Pre Calculus is usually taken in 11th grade but you can switch up when subjects are taken. I’ll be adding the printable soon.

**Functions**

Domain and range

Identify functions

Find the slope of a linear function

Graph a linear function

Write the equation of a linear function

Linear functions over unit intervals

Evaluate functions

Find values using function graphs

Complete a table for a function graph

Add, subtract, multiply and divide functions Composition of functions

Identify inverse functions

Find values of inverse functions from tables Find values of inverse functions from graphs Find inverse functions and relations

Identify graphs of continuous functions

**Families of functions**

Translations of functions Reflections of functions

Dilations of functions Transformations of functions Function transformation rules Describe function transformations

**Quadratic relations**

Characteristics of quadratic functions

Find the maximum or minimum value of a quadratic function Graph a quadratic function

Match quadratic functions and graphs

Solve a quadratic equation using square roots

Solve a quadratic equation by factoring

Solve a quadratic equation by completing the square

Solve a quadratic equation using the quadratic formula Using the discriminant

**Precalculus**

**Polynomials**

Divide polynomials using long division Write a polynomial from its roots

Find the roots of factored polynomials Rational root theorem

Complex conjugate theorem

Conjugate root theorems

Descartes’ Rule of Signs

Fundamental Theorem of Algebra

Match polynomials and graphs

Factor sums and differences of cubes

Solve equations with sums and differences of cubes Factor using a quadratic pattern

Solve equations using a quadratic pattern Pascal’s triangle

Pascal’s triangle and the Binomial Theorem Binomial Theorem

**Rational functions**

Rational functions: asymptotes and excluded values Solve rational equations

Check whether two rational functions are inverses

**Logarithms**

Convert between exponential and logarithmic form: rational bases Evaluate logarithms

Change of base formula

Identify properties of logarithms

Product property of logarithms Quotient property of logarithms

Power property of logarithms Properties of logarithms: mixed review Evaluate logarithms: mixed review

**Exponential and logarithmic functions**

Domain and range of exponential and logarithmic functions Evaluate exponential functions

Match exponential functions and graphs

Solve exponential equations by factoring

Solve exponential equations using common logarithms Solve logarithmic equations I

Identify linear and exponential functions Exponential functions over unit intervals

Describe linear and exponential growth and decay Exponential growth and decay: word problems Compound interest: word problems

Continuously compounded interest: word problems

**Radical functions**

Domain and range of radical functions Solve radical equations

**Roots and rational exponents**

Roots of integers

Roots of rational numbers

Find roots using a calculator

Evaluate rational exponents

Operations with rational exponents

Nth roots

Simplify radical expressions with variables Simplify expressions involving rational exponents

**Systems of equations**

Solve a system of equations by graphing

Solve a system of equations by graphing: word problems

Classify a system of equations

Solve a system of equations using substitution

Solve a system of equations using substitution: word problems

Solve a system of equations using elimination

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

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

**Systems of inequalities**

Solve systems of inequalities by graphing Find the vertices of a solution set

Linear programming

**Nonlinear inequalities**

Graph solutions to quadratic inequalities Solve quadratic inequalities

Graph solutions to higher-degree inequalities Solve higher-degree inequalities

**Matrices**

Matrix vocabulary

Matrix operation rules

Add and subtract matrices

Multiply a matrix by a scalar

Linear combinations of matrices Multiply two matrices

Simplify matrix expressions

Solve matrix equations

Determinant of a matrix

Is a matrix invertible?

Inverse of a 2 x 2 matrix

Inverse of a 3 x 3 matrix

Identify inverse matrices

Solve matrix equations using inverses

**Trigonometry**

Convert between radians and degrees Radians and arc length

Quadrants

Coterminal and reference angles

Find trigonometric ratios using right triangles Find trigonometric ratios using the unit circle Find trigonometric ratios using reference angles Inverses of trigonometric functions

Solve trigonometric equations Trigonometric ratios: find a side length Trigonometric ratios: find an angle measure Solve a right triangle

