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Year 12 Maths Topics
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1. Introduction to Relations and Functions
2. Functions
2.1 Function notation
2.2 Operations with functions
2.3 Adding functions
2.4 Subtracting functions
2.5 Multiplying functions
2.6 Dividing functions
2.7 Composite functions
2.8 Inequalities of combined functions
2.9 Inverse functions
2.10 One to one functions
2.11 Difference quotient: applications of functions
3. Transformations of Functions
3.1 Transformations of functions: Horizontal translations
3.2 Transformations of functions: Vertical translations
3.3 Reflection across the y-axis: y = f(-x)
3.4 Reflection across the x-axis: y = -f(x)
3.5 Transformations of functions: Horizontal stretches
3.6 Transformations of functions: Vertical stretches
3.7 Combining transformations of functions
3.8 Even and odd functions
4. Factorising Polynomial
5. Quadratic Functions
5.1 Characteristics of quadratic functions
5.2 Transformations of quadratic functions
5.3 Quadratic function in general form: y = ax^2 + bx + c
5.4 Quadratic function in vertex form: y = a(x-p)^2 + q
5.5 Completing the square
5.6 Converting from general to vertex form by completing the square
5.7 Shortcut: Vertex formula
5.8 Graphing parabolas for given quadratic functions
5.9 Finding the quadratic functions for given parabolas
5.10 Applications of quadratic functions
6. Polynomial Functions
7. Radicals
8. Radical Functions
9. Exponents
10. Rational Functions
11. Exponential Functions
11.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
11.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
11.3 Exponents: Power rule (a^x)^y = a^(x * y)
11.4 Exponents: Negative exponents
11.5 Exponents: Zero exponent: a^0 = 1
11.6 Exponents: Rational exponents
11.7 Graphing exponential functions
11.8 Graphing transformations of exponential functions
11.9 Finding an exponential function given its graph
12. Logarithmic Functions
12.1 What is a logarithm?
12.2 Converting from logarithmic form to exponential form
12.3 Evaluating logarithms without a calculator
12.4 Common logarithms
12.5 Natural log: ln
12.6 Evaluating logarithms using change-of-base formula
12.7 Converting from exponential form to logarithmic form
12.8 Solving exponential equations with logarithms
12.9 Product rule of logarithms
12.10 Quotient rule of logarithms
12.11 Combining product rule and quotient rule in logarithms
12.12 Evaluating logarithms using logarithm rules
12.13 Solving logarithmic equations
12.14 Graphing logarithmic functions
12.15 Finding a logarithmic function given its graph
13. Applications of Exponential and Logarithmic Functions
13.1 Exponential growth and decay by a factor
13.2 Exponential decay: Half-life
13.3 Exponential growth and decay by percentage
13.4 Finance: Compound interest
13.5 Continuous growth and decay
13.6 Logarithmic scale: Richter scale (earthquake)
13.7 Logarithmic scale: pH scale
13.8 Logarithmic scale: dB scale
13.9 Finance: Future value and present value
14. Solving Simultaneous Equations
14.1 Determining number of solutions to linear equations
14.2 Solving simultaneous equations by graphing
14.3 Solving simultaneous equations by elimination
14.4 Solving simultaneous equations by substitution
14.5 Money related questions in linear equations
14.6 Unknown number related questions in linear equations
14.7 Distance and time related questions in linear equations
14.8 Rectangular shape related questions in linear equations
15. Inequalities in Two Variables
15.1 Graphing linear inequalities in two variables
15.2 Graphing simultaneous linear inequalities
15.3 Graphing quadratic inequalities in two variables
15.4 Graphing simultaneous quadratic inequalities
15.5 Applications of inequalities
15.6 What is linear programming?
15.7 Linear programming word problems
16. Introduction to Trigonometry
16.1 Use sine ratio to calculate angles and sides (Sin = )
16.2 Use cosine ratio to calculate angles and sides (Cos = )
16.3 Use tangent ratio to calculate angles and sides (Tan = )
16.4 Combination of SohCahToa questions
16.5 Solving expressions using 45-45-90 special right triangles
16.6 Solving expressions using 30-60-90 special right triangles
16.7 Word problems relating ladder in trigonometry
16.8 Word problems relating guy wire in trigonometry
16.9 Other word problems relating angles in trigonometry
17. Trigonometric Ratios and Angle Measure
18. Bearings
19. Graphing Trigonometric Functions
20. Applications of Trigonometric Functions
21. Trigonometric Identities
23. Imaginary and Complex Numbers
23.1 Introduction to imaginary numbers
23.2 Complex numbers and complex planes
23.3 Adding and subtracting complex numbers
23.4 Complex conjugates
23.5 Multiplying and dividing complex numbers
23.6 Distance and midpoint of complex numbers
23.7 Angle and absolute value of complex numbers
23.8 Polar form of complex numbers
23.9 Operations on complex numbers in polar form
24. Vectors
25. Sequences and Series
26. Permutations and Combinations
27. Introduction to Probability
28. Probability
29. Derivatives
29.1 Definition of derivative
29.2 Power rule
29.3 Gradient and equation of tangent line
29.4 Chain rule
29.5 Derivative of trigonometric functions
29.6 Derivative of exponential functions
29.7 Product rule
29.8 Quotient rule
29.9 Implicit differentiation
29.10 Derivative of inverse trigonometric functions
29.11 Derivative of logarithmic functions
29.12 Higher order derivatives
30. Introduction to Matrices
31. Properties of Matrices
32. Determinants and Inverses of Matrices
32.1 The determinant of a 2 x 2 matrix
32.2 The determinant of a 3 x 3 matrix (General & Shortcut Method)
32.3 The inverse of a 2 x 2 matrix
32.4 The inverse of 3 x 3 matrices with matrix row operations
32.5 The inverse of 3 x 3 matrix with determinants and adjugate
32.6 2 x 2 invertible matrix
32.7 Solving linear systems using Cramer's Rule
32.8 Solving linear systems using 2 x 2 inverse matrices
33. Transformations with Matrices
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