Grade 12 Mathematics

Find values of functions from graphs

Find values of functions from graphs

Add, subtract, multiply, and divide functions

Add, subtract, multiply, and divide functions

Composition of functions

Composition of functions

Identify inverse functions

Identify inverse functions

Find values of inverse functions from tables

Find values of inverse functions from tables

Find values of inverse functions from graphs

Find values of inverse functions from graphs

Find inverse functions and relations

Find inverse functions and relations

Find values using function graphs

Find values using function graphs

Linear functions

Linear functions

Average rate of change

Average rate of change

Complete a table for a function graph

Complete a table for a function graph

Function transformation rules

Function transformation rules

Translations of functions

Translations of functions

Reflections of functions

Reflections of functions

Dilations of functions

Dilations of functions

Transformations of functions

Transformations of functions

Describe function transformations

Describe function transformations

Solve a system of equations by graphing: word problems (Tutorial only)

Solve a system of equations by graphing: word problems (Tutorial only)

Solve a system of equations by graphing (Tutorial only)

Solve a system of equations by graphing (Tutorial only)

Solve a system of equations using substitution: word problems

Solve a system of equations using substitution: word problems

Solve a system of equations using elimination

Solve a system of equations using elimination

Convert between radians and degrees

Convert between radians and degrees

Quadrants

Quadrants

Coterminal and reference angles

Coterminal and reference angles

Find trigonometric ratios using right triangles

Find trigonometric ratios using right triangles

Find trigonometric ratios using the unit circle

Find trigonometric ratios using the unit circle

Find trigonometric ratios using reference angles

Find trigonometric ratios using reference angles

Inverses of trigonometric functions

Inverses of trigonometric functions

Find properties of sine functions

Find properties of sine functions

Write equations of sine functions from graphs

Write equations of sine functions from graphs

Write equations of sine functions using properties

Write equations of sine functions using properties

Graph sine functions

Graph sine functions

Find properties of cosine functions

Find properties of cosine functions

Write equations of cosine functions from graphs

Write equations of cosine functions from graphs

Write equations of cosine functions using properties

Write equations of cosine functions using properties

Graph cosine functions

Graph cosine functions

Graph sine and cosine functions

Graph sine and cosine functions

Find limits using graphs

Find limits using graphs

Find one-sided limits using graphs

Find one-sided limits using graphs

Determine if a limit exists

Determine if a limit exists

Count on twenty frames (up to 20)

Count on twenty frames (up to 20)

Represent numbers (up to 20)

Represent numbers (up to 20)

Find limits using addition, subtraction, and multiplication laws

Find limits using addition, subtraction, and multiplication laws

Find limits using the division law

Find limits using the division law

Find limits using power and root laws

Find limits using power and root laws

Find limits using limit laws

Find limits using limit laws

Find limits of polynomials and rational functions

Find limits of polynomials and rational functions

Find limits involving factorization and rationalization

Find limits involving factorization and rationalization

Find terms of a recursive sequence

Find terms of a recursive sequence

Convert a recursive formula to an explicit formula

Convert a recursive formula to an explicit formula

Find recursive and explicit formulas

Find recursive and explicit formulas

Convert between explicit and recursive formulas

Convert between explicit and recursive formulas

Convert an explicit formula to a recursive formula

Convert an explicit formula to a recursive formula

Introduction to partial sums

Introduction to partial sums

Find the sum of a finite arithmetic or geometric series

Find the sum of a finite arithmetic or geometric series

Partial sums of geometric series

Partial sums of geometric series

Partial sums of arithmetic series

Partial sums of arithmetic series

Find the value of an infinite geometric series

Find the value of an infinite geometric series

Partial sums mixed review

Partial sums mixed review

Find limits at vertical asymptotes using graphs

Find limits at vertical asymptotes using graphs

Determine end behavior using graphs

Determine end behavior using graphs

Determine end behavior of polynomial and rational functions

Determine end behavior of polynomial and rational functions

Calculate probabilities of events

Calculate probabilities of events

Find probabilities using twoway frequency tables

Find probabilities using twoway frequency tables

Find probabilities using combinations and permutations

Find probabilities using combinations and permutations

Find conditional probabilities

Find conditional probabilities

Independence and conditional probability

Independence and conditional probability

Find conditional probabilities using two-way frequency tables

Find conditional probabilities using two-way frequency tables

Find probabilities using the addition rule

Find probabilities using the addition rule

Find the limit at a vertical asymptote of a rational function I

Find the limit at a vertical asymptote of a rational function I

Find the limit at a vertical asymptote of a rational function II

Find the limit at a vertical asymptote of a rational function II

Graph a discrete probability distribution (Tutorial Only)

