Precalculus

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IXL offers hundreds of Precalculus skills to explore and learn! Not sure where to start? Go to your personalized Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, state standards, or standardized test.

IXL offers hundreds of Precalculus skills to explore and learn! Not sure where to start? Go to your personalized Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, state standards, or standardized test.

A. Function concepts

1
Domain and range

2
Identify functions

3
Evaluate functions

4
Find values using function graphs

5
Complete a table for a function graph

6
Identify graphs: word problems

7
Add, subtract, multiply, and divide functions

8
Composition of functions

B. Inverse functions

1
Identify inverse functions

2
Find values of inverse functions from tables

3
Find values of inverse functions from graphs

4
Find inverse functions and relations

C. Function transformations

1
Function transformation rules

2
Translations of functions

3
Reflections of functions

4
Dilations of functions

5
Transformations of functions

6
Describe function transformations

D. Quadratic functions

1
Find the maximum or minimum value of a quadratic function

2
Characteristics of quadratic functions

3
Graph a quadratic function

4
Match quadratic functions and graphs

5
Solve a quadratic equation using square roots

6
Solve a quadratic equation by factoring

7
Solve a quadratic equation by completing the square

8
Solve a quadratic equation using the quadratic formula

9
Solve quadratic equations: word problems

10
Using the discriminant

E. Polynomial expressions and equations

1
Polynomial vocabulary

2
Divide polynomials using long division

3
Divide polynomials using synthetic division

4
Evaluate polynomials using synthetic division

5
Factor sums and differences of cubes

6
Solve equations with sums and differences of cubes

7
Factor using a quadratic pattern

8
Solve equations using a quadratic pattern

9
Pascal's triangle

10
Pascal's triangle and the Binomial Theorem

11
Binomial Theorem I

12
Binomial Theorem II

F. Polynomial functions

1
Find the roots of factored polynomials

2
Write a polynomial from its roots

3
Rational root theorem

4
Complex conjugate theorem

5
Conjugate root theorems

6
Descartes' Rule of Signs

7
Fundamental Theorem of Algebra

8
Match polynomials and graphs using end behavior

9
Match polynomials and graphs using zeros

10
Match polynomials and graphs

11
Domain and range of polynomials

12
Even and odd functions

G. Rational functions

1
Rational functions: asymptotes and excluded values

2
Solve rational equations

3
Check whether two rational functions are inverses

H. Exponential functions

1
Domain and range of exponential functions

2
Match exponential functions and graphs

3
Linear and exponential functions over unit intervals

4
Identify linear and exponential functions

5
Describe linear and exponential growth and decay

I. Logarithms

1
Convert between exponential and logarithmic form

2
Evaluate logarithms

3
Change of base formula

4
Product property of logarithms

5
Quotient property of logarithms

6
Power property of logarithms

7
Properties of logarithms: mixed review

8
Evaluate logarithms using properties

J. Logarithmic functions

1
Domain and range of logarithmic functions

2
Graph logarithmic functions

K. Exponential and logarithmic equations

1
Solve exponential equations by rewriting the base

2
Solve exponential equations using logarithms

3
Solve logarithmic equations with one logarithm

4
Solve logarithmic equations with multiple logarithms

5
Exponential growth and decay: word problems

6
Compound interest: word problems

L. Radical expressions and functions

1
Simplify radical expressions with variables

2
Nth roots

3
Domain and range of radical functions

4
Graph square root functions

5
Solve radical equations

M. Rational exponents

1
Evaluate rational exponents

2
Convert between rational exponents and radicals

3
Operations with rational exponents

4
Simplify expressions involving rational exponents

5
Solve equations with rational exponents

N. Systems of equations

1
Solve a system of equations by graphing

2
Solve a system of equations by graphing: word problems

3
Classify a system of equations

4
Solve a system of equations using substitution

5
Solve a system of equations using substitution: word problems

6
Solve a system of equations using elimination

7
Solve a system of equations using elimination: word problems

8
Solve a system of equations using augmented matrices

9
