# NZ Year 12 Maths Help & Practice!

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##### 1Solving Linear Equations

##### 2Linear Inequalities

##### 3Linear Functions

- 3.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 3.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 3.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 3.4Gradient intercept form: y = mx + b
- 3.5General form: Ax + By + C = 0
- 3.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 3.7Rate of change
- 3.8Graphing linear functions using table of values
- 3.9Graphing linear functions using x- and y-intercepts
- 3.10Graphing from gradient-intercept form y=mx+b
- 3.11Graphing linear functions using a single point and gradient
- 3.12Word problems of graphing linear functions
- 3.13Parallel and perpendicular lines in linear functions
- 3.14Applications of linear relations

- 3.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 4Factorising

##### 5Quadratic Functions

- 5.1Characteristics of quadratic functions
- 5.2Transformations of quadratic functions
- 5.3Quadratic function in general form:
*y = ax^2 + bx + c* - 5.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 5.5Completing the square
- 5.6Converting from general to vertex form by completing the square
- 5.7Shortcut: Vertex formula
- 5.8Graphing parabolas for given quadratic functions
- 5.9Finding the quadratic functions for given parabolas
- 5.10Applications of quadratic functions

- 5.1Characteristics of quadratic functions
##### 6Quadratic Equations and Inequalities

##### 7Solving Simultaneous Equations

- 7.1Determining number of solutions to linear equations
- 7.2Solving simultaneous equations by graphing
- 7.3Solving simultaneous equations by elimination
- 7.4Solving simultaneous equations by substitution
- 7.5Money related questions in linear equations
- 7.6Unknown number related questions in linear equations
- 7.7Distance and time related questions in linear equations
- 7.8Rectangular shape related questions in linear equations

- 7.1Determining number of solutions to linear equations
##### 8Simultaneous Equations (Advanced)

- 8.1Simultaneous linear equations
- 8.2Simultaneous linear-quadratic equations
- 8.3Simultaneous quadratic-quadratic equations
- 8.4Solving 3 variable simultaneous equations by substitution
- 8.5Solving 3 variable simultaneous equations by elimination
- 8.6Solving 3 variable simultaneous equations with no or infinite solutions
- 8.7Word problems relating 3 variable simultaneous equations

- 8.1Simultaneous linear equations
##### 9Inequalities in two variables (Advanced)

##### 10Imaginary and Complex Numbers

- 10.1Introduction to imaginary numbers
- 10.2Complex numbers and complex planes
- 10.3Adding and subtracting complex numbers
- 10.4Complex conjugates
- 10.5Multiplying and dividing complex numbers
- 10.6Distance and midpoint of complex numbers
- 10.7Angle and absolute value of complex numbers
- 10.8Polar form of complex numbers
- 10.9Operations on complex numbers in polar form

- 10.1Introduction to imaginary numbers
##### 11Polynomial Functions

- 11.1What is a polynomial function?
- 11.2Polynomial long division
- 11.3Polynomial synthetic division
- 11.4Remainder theorem
- 11.5Factor theorem
- 11.6Rational zero theorem
- 11.7Characteristics of polynomial graphs
- 11.8Multiplicities of polynomials
- 11.9Imaginary zeros of polynomials
- 11.10Determining the equation of a polynomial function
- 11.11Applications of polynomial functions
- 11.12Solving polynomial inequalities
- 11.13Fundamental theorem of algebra
- 11.14Descartes' rule of signs

- 11.1What is a polynomial function?
##### 12Radicals

##### 13Exponents

- 13.1Product rule of exponents
- 13.2Quotient rule of exponents
- 13.3Power of a product rule
- 13.4Power of a quotient rule
- 13.5Power of a power rule
- 13.6Negative exponent rule
- 13.7Combining the exponent rules
- 13.8Scientific notation
- 13.9Convert between radicals and rational exponents
- 13.10Solving for exponents