Graph a discrete probability distribution (Tutorial Only)

Expected values of random variables

Expected values of random variables

Write the probability distribution for a game of chance

Write the probability distribution for a game of chance

Variance and standard deviation of random variables

Variance and standard deviation of random variables

Expected values for a game of chance

Expected values for a game of chance

Choose the better bet

Choose the better bet

Mean variance and standard deviation of binomial distributions

Mean variance and standard deviation of binomial distributions

Find probabilities using the binomial distribution

Find probabilities using the binomial distribution

Find z-values

Find z-values

Find probabilities using the normal distribution

Find probabilities using the normal distribution

Distributions of sample means

Distributions of sample means

Find values of normal variables

Find values of normal variables

Use normal distributions to approximate binomial distributions

Use normal distributions to approximate binomial distributions

The Central Limit Theorem

The Central Limit Theorem

Rational functions asymptotes and excluded values

Rational functions asymptotes and excluded values

Solve rational equations

Solve rational equations

Identify graphs of continuous functions

Identify graphs of continuous functions

Determine continuity using graphs

Determine continuity using graphs

Determine one-sided continuity using graphs

Determine one-sided continuity using graphs

Find and analyze points of discontinuity using graphs

Find and analyze points of discontinuity using graphs

Determine continuity on an interval using graphs

Determine continuity on an interval using graphs

Determine the continuity of a piecewise defined function at a point

Determine the continuity of a piecewise defined function at a point

Intermediate Value Theorem

Intermediate Value Theorem

Calculate correlation coefficients

Calculate correlation coefficients

Interpret regression lines

Interpret regression lines

Analyze a regression line of a data set

Analyze a regression line of a data set

Find confidence intervals for population means

Find confidence intervals for population means

Analyze a regression line using statistics of a data set

Analyze a regression line using statistics of a data set

Find confidence intervals for population proportions

Find confidence intervals for population proportions

Analyze the results of an experiment using simulations

Analyze the results of an experiment using simulations

Identify an outlier

Identify an outlier

Variance and standard deviation

Variance and standard deviation

Average rate of change I

Average rate of change I

Average rate of change II

Average rate of change II

Find instantaneous rates of change

Find instantaneous rates of change

Velocity as a rate of change

Velocity as a rate of change

Find values of derivatives using limits

Find values of derivatives using limits

Find the slope of a tangent line using limits

Find the slope of a tangent line using limits

Find equations of tangent lines using limits

Find equations of tangent lines using limits

Sum and difference rules

Sum and difference rules

Product rule

Product rule

Quotient rule

Quotient rule

Power rule I

Power rule I

Power rule II

Power rule II

Find derivatives of polynomials

Find derivatives of polynomials

Find derivatives of rational functions

Find derivatives of rational functions

Find derivatives of trigonometric functions

Find derivatives of trigonometric functions

Chain rule

Chain rule

Find derivatives using implicit differentiation

Find derivatives using implicit differentiation

Find tangent lines using implicit differentiation

Find tangent lines using implicit differentiation

Find derivatives of exponential functions

Find derivatives of exponential functions

Find derivatives of logarithmic functions

Find derivatives of logarithmic functions

Find derivatives using the product rule I

Find derivatives using the product rule I

Find derivatives using the product rule II

Find derivatives using the product rule II

Find derivatives using the quotient rule I

Find derivatives using the quotient rule I

Find derivatives using the quotient rule II

Find derivatives using the quotient rule II

Find the maximum or minimum value of a quadratic function

Find the maximum or minimum value of a quadratic function

Graph a quadratic function

Graph a quadratic function

Characteristics of quadratic functions

Characteristics of quadratic functions

Solve a quadratic equation using square roots

Solve a quadratic equation using square roots

Match quadratic functions and graphs

Match quadratic functions and graphs

Solve a quadratic equation by completing the square

Solve a quadratic equation by completing the square

Solve a quadratic equation using the quadratic formula

Solve a quadratic equation using the quadratic formula

Using the discriminant

Using the discriminant