Law of Sines

Law of Cosines

Solve a triangle

Area of a triangle: sine formula

Area of a triangle: Heron’s formula

**Trigonometric functions**

Find properties of sine functions

Write equations of sine functions from graphs

Write equations of sine functions using properties Graph sine functions

Find properties of cosine functions

Write equations of cosine functions from graphs Write equations of cosine functions using properties Graph cosine functions

Graph sine and cosine functions

Trigonometric identities

Complementary angle identities

Symmetry and periodicity of trigonometric functions Trigonometric identities

**Conic sections**

Find properties of parabolas

Write equations of parabolas in vertex form

Graph parabolas

Find properties of circles

Write equations of circles in standard form

Graph circles

Find properties of ellipses

Find the eccentricity of an ellipse

Write equations of ellipses in standard form

Find properties of hyperbolas

Find the eccentricity of a hyperbola

Write equations of hyperbolas in standard form

Convert equations of conic sections from general to standard form

**Complex numbers**

Introduction to complex numbers

Add and subtract complex numbers

Complex conjugates

Multiply and divide complex numbers

Add, subtract, multiply and divide complex numbers Absolute values of complex numbers

Powers of i

**Complex plane**

Introduction to the complex plane Graph complex numbers Addition in the complex plane Subtraction in the complex plane

Graph complex conjugates Absolute value in the complex plane Midpoints in the complex plane Distance in the complex plane

**Polar form**

Find the modulus and argument of a complex number

Convert complex numbers from rectangular to polar form Convert complex numbers from polar to rectangular form Convert complex numbers between rectangular and polar form Match polar equations and graphs

**Two-dimensional vectors**

Find the magnitude of a vector

Find the direction angle of a vector

Find the component form of a vector

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

Add and subtract vectors

Multiply a vector by a scalar

Find the magnitude or direction of a vector scalar multiple

Find the magnitude and direction of a vector sum

Linear combinations of vectors

Graph a resultant vector using the triangle method

Graph a resultant vector using the parallelogram method

**Three-dimensional vectors**

Find the magnitude of a three-dimensional vector

Find the component form of a three-dimensional vector Find a three-dimensional unit vector

Add and subtract three-dimensional vectors

Scalar multiples of three-dimensional vectors

Linear combinations of three-dimensional vectors

**Sequences and series**

Find terms of a sequence

Find terms of a recursive sequence

Identify a sequence as explicit or recursive

Find a recursive formula

Find recursive and explicit formulas

Convert a recursive formula to an explicit formula

Convert an explicit formula to a recursive formula Convert between explicit and recursive formulas Introduction to sigma notation

Identify arithmetic and geometric series

Find the sum of a finite arithmetic or geometric series Introduction to partial sums

Partial sums of arithmetic series

Partial sums of geometric series

Partial sums: mixed review

Convergent and divergent geometric series Find the value of an infinite geometric series Write a repeating decimal as a fraction

**Logic**

Identify hypotheses and conclusions Counterexamples

Conditionals

Negations

Converses, inverses and contrapositives Biconditionals

**Probability**

Introduction to probability

Calculate probabilities of events

Combinations and permutations

Find probabilities using combinations and permutations

Find probabilities using two-way frequency tables

Identify independent events

Find conditional probabilities

Independence and conditional probability

Find conditional probabilities using two-way frequency tables Find probabilities using the addition rule

**Probability distributions**

Identify discrete and continuous random variables Write a discrete probability distribution

Graph a discrete probability distribution

Expected values of random variables

Variance of random variables

Standard deviation of random variables

Write the probability distribution for a game of chance Expected values for a game of chance

Choose the better bet

Find probabilities using the binomial distribution

Mean, variance and standard deviation of binomial distributions Find probabilities using the normal distribution I

Find probabilities using the normal distribution II

Find z-values

Find values of normal variables

Distributions of sample means

The Central Limit Theorem

Use normal distributions to approximate binomial distributions

**Statistics**

Identify biased samples

Variance and standard deviation

Identify an outlier

Identify an outlier and describe the effect of removing it Outliers in scatter plots

Match correlation coefficients to scatter plots

Calculate correlation coefficients

Find the equation of a regression line

Interpret regression lines

Analyze a regression line of a data set

Analyze a regression line using statistics of a data set Find confidence intervals for population means

Find confidence intervals for population proportions Interpret confidence intervals for population means