Solve a system of equations using augmented matrices: word problems

10
Solve a system of equations in three variables using substitution

11
Solve a system of equations in three variables using elimination

12
Determine the number of solutions to a system of equations in three variables

O. Systems of inequalities

1
Solve systems of linear inequalities by graphing

2
Solve systems of linear and absolute value inequalities by graphing

3
Find the vertices of a solution set

4
Linear programming

P. Nonlinear inequalities

1
Graph solutions to quadratic inequalities

2
Solve quadratic inequalities

3
Graph solutions to higher-degree inequalities

4
Solve higher-degree inequalities

Q. Matrices

1
Matrix vocabulary

2
Matrix operation rules

3
Add and subtract matrices

4
Multiply a matrix by a scalar

5
Add and subtract scalar multiples of matrices

6
Multiply two matrices

7
Simplify matrix expressions

8
Properties of matrices

9
Solve matrix equations

10
Determinant of a matrix

11
Is a matrix invertible?

12
Inverse of a 2 x 2 matrix

13
Inverse of a 3 x 3 matrix

14
Identify inverse matrices

15
Solve matrix equations using inverses

16
Identify transformation matrices

17
Transformation matrices: write the vertex matrix

18
Transformation matrices: graph the image

R. Trigonometry

1
Convert between radians and degrees

2
Radians and arc length

3
Quadrants

4
Coterminal and reference angles

5
Find trigonometric ratios using right triangles

6
Find trigonometric ratios using the unit circle

7
Find trigonometric ratios of special angles

8
Find trigonometric ratios using reference angles

9
Inverses of trigonometric functions

10
Inverses of trigonometric functions using a calculator

11
Solve trigonometric equations

12
Trigonometric ratios: find a side length

13
Trigonometric ratios: find an angle measure

14
Solve a right triangle

15
Law of Sines

16
Law of Cosines

17
Solve a triangle

18
Area of a triangle: sine formula

19
Area of a triangle: Heron's formula

S. Trigonometric functions

1
Find properties of sine functions

2
Write equations of sine functions from graphs

3
Write equations of sine functions using properties

4
Graph sine functions

5
Graph translations of sine functions

6
Find properties of cosine functions

7
Write equations of cosine functions from graphs

8
Write equations of cosine functions using properties

9
Graph cosine functions

10
Graph translations of cosine functions

11
Find properties of sine and cosine functions

12
Write equations of sine and cosine functions from graphs

13
Write equations of sine and cosine functions using properties

14
Graph sine and cosine functions

15
Graph translations of sine and cosine functions

T. Trigonometric identities

1
Complementary angle identities

2
Symmetry and periodicity of trigonometric functions

3
Find trigonometric ratios using a Pythagorean or reciprocal identity

4
Find trigonometric ratios using multiple identities

5
Trigonometric sum and difference identities

6
Solve trigonometric equations using sum and difference identities

U. Conic sections

1
Find properties of parabolas

2
Write equations of parabolas in vertex form

3
Graph parabolas

4
Find properties of circles

5
Write equations of circles in standard form

6
Graph circles

7
Find properties of ellipses

8
Find the eccentricity of an ellipse

9
Write equations of ellipses in standard form

10
Find properties of hyperbolas

11
Find the eccentricity of a hyperbola

12
Write equations of hyperbolas in standard form

13
Convert equations of conic sections from general to standard form

V. Complex numbers

1
Add and subtract complex numbers

2
Complex conjugates

3
Multiply and divide complex numbers

4
Add, subtract, multiply, and divide complex numbers

5
Absolute values of complex numbers

6
Powers of i

W. Complex plane

1
Introduction to the complex plane

2
Graph complex numbers

3
Addition in the complex plane

4
Subtraction in the complex plane

5
Graph complex conjugates

6
Absolute value in the complex plane

7
Midpoints in the complex plane

8
Distance in the complex plane

X. Polar form

1
Find the modulus and argument of a complex number

2
Convert complex numbers from rectangular to polar form

3
Convert complex numbers from polar to rectangular form

4
Convert complex numbers between rectangular and polar form

5
Match polar equations and graphs

Y. Two-dimensional vectors

1
Find the magnitude of a vector

2
Find the component form of a vector

3
Find the direction angle of a vector

4
Find the component form of a vector from its magnitude and direction angle

5
