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Resources for Grade twelve

Functions

How to determine domain and range of functions

How to add, subtract, multiply and divide fractions

How to compose functions

How to find inverse functions and relations

How to identify transformations of functions

What are the function transformation rules

What are the characteristics of quadratic functions

How to find the maximum or minimum value of a quadratic function

How to graph a quadratic function

How to solve quadratic equations

Polynomials

How to divide polynomials

How to find the roots of factored polynomials

How to use the binomial theorem

How to factor sums and differences of cubes

How to use the complex conjugate theorem

How to use the conjugate roots theorems

How to use the fundamental theorem of algebra

How to sole equations using a quadratic pattern

How to use the Descartes rule of signs

Rational functions

How to solve rational equations

How to find asymptotes and excluded values of rational functions

Exponential and logarithmic functions

How to determine the domain and the range of logarithmic and exponential functions

How to convert between exponential and logarithmic form

How to solve exponential equations

How to solve logarithmic equations

How to identify linear and exponential functions

How to evaluate logarithms

Radical functions

How to determine the domain and the range of radical functions

How to solve radical equations

Roots and rational exponents

Roots of integers and rational numbers

How to evaluate rational exponents

How to simplify radical expressions with variables

Simplify expressions involving rational exponents

How to find the Nth root

Systems of equations

How to solve a system of equation by graphing

How to classify a system of equations

How to solve a system of equations using elimination and substitution

How to solve a system of equations in three variables using elimination and substitution

How to determine the number of solutions to a system of equations in three variables

Inequalities

How to solve systems of linear and absolute value inequalities by graphing

What is linear programming

How to graph solutions to quadratic inequalities

How to solve quadratic inequalities

How t solve higher-degree inequalities

Matrices

How to add, subtract and multiply matrices

How to solve matrix equations

How to perform a linear combination of matrices

How to calculate the inverse of a two by two matrix

How to calculate the inverse of a three by three matrix

How to identify inverse matrices

How to solve matrix equations using inverses

Trigonometry

How to convert between radians and degrees

How to find trigonometric ratios

How to solve trigonometric equations

What are the laws of Sine and Cosine

How to graph sine and cosine functions

How to write equations of sine and cosine functions from graph

How to determine the symmetry and the periodicity of trigonometric functions

Conic sections

How to find properties of parabolas and hyperbolas

How to graph parabolas and hyperbolas

What are the properties of circles and ellipses

How to graphs circles and ellipses

How to convert equations of conic sections from general to standard form

Complex numbers

How to add, subtract, multiply and divide complex numbers

How to determine absolute values of complex numbers

How to compute the powers of i

How to add and subtract in the complex plane

How to determine absolute values in the complex plane

Midpoints and distance in the complex plane

How to find the modulus and argument of a complex number

How to convert complex numbers between rectangular and polar form

How to graph polar equations

Vectors

How to determine the magnitude of two and three-dimensional vectors

How to add and subtract three-dimensional vectors

How to graph a resultant vector

How to process linear combinations of three vectors

How to multiply a vector by a scalar

How to find the magnitude and direction of a vector sum

Sequences and series

How to find terms of a recursive sequence

How to find a recursive formula

How to convert between explicit and recursive formula

How to find the sum of finite arithmetic or geometric series

Find the value of an infinite geometric series

Probability

How to calculate probabilities of events

How to use combinations and permutations

How to identify independent or dependent events

How to find conditional probabilities

How to find probabilities using the addition rule

How to identify discrete and random variables

How to determine expected values of random variables

How to find probabilities using the binomial distribution

How to find mean, variance and standard deviation of binomial distributions

How to use the central limit theorem

How to find values of normal variables

How to use normal distributions to approximate binomial distributions

How to identify biased samples

How to find the variance and standard deviation

How to find the equation of a regression line

How to calculate variance, standard deviation and correlation coefficients

How to interpret regression lines

How to find confidence intervals

How to identify an outlier