NZ Year 13 Maths Tutor, Help and Practice Online

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1Functions
1. 1.1Function notation
2. 1.2Operations with functions
3. 1.3Adding functions
4. 1.4Subtracting functions
5. 1.5Multiplying functions
6. 1.6Dividing functions
7. 1.7Composite functions
8. 1.8Inequalities of combined functions
9. 1.9Inverse functions
10. 1.10One to one functions
11. 1.11Difference quotient: applications of functions
2Transformations of Functions
1. 2.1Transformations of functions: Horizontal translations
2. 2.2Transformations of functions: Vertical translations
3. 2.3Reflection across the y-axis: $y = f(-x)$ $y = f (- x)$
4. 2.4Reflection across the x-axis: $y = -f(x)$ $y = - f (x)$
5. 2.5Transformations of functions: Horizontal stretches
6. 2.6Transformations of functions: Vertical stretches
7. 2.7Combining transformations of functions
8. 2.8Even and odd functions
3Quadratic Functions
1. 3.1Characteristics of quadratic functions
2. 3.2Transformations of quadratic functions
3. 3.3Quadratic function in general form: $y = ax^2 + bx+c$ $y = a x^{2} + b x + c$
4. 3.4Quadratic function in vertex form: $y = a(x-p)^2 + q$ $y = a (x - p)^{2} + q$
5. 3.5Completing the square
6. 3.6Converting from general to vertex form by completing the square
7. 3.7Shortcut: Vertex formula
8. 3.8Graphing parabolas for given quadratic functions
9. 3.9Finding the quadratic functions for given parabolas
10. 3.10Applications of quadratic functions
4Polynomial Functions
1. 4.1What is a polynomial function?
2. 4.2Polynomial long division
3. 4.3Polynomial synthetic division
4. 4.4Remainder theorem
5. 4.5Factor theorem
6. 4.6Rational zero theorem
7. 4.7Characteristics of polynomial graphs
8. 4.8Multiplicities of polynomials
9. 4.9Imaginary zeros of polynomials
10. 4.10Determining the equation of a polynomial function
11. 4.11Applications of polynomial functions
12. 4.12Solving polynomial inequalities
13. 4.13Fundamental theorem of algebra
14. 4.14Descartes' rule of signs
5Rational Functions
1. 5.1What is a rational function?
2. 5.2Point of discontinuity
3. 5.3Vertical asymptote
4. 5.4Horizontal asymptote
5. 5.5Slant asymptote
6. 5.6Graphs of rational functions
7. 5.7Solving equations with algebraic fractions
8. 5.8Solving rational inequalities
6Exponential Functions
1. 6.1Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$ $(a^{x}) (a^{y}) = a^{(x + y)}$
2. 6.2Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$ $\frac{a ^{x}}{a ^{y}} = a^{(x - y)}$
3. 6.3Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$ $(a^{x})^{y} = a^{(x \cdot y)}$
4. 6.4Exponents: Negative exponents
5. 6.5Exponents: Zero exponent: $a^0 = 1$ $a^{0} = 1$
6. 6.6Exponents: Rational exponents
7. 6.7Graphing exponential functions
8. 6.8Graphing transformations of exponential functions
9. 6.9Finding an exponential function given its graph
7Logarithmic Functions
1. 7.1What is a logarithm?
2. 7.2Converting from logarithmic form to exponential form
3. 7.3Evaluating logarithms without a calculator
4. 7.4Common logarithms
5. 7.5Natural log: ln
6. 7.6Evaluating logarithms using change-of-base formula
7. 7.7Converting from exponential form to logarithmic form
8. 7.8Solving exponential equations with logarithms
9. 7.9Product rule of logarithms
10. 7.10Quotient rule of logarithms
11. 7.11Combining product rule and quotient rule in logarithms
12. 7.12Evaluating logarithms using logarithm rules
13. 7.13Solving logarithmic equations
14. 7.14Graphing logarithmic functions
15. 7.15Finding a logarithmic function given its graph
8Applications of Exponential and Logarithmic Functions
1. 8.1Exponential growth and decay by a factor
2. 8.2Exponential decay: Half-life
3. 8.3Exponential growth and decay by percentage
4. 8.4Finance: Compound interest
5. 8.5Continuous growth and decay
6. 8.6Logarithmic scale: Richter scale (earthquake)
7. 8.7Logarithmic scale: pH scale
8. 8.8Logarithmic scale: dB scale
9. 8.9Finance: Future value and present value
9Quadratic Equations and Inequalities
1. 9.1Solving quadratic equations by factorising
2. 9.2Solving quadratic equations by completing the square
3. 9.3Using quadratic formula to solve quadratic equations
4. 9.4Nature of roots of quadratic equations: The discriminant
5. 9.5Applications of quadratic equations
6. 9.6Solving quadratic inequalities
10Solving Simultaneous Equations
1. 10.1Determining number of solutions to linear equations
2. 10.2Solving simultaneous equations by graphing
3. 10.3Solving simultaneous equations by elimination
4. 10.4Solving simultaneous equations by substitution
5. 10.5Money related questions in linear equations
6. 10.6Unknown number related questions in linear equations
