# Precalculus

Here is a list of all of the skills students learn in Precalculus! These skills are organized into categories, and you can move your mouse over any skill name to view a sample question. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Functions

- A.1Domain and range
- A.2Identify functions
- A.3Linear functions
- A.4Linear functions over unit intervals
- A.5Evaluate functions
- A.6Add, subtract, multiply, and divide functions
- A.7Composition of functions
- A.8Identify inverse functions
- A.9Find values of inverse functions from tables
- A.10Find values of inverse functions from graphs
- A.11Find inverse functions and relations

## Families of functions

## Quadratic functions

- C.1Characteristics of quadratic functions
- C.2Find the maximum or minimum value of a quadratic function
- C.3Graph a quadratic function
- C.4Match quadratic functions and graphs
- C.5Solve a quadratic equation using square roots
- C.6Solve a quadratic equation by factoring
- C.7Solve a quadratic equation by completing the square
- C.8Solve a quadratic equation using the quadratic formula
- C.9Using the discriminant

## Polynomials

- D.1Divide polynomials using long division
- D.2Divide polynomials using synthetic division
- D.3Evaluate polynomials using synthetic division
- D.4Write a polynomial from its roots
- D.5Find the roots of factored polynomials
- D.6Rational root theorem
- D.7Complex conjugate theorem
- D.8Conjugate root theorems
- D.9Descartes' Rule of Signs
- D.10Fundamental Theorem of Algebra
- D.11Match polynomials and graphs
- D.12Factor sums and differences of cubes
- D.13Solve equations with sums and differences of cubes
- D.14Factor using a quadratic pattern
- D.15Solve equations using a quadratic pattern
- D.16Pascal's triangle
- D.17Pascal's triangle and the Binomial Theorem
- D.18Binomial Theorem I
- D.19Binomial Theorem II

## Rational functions

## Exponential and logarithmic functions

- F.1Domain and range of exponential and logarithmic functions
- F.2Convert between exponential and logarithmic form
- F.3Evaluate logarithms
- F.4Change of base formula
- F.5Product property of logarithms
- F.6Quotient property of logarithms
- F.7Power property of logarithms
- F.8Evaluate logarithms using properties
- F.9Solve exponential equations using factoring
- F.10Solve exponential equations using logarithms
- F.11Solve logarithmic equations with one logarithm
- F.12Solve logarithmic equations with multiple logarithms
- F.13Identify linear and exponential functions
- F.14Exponential functions over unit intervals
- F.15Describe linear and exponential growth and decay
- F.16Exponential growth and decay: word problems
- F.17Compound interest: word problems

## Radical functions

## Systems of equations

- I.1Solve a system of equations by graphing
- I.2Solve a system of equations by graphing: word problems
- I.3Classify a system of equations
- I.4Solve a system of equations using substitution
- I.5Solve a system of equations using substitution: word problems
- I.6Solve a system of equations using elimination
- I.7Solve a system of equations using elimination: word problems
- I.8Solve a system of equations in three variables using substitution
- I.9Solve a system of equations in three variables using elimination
- I.10Determine the number of solutions to a system of equations in three variables

## Systems of inequalities

## Nonlinear inequalities

## Matrices

- L.1Matrix vocabulary
- L.2Matrix operation rules
- L.3Add and subtract matrices
- L.4Multiply a matrix by a scalar
- L.5Linear combinations of matrices
- L.6Multiply two matrices
- L.7Simplify matrix expressions
- L.8Solve matrix equations
- L.9Determinant of a matrix
- L.10Is a matrix invertible?
- L.11Inverse of a 2 x 2 matrix
- L.12Inverse of a 3 x 3 matrix
- L.13Identify inverse matrices
- L.14Solve matrix equations using inverses