Divide polynomials using long division

Divide polynomials using long division

Divide polynomials using synthetic division

Divide polynomials using synthetic division

Evaluate polynomials using synthetic division

Evaluate polynomials using synthetic division

Find the roots of factored polynomials

Find the roots of factored polynomials

Write a polynomial from its roots

Write a polynomial from its roots

Rational root theorem

Rational root theorem

Conjugate root theorems

Conjugate root theorems

Complex conjugate theorem

Complex conjugate theorem

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

Descartes' Rule of Signs

Descartes' Rule of Signs

Factor sums and differences of cubes

Factor sums and differences of cubes

Solve equations with sums and differences of cubes

Solve equations with sums and differences of cubes

Factor using a quadratic pattern

Factor using a quadratic pattern

Solve equations using a quadratic pattern

Solve equations using a quadratic pattern

Pascal's triangle and the Binomial Theorem

Pascal's triangle and the Binomial Theorem

Pascal's triangle

Pascal's triangle

Binomial Theorem I

Binomial Theorem I

Binomial Theorem II

Binomial Theorem II

Find the component form of a threedimensional vector

Find the component form of a threedimensional vector

Find the magnitude of a threedimensional vector

Find the magnitude of a threedimensional vector

Add and subtract threedimensional vectors

Add and subtract threedimensional vectors

Scalar multiples of threedimensional vectors

Scalar multiples of threedimensional vectors

Linear combinations of threedimensional vectors

Linear combinations of threedimensional vectors

Find a threedimensional unit vector

Find a threedimensional unit vector

Quotient property of logarithms

Quotient property of logarithms

Power property of logarithms

Power property of logarithms

Evaluate logarithms using properties

Evaluate logarithms using properties

Solve logarithmic equations with one logarithm

Solve logarithmic equations with one logarithm

Solve exponential equations using logarithms

Solve exponential equations using logarithms

Exponential growth and decay word problems

Exponential growth and decay word problems

Solve logarithmic equations with multiple logarithms

Solve logarithmic equations with multiple logarithms

Compound interest word problems

Compound interest word problems

Identify linear and exponential functions

Identify linear and exponential functions

Domain and range of exponential and logarithmic functions

Domain and range of exponential and logarithmic functions

Convert between exponential and logarithmic form

Convert between exponential and logarithmic form

Evaluate logarithms

Evaluate logarithms

Change of base formula

Change of base formula

Product property of logarithms

Product property of logarithms

Describe linear and exponential growth and decay

Describe linear and exponential growth and decay

Solve systems of linear and absolute value inequalities by graphing

Solve systems of linear and absolute value inequalities by graphing

Solve systems of linear inequalities by graphing

Solve systems of linear inequalities by graphing

Linear programming

Linear programming

Find the vertices of a solution set

Find the vertices of a solution set

Graph solutions to quadratic inequalities

Graph solutions to quadratic inequalities

Solve quadratic inequalities

Solve quadratic inequalities

Solve higher degree inequalities

Solve higher degree inequalities

Graph solutions to higherdegree inequalities

Graph solutions to higherdegree inequalities

Multiply a matrix by a scalar

Multiply a matrix by a scalar

Add and subtract matrices

Add and subtract matrices

Add and subtract scalar multiples of matrices

Add and subtract scalar multiples of matrices

Solve matrix equations

Solve matrix equations

Inverse of a 2 x 2 matrix

Inverse of a 2 x 2 matrix

Determinant of a matrix

Determinant of a matrix

Solve matrix equations using inverses

Solve matrix equations using inverses

Matrix vocabulary

Matrix vocabulary

Matrix operation rules

Matrix operation rules

Multiply two matrices

Multiply two matrices

Inverse of a 3 x 3 matrix

Inverse of a 3 x 3 matrix

Simplify matrix expressions

Simplify matrix expressions

Transformation matrices graph the image

Transformation matrices graph the image

Transformation matrices write the vertex matrix

Transformation matrices write the vertex matrix

Radians and arc length

Radians and arc length

Convert between radians and degrees

Convert between radians and degrees

Coterminal and reference angles

Coterminal and reference angles

Find trigonometric ratios using right triangles

Find trigonometric ratios using right triangles

Find trigonometric ratios using the unit circle

Find trigonometric ratios using the unit circle

Find trigonometric ratios using reference angles

Find trigonometric ratios using reference angles

Inverses of trigonometric functions