7. 10.7Distance and time related questions in linear equations
8. 10.8Rectangular shape related questions in linear equations
11Simultaneous Equations (Advanced)
1. 11.1Simultaneous linear equations
2. 11.2Simultaneous linear-quadratic equations
3. 11.3Simultaneous quadratic-quadratic equations
4. 11.4Solving 3 variable simultaneous equations by substitution
5. 11.5Solving 3 variable simultaneous equations by elimination
6. 11.6Solving 3 variable simultaneous equations with no or infinite solutions
7. 11.7Word problems relating 3 variable simultaneous equations
12Introduction to Trigonometry
1. 12.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ $\frac{o}{h}$ )
2. 12.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ $\frac{a}{h}$ )
3. 12.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ $\frac{o}{a}$ )
4. 12.4Combination of SohCahToa questions
5. 12.5Solving expressions using 45-45-90 special right triangles
6. 12.6Solving expressions using 30-60-90 special right triangles
7. 12.7Word problems relating ladder in trigonometry
8. 12.8Word problems relating guy wire in trigonometry
9. 12.9Other word problems relating angles in trigonometry
13Trigonometric Ratios and Angle Measure
1. 13.1Standard angle
2. 13.2Coterminal angles
3. 13.3Reference angles
4. 13.4Find the exact value of trigonometric ratios
5. 13.5ASTC rule in trigonometry (All Students Take Calculus)
6. 13.6Unit circle
7. 13.7Law of sines
8. 13.8Law of cosines
9. 13.9Applications of the sine law and cosine law
14Bearings
1. 14.1Introduction to bearings
2. 14.2Bearings and direction word problems
3. 14.3Angle of elevation and depression
15Graphing Trigonometric Functions
1. 15.1Sine graph: y = sin x
2. 15.2Cosine graph: y = cos x
3. 15.3Tangent graph: y = tan x
4. 15.4Cotangent graph: y = cot x
5. 15.5Secant graph: y = sec x
6. 15.6Cosecant graph: y = csc x
7. 15.7Graphing transformations of trigonometric functions
8. 15.8Determining trigonometric functions given their graphs
16Trigonometric Identities
1. 16.1Quotient identities and reciprocal identities
2. 16.2Pythagorean identities
3. 16.3Sum and difference identities
4. 16.4Cofunction identities
5. 16.5Double-angle identities
17Conics
1. 17.1Conics - Parabola
2. 17.2Conics - Ellipse
3. 17.3Conics - Circle
4. 17.4Conics - Hyperbola
18Imaginary and Complex Numbers
1. 18.1Introduction to imaginary numbers
2. 18.2Complex numbers and complex planes
3. 18.3Adding and subtracting complex numbers
4. 18.4Complex conjugates
5. 18.5Multiplying and dividing complex numbers
6. 18.6Distance and midpoint of complex numbers
7. 18.7Angle and absolute value of complex numbers
8. 18.8Polar form of complex numbers
9. 18.9Operations on complex numbers in polar form
19Sequences and Series
1. 19.1Arithmetic sequences
2. 19.2Arithmetic series
3. 19.3Geometric sequences
4. 19.4Geometric series
5. 19.5Infinite geometric series
6. 19.6Sigma notation
7. 19.7Arithmetic mean vs. Geometric mean
20Probability
1. 20.1Determining probabilities using tree diagrams and tables
2. 20.2Probability of independent events
3. 20.3Probability with Venn diagrams
21Statistics
1. 21.1Median and mode
2. 21.2Mean
3. 21.3Range and outliers
4. 21.4Application of averages
22Limits
1. 22.1Finding limits from graphs
2. 22.2Continuity
3. 22.3Finding limits algebraically - direct substitution
4. 22.4Finding limits algebraically - when direct substitution is not possible
5. 22.5Infinite limits - vertical asymptotes
6. 22.6Limits at infinity - horizontal asymptotes
7. 22.7Intermediate value theorem
8. 22.8Squeeze theorem
23Derivatives
1. 23.1Definition of derivative
2. 23.2Power rule
3. 23.3Gradient and equation of tangent line
4. 23.4Chain rule
5. 23.5Derivative of trigonometric functions
6. 23.6Derivative of exponential functions
7. 23.7Product rule
8. 23.8Quotient rule
9. 23.9Implicit differentiation
10. 23.10Derivative of inverse trigonometric functions
11. 23.11Derivative of logarithmic functions
12. 23.12Higher order derivatives

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NZ Year 13 Maths made completely easy!

1Functions

2Transformations of Functions

3Quadratic Functions

4Polynomial Functions

5Rational Functions

6Exponential Functions

7Logarithmic Functions

8Applications of Exponential and Logarithmic Functions

9Quadratic Equations and Inequalities

10Solving Simultaneous Equations

11Simultaneous Equations (Advanced)

12Introduction to Trigonometry

13Trigonometric Ratios and Angle Measure

14Bearings

15Graphing Trigonometric Functions

16Trigonometric Identities

17Conics

18Imaginary and Complex Numbers

19Sequences and Series

20Probability

21Statistics

22Limits

23Derivatives

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