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Year 13 Maths Topics

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1. Functions

1.1 Domain and range of a function
1.2 Function notation
1.3 Operations with functions
1.4 Adding functions
1.5 Subtracting functions
1.6 Multiplying functions
1.7 Dividing functions
1.8 Composite functions
1.9 Inequalities of combined functions
1.10 Inverse functions
1.11 One to one functions
1.12 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. Quadratic Equations and Inequalities

4.1 Solving quadratic equations by factorising
4.2 Solving quadratic equations by completing the square
4.3 Using quadratic formula to solve quadratic equations
4.4 Nature of roots of quadratic equations: The discriminant
4.5 Applications of quadratic equations
4.6 Solving quadratic inequalities

5. Polynomial Functions

5.1 What is a polynomial function?
5.2 Polynomial long division
5.3 Polynomial synthetic division
5.4 Remainder theorem
5.5 Factor theorem
5.6 Rational zero theorem
5.7 Characteristics of polynomial graphs
5.8 Multiplicities of polynomials
5.9 Imaginary zeros of polynomials
5.10 Determining the equation of a polynomial function
5.11 Applications of polynomial functions
5.12 Solving polynomial inequalities
5.13 Fundamental theorem of algebra
5.14 Descartes' rule of signs

6. Rational Functions

6.1 What is a rational function?
6.2 Point of discontinuity
6.3 Vertical asymptote
6.4 Horizontal asymptote
6.5 Slant asymptote
6.6 Graphs of rational functions
6.7 Solving equations with algebraic fractions
6.8 Solving rational inequalities

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 Solving exponential equations using exponent rules
7.8 Graphing exponential functions
7.9 Graphing transformations of exponential functions
7.10 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. Radical Functions

9.1 Basic radical functions
9.2 Transformations of radical functions
9.3 Square root of a function
9.4 Solving radical equations

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. Trigonometry

11.1 Sine rule
11.2 Cosine rule
11.3 Applications of the sine rule and cosine rule

12. Bearings

12.1 Introduction to bearings
12.2 Bearings and direction word problems
12.3 Angle of elevation and depression

13. Trigonometric Ratios and Angle Measure

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

14. Graphing Trigonometric Functions

14.1 Sine graph: y = sin x
14.2 Cosine graph: y = cos x
14.3 Tangent graph: y = tan x
14.4 Cotangent graph: y = cot x
14.5 Secant graph: y = sec x
14.6 Cosecant graph: y = csc x
14.7 Graphing transformations of trigonometric functions
14.8 Determining trigonometric functions given their graphs

15. Trigonometric Identities

15.1 Quotient identities and reciprocal identities
15.2 Pythagorean identities
15.3 Sum and difference identities
15.4 Cofunction identities
15.5 Double-angle identities

16. Parabolas and Circles

16.1 Conics - Parabola
16.2 Conics - Circle

17. Two-dimensional vectors

17.1 Introduction to vectors
17.2 Magnitude of a vector
17.3 Direction angle of a vector
17.4 Scalar multiplication
17.5 Equivalent vectors
17.6 Adding and subtracting vectors in component form
17.7 Operations on vectors in magnitude and direction form
17.8 Unit Vector
17.9 Word problems on vectors

18. Sequences and Series

18.1 Arithmetic sequences
18.2 Arithmetic series
18.3 Geometric sequences
18.4 Geometric series
18.5 Infinite geometric series
18.6 Sigma notation
18.7 Arithmetic mean vs. Geometric mean

19. Data Interpretation

19.1 Center of a data set: mean, median, mode
19.2 Spread of a data set - standard deviation & variance
19.3 Measures of relative standing - z-score, quartiles, percentiles
19.4 Bivariate, scatter plots and correlation
19.5 Regression analysis
19.6 Equation of the best fit line

20. Discrete Probabilities

20.1 Probability distribution - histogram, mean, variance & standard deviation
20.2 Binomial distribution
20.3 Mean and standard deviation of binomial distribution
20.4 Poisson distribution
20.5 Geometric distribution
20.6 Negative binomial distribution

21. Probability

21.1 Addition rule for "OR"
21.2 Multiplication rule for "AND"
21.3 Conditional probability
21.4 Probability with permutations and combinations
21.5 Law of total probability
21.6 Bayes' rule

22. Permutations and Combinations

22.1 Fundamental counting principle
22.2 Factorial notation
22.3 Path counting problems
22.4 Permutation vs. Combination
22.5 Permutations
22.6 Combinations
22.7 Problems involving both permutations and combinations
22.8 Pascal's triangle
22.9 Binomial theorem

23. Integration Techniques

23.1 U-Substitution
23.2 Integration by parts
23.3 Integration using trigonometric identities
23.4 Trigonometric substitution
23.5 Integration of rational functions by partial fractions
23.6 Improper integrals

24. Derivatives

24.1 Definition of derivative
24.2 Power rule
24.3 Slope and equation of tangent line
24.4 Chain rule
24.5 Derivative of trigonometric functions
24.6 Derivative of exponential functions
24.7 Product rule
24.8 Quotient rule
24.9 Implicit differentiation
24.10 Derivative of inverse trigonometric functions
24.11 Derivative of logarithmic functions
24.12 Higher order derivatives
24.13 Tangent and concavity of parametric equations

25. Integration Applications

25.1 Areas between curves
25.2 Volumes of solids with known cross-sections
25.3 Volumes of solids of revolution - Disc method
25.4 Volumes of solids of revolution - Shell method
25.5 Average value of a function
25.6 Arc length

25 Chapters · 193 Topics · 1157 Videos

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