Inverses of trigonometric functions

Trigonometric ratios find a side length

Trigonometric ratios find a side length

Trigonometric ratios find an angle measure

Trigonometric ratios find an angle measure

Law of Cosines

Law of Cosines

Area of a triangle sine formula

Area of a triangle sine formula

Area of a triangle Heron's formula

Area of a triangle Heron's formula

Solve trigonometric equations

Solve a triangle

Law of Sines

Complementary angle identities

Complementary angle identities

Trigonometric identities I

Trigonometric identities I

Trigonometric identities II

Trigonometric identities II

Write equations of parabolas in vertex form

Write equations of parabolas in vertex form

Graph parabolas

Graph parabolas

Find properties of circles

Find properties of circles

Write equations of circles in standard form

Write equations of circles in standard form

Graph circles (Tutorial Only)

Graph circles (Tutorial Only)

Find properties of ellipses

Find properties of ellipses

Find the eccentricity of an ellipse

Find the eccentricity of an ellipse

Write equations of ellipses in standard form

Write equations of ellipses in standard form

Find properties of hyperbolas (Tutorial)

Find properties of hyperbolas (Tutorial)

Write equations of hyperbolas in standard form

Write equations of hyperbolas in standard form

Find the eccentricity of a hyperbola

Find the eccentricity of a hyperbola

Convert equations of conic sections from general to standard form

Convert equations of conic sections from general to standard form

Add and subtract complex numbers

Add and subtract complex numbers

Complex conjugates

Complex conjugates

Multiply and divide complex numbers

Multiply and divide complex numbers

Absolute values of complex numbers

Absolute values of complex numbers

Add subtract multiply and divide complex numbers

Add subtract multiply and divide complex numbers

Powers of i

Powers of i

Introduction to the complex plane

Introduction to the complex plane

Graph complex numbers

Graph complex numbers

Addition in the complex plane

Addition in the complex plane

Graph complex conjugates

Graph complex conjugates

Subtraction in the complex plane

Subtraction in the complex plane

Midpoints in the complex plane

Midpoints in the complex plane

Absolute value in the complex plane

Absolute value in the complex plane

Distance in the complex plane

Distance in the complex plane

Find the modulus and argument of a complex number

Find the modulus and argument of a complex number

Convert complex numbers from polar to rectangular form

Convert complex numbers from polar to rectangular form

Convert complex numbers from rectangular to polar form

Convert complex numbers from rectangular to polar form

Match polar equations and graphs

Match polar equations and graphs

Convert complex numbers between rectangular and polar form

Convert complex numbers between rectangular and polar form

What does the punctuation suggest?

Commas with nonrestrictive elements

Use dashes

Use hyphens in compound adjectives

Classify a system of equations

Determine the number of solutions to a system of equations in three variables

Solve a system of equations using substitution

Solve a system of equations using elimination: word problems

Solve a system of equations in three variables using substitution

Solve a system of equations in three variables using elimination

Domain and range of radical functions

Solve radical equations

Classify rational and irrational numbers

Properties of operations on rational and irrational numbers

Find a recursive formula

Identify a sequence as explicit or recursive

Identify arithmetic and geometric series

Introduction to sigma notation

Convergent and divergent geometric series

Find terms of a sequence

Introduction to probability

Identify independent events

Combinations and permutations

Identify discrete and continuous random variables

Write a discrete probability distribution

Identify biased samples

Identify an outlier and describe the effect of removing it

Experiment design

Interpret confidence intervals for population means

Outliers in scatter plots

Match correlation coefficients to scatter plots (Tutorial Only)

Find the equation of a regression line

Roots of rational numbers

Find roots using a calculator

Evaluate rational exponents

Simplify radical expressions with variables

Operations with rational exponents

Nth roots

Simplify expressions involving rational exponents

Find the magnitude of a vector

Find the component form of a vector

Find the direction angle of a vector

Find the component form of a vector from its magnitude and direction angle

Graph a resultant vector using the triangle method (Tutorial)

Graph a resultant vector using the parallelogram method (Tutorial)

Add and subtract vectors

Find the magnitude and direction of a vector sum

Multiply a vector by a scalar

Find the magnitude or direction of a vector scalar multiple

Find a unit vector

Linear combinations of vectors