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Maths Extension 1 Topics

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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 or 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. Circles

20.1 Angles in a circle
20.2 Chord properties
20.3 Tangent properties
20.4 Circle and circumference
20.5 Arcs of a circle
20.6 Areas and sectors of circles
20.7 Inscribed Angles and Proofs
20.8 Central and inscribed angles in circles

21. Functions

21.1 Function notation
21.2 Operations with functions
21.3 Adding functions
21.4 Subtracting functions
21.5 Multiplying functions
21.6 Dividing functions
21.7 Composite functions
21.8 Even and odd functions

22. Polynomial Functions

22.1 What is a polynomial function?
22.2 Polynomial long division
22.3 Polynomial synthetic division
22.4 Remainder theorem
22.5 Factor theorem
22.6 Rational zero theorem
22.7 Characteristics of polynomial graphs
22.8 Multiplicities of polynomials
22.9 Imaginary zeros of polynomials
22.10 Determining the equation of a polynomial function
22.11 Applications of polynomial functions
22.12 Solving polynomial inequalities
22.13 Fundamental theorem of algebra
22.14 Descartes' rule of signs

23. Rational Functions

23.1 What is a rational function?
23.2 Point of discontinuity
23.3 Vertical asymptote
23.4 Horizontal asymptote
23.5 Slant asymptote
23.6 Graphs of rational functions
23.7 Solving rational inequalities

24. Indices

24.1 Indices: Product rule (a^x)(a^y) = a^(x+y)
24.2 Indices: Division rule (a^x / a^y) = a^(x-y)
24.3 Indices: Power rule (a^x)^y = a^(x * y)
24.4 Indices: Negative exponents
24.5 Indices: Zero exponent: a^0 = 1
24.6 Indices: Rational exponents
24.7 Combining laws of indices
24.8 Scientific notation
24.9 Convert between radicals and rational exponents
24.10 Solving for indices

25. Exponential Functions

25.1 Solving exponential equations using exponent rules
25.2 Graphing exponential functions
25.3 Graphing transformations of exponential functions
25.4 Finding an exponential function given its graph

26. Logarithmic Functions

26.1 What is a logarithm?
26.2 Converting from logarithmic form to exponential form
26.3 Evaluating logarithms without a calculator
26.4 Common logarithms
26.5 Natural log: ln
26.6 Evaluating logarithms using change-of-base formula
26.7 Converting from exponential form to logarithmic form
26.8 Solving exponential equations with logarithms
26.9 Product rule of logarithms
26.10 Quotient rule of logarithms
26.11 Combining product rule and quotient rule in logarithms
26.12 Evaluating logarithms using logarithm rules
26.13 Solving logarithmic equations
26.14 Graphing logarithmic functions
26.15 Finding a logarithmic function given its graph

27. Trigonometric Ratios and Angle Measure

27.1 Angle in standard position
27.2 Coterminal angles
27.3 Reference angle
27.4 Find the exact value of trigonometric ratios
27.5 ASTC rule in trigonometry (All Students Take Calculus)
27.6 Unit circle
27.7 Converting between degrees and radians
27.8 Trigonometric ratios of angles in radians
27.9 Radian measure and arc length

28. Sine Rule and Cosine Rule

28.1 Sine rule
28.2 Cosine rule
28.3 Sine rule and cosine rule word problems

29. Trigonometric Graphs

29.1 Sine graph: y = sin x
29.2 Cosine graph: y = cos x
29.3 Tangent graph: y = tan x

30. Trigonometric Identities

30.1 Quotient identities and reciprocal identities
30.2 Pythagorean identities
30.3 Sum and difference identities
30.4 Cofunction identities
30.5 Double-angle identities

31. Solving Trigonometric Equations

31.1 Solving first degree trigonometric equations
31.2 Determining non-permissible values for trig expressions
31.3 Solving second degree trigonometric equations
31.4 Solving trigonometric equations involving multiple angles
31.5 Solving trigonometric equations using pythagorean identities
31.6 Solving trigonometric equations using sum and difference identities
31.7 Solving trigonometric equations using double-angle identities

32. Inverse Trigonometric Functions

32.1 Finding inverse trigonometric function from its graph
32.2 Evaluating inverse trigonometric functions
32.3 Finding inverse reciprocal trigonometric function from its graph
32.4 Finding exact value of inverse reciprocal trig functions

33. Bearings

33.1 Introduction to bearings
33.2 Bearings and direction word problems
33.3 Angle of elevation and depression

34. Series

34.1 Arithmetic series
34.2 Geometric series
34.3 Convergence and divergence of normal infinite series
34.4 Convergence & divergence of geometric series

35. Growth and Decay

35.1 Exponential growth and decay by a factor
35.2 Exponential growth and decay by percentage
35.3 Finance: Compound interest
35.4 Finance: Future value and present value

36. Conics

36.1 Conics - Parabola
36.2 Conics - Ellipse
36.3 Conics - Circle
36.4 Conics - Hyperbola

37. Permutations and Combinations

37.1 Fundamental counting principle
37.2 Factorial notation
37.3 Path counting problems
37.4 Permutation vs. Combination
37.5 Permutations
37.6 Combinations
37.7 Problems involving both permutations and combinations
37.8 Pascal's triangle
37.9 Binomial theorem

38. Discrete Probabilities

38.1 Probability distribution - histogram, mean, variance & standard deviation
38.2 Binomial distribution
38.3 Mean and standard deviation of binomial distribution

39. Probability

39.1 Addition rule for "OR"
39.2 Multiplication rule for "AND"

40. Limits

40.1 Finding limits from graphs
40.2 Continuity
40.3 Finding limits algebraically - direct substitution
40.4 Finding limits algebraically - when direct substitution is not possible
40.5 Limit laws

41. Derivatives

41.1 Definition of derivative
41.2 Power rule
41.3 Slope and equation of tangent line
41.4 Chain rule
41.5 Derivative of trigonometric functions
41.6 Derivative of exponential functions
41.7 Product rule
41.8 Quotient rule
41.9 Derivative of inverse trigonometric functions
41.10 Derivative of logarithmic functions
41.11 Higher order derivatives

42. Derivative Applications

42.1 Rectilinear Motion: Derivative
42.2 Critical number & maximum and minimum values
42.3 l'Hospital's rule
42.4 Curve sketching
42.5 Related rates

43. Integrals

43.1 Antiderivatives
43.2 Riemann sum
43.3 Definite integral
43.4 Fundamental theorem of calculus
43.5 U-Substitution
43.6 Integration using trigonometric identities

44. Integral Applications

44.1 Areas between curves
44.2 Volumes of solids of revolution - Disc method
44.3 Volumes of solids of revolution - Shell method

45. Parametric Equations

45.1 Defining curves with parametric equations
45.2 Tangent and concavity of parametric equations

45 Chapters · 282 Topics · 1952 Videos

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Yes — our Maths Extension 1 content covers all major topics regardless of textbook, aligned to the NSW HSC syllabus and Australian curriculum standards.

What topics are covered in Maths Extension 1?

All Year 11 Extension 1 topics including trigonometry, polynomials, combinatorics, calculus introduction, functions, binomial theorem, and more.

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