Graph a resultant vector using the triangle method

6
Graph a resultant vector using the parallelogram method

7
Add vectors

8
Subtract vectors

9
Find the magnitude and direction of a vector sum

10
Multiply a vector by a scalar

11
Find the magnitude of a vector scalar multiple

12
Determine the direction of a vector scalar multiple

13
Find a unit vector

14
Linear combinations of vectors

Z. Three-dimensional vectors

1
Find the magnitude of a three-dimensional vector

2
Find the component form of a three-dimensional vector

3
Add and subtract three-dimensional vectors

4
Scalar multiples of three-dimensional vectors

5
Find a three-dimensional unit vector

6
Linear combinations of three-dimensional vectors

AA. Sequences

1
Find terms of a sequence

2
Find terms of a recursive sequence

3
Identify a sequence as explicit or recursive

4
Find a recursive formula

5
Find recursive and explicit formulas

6
Convert a recursive formula to an explicit formula

7
Convert an explicit formula to a recursive formula

8
Convert between explicit and recursive formulas

BB. Series

1
Identify arithmetic and geometric series

2
Introduction to sigma notation

3
Find the sum of an arithmetic series

4
Find the sum of a finite geometric series

5
Introduction to partial sums

6
Partial sums of arithmetic series

7
Partial sums of geometric series

8
Partial sums: mixed review

9
Convergent and divergent geometric series

10
Find the value of an infinite geometric series

11
Write a repeating decimal as a fraction

CC. Probability

1
Calculate probabilities of events

2
Combinations and permutations

3
Find probabilities using combinations and permutations

4
Find probabilities using two-way frequency tables

5
Identify independent events

6
Find conditional probabilities

7
Independence and conditional probability

8
Find conditional probabilities using two-way frequency tables

9
Find probabilities using the addition rule

DD. Probability distributions

1
Identify probability distributions

2
Identify discrete and continuous random variables

3
Write a discrete probability distribution

4
Graph a discrete probability distribution

5
Expected values of random variables

6
Variance of random variables

7
Standard deviation of random variables

8
Write the probability distribution for a game of chance

9
Expected values for a game of chance

10
Choose the better bet

EE. Binomial and normal distributions

1
Find probabilities using the binomial distribution

2
Mean, variance, and standard deviation of binomial distributions

3
Find probabilities using the normal distribution I

4
Find probabilities using the normal distribution II

5
Find z-values

6
Find values of normal variables

7
Distributions of sample means

8
The Central Limit Theorem

9
Use normal distributions to approximate binomial distributions

FF. Single-variable statistics

1
Identify biased samples

2
Variance and standard deviation

3
Identify an outlier

4
Identify an outlier and describe the effect of removing it

5
Find confidence intervals for population means

6
Find confidence intervals for population proportions

7
Interpret confidence intervals for population means

8
Experiment design

9
Analyze the results of an experiment using simulations

GG. Bivariate statistics

1
Outliers in scatter plots

2
Match correlation coefficients to scatter plots

3
Calculate correlation coefficients

4
Find the equation of a regression line

5
Interpret regression lines

6
Analyze a regression line of a data set

7
Analyze a regression line using statistics of a data set

HH. Limits

1
Find limits using graphs

2
Find one-sided limits using graphs

3
Determine if a limit exists

4
Find limits at vertical asymptotes using graphs

5
Determine end behavior using graphs

6
Find limits using addition, subtraction, and multiplication laws

7
Find limits using the division law

8
Find limits using power and root laws

9
Find limits using limit laws

10
Find limits of polynomials and rational functions

11
Find limits involving factorization and rationalization

II. Continuity

1
Identify graphs of continuous functions

2
Determine continuity using graphs

3
Determine one-sided continuity using graphs

4
Find and analyze points of discontinuity using graphs

5
Determine continuity on an interval using graphs

JJ. Introduction to derivatives

1
Average rate of change I

2
Average rate of change II

3
Find instantaneous rates of change

4
Velocity as a rate of change

5
Find values of derivatives using limits

6
Find the slope of a tangent line using limits

7
Find equations of tangent lines using limits