Pre Calculus

Pre Calculus

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

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