent by ASA and AAS Proofs

20. Functions

20.1 Function notation
20.2 Operations with functions
20.3 Adding functions
20.4 Subtracting functions
20.5 Multiplying functions
20.6 Dividing functions
20.7 Composite functions
20.8 Even and odd functions

21. Rational Functions

21.1 What is a rational function?
21.2 Point of discontinuity
21.3 Vertical asymptote
21.4 Horizontal asymptote
21.5 Slant asymptote
21.6 Graphs of rational functions

22. Indices

22.1 Indices: Product rule (a^x)(a^y) = a^(x+y)
22.2 Indices: Division rule (a^x / a^y) = a^(x-y)
22.3 Indices: Power rule (a^x)^y = a^(x * y)
22.4 Indices: Negative exponents
22.5 Indices: Zero exponent: a^0 = 1
22.6 Indices: Rational exponents
22.7 Combining laws of indices
22.8 Scientific notation
22.9 Convert between radicals and rational exponents
22.10 Solving for indices

23. Exponential Functions

23.1 Solving exponential equations using exponent rules
23.2 Graphing exponential functions
23.3 Graphing transformations of exponential functions
23.4 Finding an exponential function given its graph

24. Logarithmic Functions

24.1 What is a logarithm?
24.2 Converting from logarithmic form to exponential form
24.3 Evaluating logarithms without a calculator
24.4 Common logarithms
24.5 Natural log: ln
24.6 Evaluating logarithms using change-of-base formula
24.7 Converting from exponential form to logarithmic form
24.8 Solving exponential equations with logarithms
24.9 Product rule of logarithms
24.10 Quotient rule of logarithms
24.11 Combining product rule and quotient rule in logarithms
24.12 Evaluating logarithms using logarithm rules
24.13 Solving logarithmic equations
24.14 Graphing logarithmic functions
24.15 Finding a logarithmic function given its graph

25. Trigonometric Ratios and Angle Measure

25.1 Angle in standard position
25.2 Coterminal angles
25.3 Reference angle
25.4 Find the exact value of trigonometric ratios
25.5 ASTC rule in trigonometry (All Students Take Calculus)
25.6 Unit circle
25.7 Converting between degrees and radians
25.8 Trigonometric ratios of angles in radians
25.9 Radian measure and arc length

26. Sine Rule and Cosine Rule

26.1 Sine rule
26.2 Cosine rule
26.3 Sine rule and cosine rule word problems

27. Trigonometric Graphs

27.1 Sine graph: y = sin x
27.2 Cosine graph: y = cos x
27.3 Tangent graph: y = tan x

28. Inverse Trigonometric Functions

28.1 Finding inverse trigonometric function from its graph
28.2 Evaluating inverse trigonometric functions
28.3 Finding inverse reciprocal trigonometric function from its graph
28.4 Finding exact value of inverse reciprocal trig functions

29. Bearings

29.1 Introduction to bearings
29.2 Bearings and direction word problems
29.3 Angle of elevation and depression

30. Series

30.1 Arithmetic series
30.2 Geometric series
30.3 Convergence and divergence of normal infinite series
30.4 Convergence & divergence of geometric series

31. Growth and Decay

31.1 Exponential growth and decay by a factor
31.2 Exponential growth and decay by percentage
31.3 Finance: Compound interest
31.4 Finance: Future value and present value

32. Conics

32.1 Conics - Parabola
32.2 Conics - Ellipse
32.3 Conics - Circle
32.4 Conics - Hyperbola

33. Probability

33.1 Addition rule for "OR"
33.2 Multiplication rule for "AND"

34. Limits

34.1 Finding limits from graphs
34.2 Continuity
34.3 Finding limits algebraically - direct substitution
34.4 Finding limits algebraically - when direct substitution is not possible
34.5 Limit laws

35. Derivatives

35.1 Definition of derivative
35.2 Power rule
35.3 Slope and equation of tangent line
35.4 Chain rule
35.5 Derivative of trigonometric functions
35.6 Derivative of exponential functions
35.7 Product rule
35.8 Quotient rule
35.9 Derivative of logarithmic functions
35.10 Higher order derivatives

36. Derivative Applications

36.1 Rectilinear Motion: Derivative
36.2 Critical number & maximum and minimum values
36.3 Curve sketching

37. Integrals

37.1 Antiderivatives
37.2 Riemann sum
37.3 Definite integral
37.4 Fundamental theorem of calculus

38. Integral Applications

38.1 Areas between curves
38.2 Volumes of solids of revolution - Disc method
38.3 Volumes of solids of revolution - Shell method

38 Chapters · 228 Topics · 1587 Videos

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Yes — our Essential Maths content covers all major topics regardless of textbook, aligned to standard Australian Year 11 curriculum for your state.

Is Essential Maths Year 11 the same in all Australian states?

While course names vary by state, we cover all essential mathematics topics including percentages, measurement, statistics, and practical applications taught across Australia.

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