## Trigonometry

- M.1Convert between radians and degrees
- M.2Radians and arc length
- M.3Quadrants
- M.4Coterminal and reference angles
- M.5Find trigonometric ratios using right triangles
- M.6Find trigonometric ratios using the unit circle
- M.7Find trigonometric ratios using reference angles
- M.8Inverses of trigonometric functions
- M.9Solve trigonometric equations
- M.10Trigonometric ratios: find a side length
- M.11Trigonometric ratios: find an angle measure
- M.12Solve a right triangle
- M.13Law of Sines
- M.14Law of Cosines
- M.15Solve a triangle
- M.16Area of a triangle: sine formula
- M.17Area of a triangle: Heron's formula

## Trigonometric functions

- N.1Find properties of sine functions
- N.2Write equations of sine functions from graphs
- N.3Write equations of sine functions using properties
- N.4Graph sine functions
- N.5Find properties of cosine functions
- N.6Write equations of cosine functions from graphs
- N.7Write equations of cosine functions using properties
- N.8Graph cosine functions
- N.9Graph sine and cosine functions

## Trigonometric identities

## Conic sections

- P.1Find properties of parabolas
- P.2Write equations of parabolas in vertex form
- P.3Graph parabolas
- P.4Find properties of circles
- P.5Write equations of circles in standard form
- P.6Graph circles
- P.7Find properties of ellipses
- P.8Find the eccentricity of an ellipse
- P.9Write equations of ellipses in standard form
- P.10Find properties of hyperbolas
- P.11Find the eccentricity of a hyperbola
- P.12Write equations of hyperbolas in standard form
- P.13Convert equations of conic sections from general to standard form

## Real numbers

## Complex plane

## Polar form

## Two-dimensional vectors

- U.1Find the magnitude of a vector
- U.2Find the direction angle of a vector
- U.3Find the component form of a vector
- U.4Find the component form of a vector from its magnitude and direction angle
- U.5Find a unit vector
- U.6Add and subtract vectors
- U.7Multiply a vector by a scalar
- U.8Find the magnitude or direction of a vector scalar multiple
- U.9Find the magnitude and direction of a vector sum
- U.10Linear combinations of vectors
- U.11Graph a resultant vector using the triangle method
- U.12Graph a resultant vector using the parallelogram method

## Three-dimensional vectors

## Sequences and series

- W.1Find terms of a sequence
- W.2Find terms of a recursive sequence
- W.3Identify a sequence as explicit or recursive
- W.4Find a recursive formula
- W.5Find recursive and explicit formulas
- W.6Convert a recursive formula to an explicit formula
- W.7Convert an explicit formula to a recursive formula
- W.8Convert between explicit and recursive formulas
- W.9Introduction to sigma notation
- W.10Identify arithmetic and geometric series
- W.11Find the sum of a finite arithmetic or geometric series
- W.12Introduction to partial sums
- W.13Partial sums of arithmetic series
- W.14Partial sums of geometric series
- W.15Partial sums: mixed review
- W.16Convergent and divergent geometric series
- W.17Find the value of an infinite geometric series
- W.18Write a repeating decimal as a fraction

## Probability

- X.1Introduction to probability
- X.2Calculate probabilities of events
- X.3Combinations and permutations
- X.4Find probabilities using combinations and permutations
- X.5Find probabilities using two-way frequency tables
- X.6Identify independent events
- X.7Find conditional probabilities
- X.8Independence and conditional probability
- X.9Find conditional probabilities using two-way frequency tables
- X.10Find probabilities using the addition rule

## Probability distributions

- Y.1Identify discrete and continuous random variables
- Y.2Write a discrete probability distribution
- Y.3Graph a discrete probability distribution
- Y.4Expected values of random variables
- Y.5Variance and standard deviation of random variables
- Y.6Write the probability distribution for a game of chance
- Y.7Expected values for a game of chance
- Y.8Choose the better bet
- Y.9Find probabilities using the binomial distribution
- Y.10Mean, variance, and standard deviation of binomial distributions
- Y.11Find probabilities using the normal distribution
- Y.12Find z-values
- Y.13Find values of normal variables
- Y.14Use normal distributions to approximate binomial distributions