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Sixth Year Maths Topics
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1. Functions
1.1 Function notation
1.2 Operations with functions
1.3 Adding functions
1.4 Subtracting functions
1.5 Multiplying functions
1.6 Dividing functions
1.7 Composite functions
1.8 Inequalities of combined functions
1.9 Inverse functions
1.10 One to one functions
1.11 Difference quotient: applications of functions
2. Transformations of Functions
2.1 Transformations of functions: Horizontal translations
2.2 Transformations of functions: Vertical translations
2.3 Reflection across the y-axis: y = f(-x)
2.4 Reflection across the x-axis: y = -f(x)
2.5 Transformations of functions: Horizontal stretches
2.6 Transformations of functions: Vertical stretches
2.7 Combining transformations of functions
2.8 Even and odd functions
3. Quadratic Functions
3.1 Characteristics of quadratic functions
3.2 Transformations of quadratic functions
3.3 Quadratic function in general form: y = ax^2 + bx + c
3.4 Quadratic function in vertex form: y = a(x-p)^2 + q
3.5 Completing the square
3.6 Converting from general to vertex form by completing the square
3.7 Shortcut: Vertex formula
3.8 Graphing parabolas for given quadratic functions
3.9 Finding the quadratic functions for given parabolas
3.10 Applications of quadratic functions
4. Polynomial Functions
4.1 What is a polynomial function?
4.2 Polynomial long division
4.3 Polynomial synthetic division
4.4 Remainder theorem
4.5 Factor theorem
4.6 Rational zero theorem
4.7 Characteristics of polynomial graphs
4.8 Multiplicities of polynomials
4.9 Imaginary zeros of polynomials
4.10 Determining the equation of a polynomial function
4.11 Applications of polynomial functions
4.12 Solving polynomial inequalities
4.13 Fundamental theorem of algebra
4.14 Descartes' rule of signs
5. Radical Functions
6. Rational Functions
7. Exponential Functions
7.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
7.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
7.3 Exponents: Power rule (a^x)^y = a^(x * y)
7.4 Exponents: Negative exponents
7.5 Exponents: Zero exponent: a^0 = 1
7.6 Exponents: Rational exponents
7.7 Graphing exponential functions
7.8 Graphing transformations of exponential functions
7.9 Finding an exponential function given its graph
8. Logarithmic Functions
8.1 What is a logarithm?
8.2 Converting from logarithmic form to exponential form
8.3 Evaluating logarithms without a calculator
8.4 Common logarithms
8.5 Natural log: ln
8.6 Evaluating logarithms using change-of-base formula
8.7 Converting from exponential form to logarithmic form
8.8 Solving exponential equations with logarithms
8.9 Product rule of logarithms
8.10 Quotient rule of logarithms
8.11 Combining product rule and quotient rule in logarithms
8.12 Evaluating logarithms using logarithm rules
8.13 Solving logarithmic equations
8.14 Graphing logarithmic functions
8.15 Finding a logarithmic function given its graph
9. Applications of Exponential and Logarithmic Functions
9.1 Exponential growth and decay by a factor
9.2 Exponential decay: Half-life
9.3 Exponential growth and decay by percentage
9.4 Finance: Compound interest
9.5 Continuous growth and decay
9.6 Logarithmic scale: Richter scale (earthquake)
9.7 Logarithmic scale: pH scale
9.8 Logarithmic scale: dB scale
9.9 Finance: Future value and present value
10. Solving Simultaneous Equations
10.1 Determining number of solutions to linear equations
10.2 Solving simultaneous equations by graphing
10.3 Solving simultaneous equations by elimination
10.4 Solving simultaneous equations by substitution
10.5 Money related questions in linear equations
10.6 Unknown number related questions in linear equations
10.7 Distance and time related questions in linear equations
10.8 Rectangular shape related questions in linear equations
11. Simultaneous Equations (Advance)
11.1 Simultaneous linear equations
11.2 Simultaneous linear-quadratic equations
11.3 Simultaneous quadratic-quadratic equations
11.4 Solving 3 variable simultaneous equations by substitution
11.5 Solving 3 variable simultaneous equations by elimination
11.6 Solving 3 variable simultaneous equations with no or infinite solutions
11.7 Word problems relating 3 variable simultaneous equations
12. Inequalities in two variables
12.1 Graphing linear inequalities in two variables
12.2 Graphing simultaneous linear inequalities
12.3 Graphing quadratic inequalities in two variables
12.4 Graphing simultaneous quadratic inequalities
12.5 Applications of inequalities
12.6 What is linear programming?
12.7 Linear programming word problems
13. Trigonometry
13.1 Angle in standard position
13.2 Coterminal angles
13.3 Reference angle
13.4 Find the exact value of trigonometric ratios
13.5 ASTC rule in trigonometry (All Students Take Calculus)
13.6 Unit circle
13.7 Converting between degrees and radians
13.8 Trigonometric ratios of angles in radians
13.9 Radian measure and arc length
13.10 Law of sines
13.11 Law of cosines
13.12 Applications of the sine law and cosine law
14. Bearings
15. Graphing Trigonometric Functions
16. Applications of Trigonometric Functions
17. Trigonometric Identities
19. Imaginary and Complex Numbers
19.1 Introduction to imaginary numbers
19.2 Complex numbers and complex planes
19.3 Adding and subtracting complex numbers
19.4 Complex conjugates
19.5 Multiplying and dividing complex numbers
19.6 Distance and midpoint of complex numbers
19.7 Angle and absolute value of complex numbers
19.8 Polar form of complex numbers
19.9 Operations on complex numbers in polar form
20. Sequences and Series
21. Probability
22. Permutations and Combinations
23. Statistics
24. Limits
24.1 Finding limits from graphs
24.2 Limit laws
24.3 Continuity
24.4 Finding limits algebraically - direct substitution
24.5 Finding limits algebraically - when direct substitution is not possible
24.6 Infinite limits - vertical asymptotes
24.7 Limits at infinity - horizontal asymptotes
24.8 Intermediate value theorem
24.9 Squeeze theorem
25. Derivatives
25.1 Definition of derivative
25.2 Power rule
25.3 Gradient and equation of tangent line
25.4 Chain rule
25.5 Derivative of trigonometric functions
25.6 Derivative of exponential functions
25.7 Product rule
25.8 Quotient rule
25.9 Implicit differentiation
25.10 Derivative of inverse trigonometric functions
25.11 Derivative of logarithmic functions
25.12 Higher order derivatives
26 Chapters · 209 Topics · 1206 Videos
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