- 13.1Product rule of exponents
##### 14Algebraic Fractions

- 14.1Simplifying algebraic fractions and restrictions
- 14.2Adding and subtracting algebraic fractions
- 14.3Multiplying algebraic fractions
- 14.4Dividing algebraic fractions
- 14.5Solving equations with algebraic fractions
- 14.6Applications of equations with algebraic fractions
- 14.7Simplifying complex fractions
- 14.8Partial fraction decomposition

- 14.1Simplifying algebraic fractions and restrictions
##### 15Reciprocal Functions

##### 16Rational Functions

##### 17Operations of Functions

- 17.1Function notation
- 17.2Operations with functions
- 17.3Adding functions
- 17.4Subtracting functions
- 17.5Multiplying functions
- 17.6Dividing functions
- 17.7Composite functions
- 17.8Inequalities of combined functions
- 17.9Inverse functions
- 17.10One to one functions
- 17.11Difference quotient: applications of functions

- 17.1Function notation
##### 18Transformations of Functions

- 18.1Transformations of functions: Horizontal translations
- 18.2Transformations of functions: Vertical translations
- 18.3Reflection across the y-axis:
*y = f(-x)* - 18.4Reflection across the x-axis:
*y = -f(x)* - 18.5Transformations of functions: Horizontal stretches
- 18.6Transformations of functions: Vertical stretches
- 18.7Combining transformations of functions
- 18.8Even and odd functions

- 18.1Transformations of functions: Horizontal translations
##### 19Exponential Functions

- 19.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 19.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 19.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 19.4Exponents: Negative exponents
- 19.5Exponents: Zero exponent:
*a^0 = 1* - 19.6Exponents: Rational exponents
- 19.7Graphing exponential functions
- 19.8Graphing transformations of exponential functions
- 19.9Finding an exponential function given its graph

- 19.1Exponents: Product rule
##### 20Logarithmic Functions

- 20.1What is a logarithm?
- 20.2Converting from logarithmic form to exponential form
- 20.3Evaluating logarithms without a calculator
- 20.4Common logarithms
- 20.5Natural log: ln
- 20.6Evaluating logarithms using change-of-base formula
- 20.7Converting from exponential form to logarithmic form
- 20.8Solving exponential equations with logarithms
- 20.9Product rule of logarithms
- 20.10Quotient rule of logarithms
- 20.11Combining product rule and quotient rule in logarithms
- 20.12Evaluating logarithms using logarithm rules
- 20.13Solving logarithmic equations
- 20.14Graphing logarithmic functions
- 20.15Finding a logarithmic function given its graph

- 20.1What is a logarithm?
##### 21Applications of Exponential and Logarithmic Functions

- 21.1Exponential growth and decay by a factor
- 21.2Exponential decay: Half-life
- 21.3Exponential growth and decay by percentage
- 21.4Finance: Compound interest
- 21.5Continuous growth and decay
- 21.6Logarithmic scale: Richter scale (earthquake)
- 21.7Logarithmic scale: pH scale
- 21.8Logarithmic scale: dB scale
- 21.9Finance: Future value and present value

- 21.1Exponential growth and decay by a factor
##### 22Introduction to Trigonometry

- 22.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 22.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 22.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 22.4Combination of SohCahToa questions
- 22.5Solving expressions using 45-45-90 special right triangles
- 22.6Solving expressions using 30-60-90 special right triangles
- 22.7Word problems relating ladder in trigonometry
- 22.8Word problems relating guy wire in trigonometry
- 22.9Other word problems relating angles in trigonometry

- 22.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 23Trigonometric Ratios and Angle Measure

##### 24Bearings

##### 25Graphing Trigonometric Functions

##### 26Trigonometric Identities

##### 27Conics

##### 28Surface Area and Volume

##### 29Sequences and Series

##### 30Probability

##### 31Permutations and Combinations

##### 32Statistics

##### 33Data and Graphs