# Algebra 2

Here is a list of all of the skills students learn in Algebra 2! 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!

## Variable expressions

## Equations

## Inequalities

- C.1Graph a linear inequality in one variable
- C.2Graph a linear inequality in the coordinate plane
- C.3Write inequalities from graphs
- C.4Write a linear inequality: word problems
- C.5Solve linear inequalities
- C.6Graph solutions to linear inequalities
- C.7Solve absolute value inequalities
- C.8Graph solutions to absolute value inequalities
- C.9Graph solutions to two-variable absolute value inequalities
- C.10Graph solutions to quadratic inequalities
- C.11Solve quadratic inequalities

## Functions

## Systems of equations

- E.1Is (x, y) a solution to the system of equations?
- E.2Solve a system of equations by graphing
- E.3Solve a system of equations by graphing: word problems
- E.4Find the number of solutions to a system of equations
- E.5Classify a system of equations
- E.6Solve a system of equations using substitution
- E.7Solve a system of equations using substitution: word problems
- E.8Solve a system of equations using elimination
- E.9Solve a system of equations using elimination: word problems
- E.10Solve a system of equations using any method
- E.11Solve a system of equations using any method: word problems
- E.12Solve a system of equations in three variables using substitution
- E.13Solve a system of equations in three variables using elimination
- E.14Determine the number of solutions to a system of equations in three variables
- E.15Solve a non-linear system of equations

## Systems of inequalities

## Matrices

- G.1Matrix vocabulary
- G.2Matrix operation rules
- G.3Add and subtract matrices
- G.4Multiply a matrix by a scalar
- G.5Linear combinations of matrices
- G.6Multiply two matrices
- G.7Simplify matrix expressions
- G.8Properties of matrices
- G.9Solve matrix equations
- G.10Determinant of a matrix
- G.11Is a matrix invertible?
- G.12Inverse of a matrix
- G.13Identify inverse matrices
- G.14Solve matrix equations using inverses
- G.15Identify transformation matrices
- G.16Transformation matrices: write the vertex matrix
- G.17Transformation matrices: graph the image
- G.18Solve a system of equations using augmented matrices
- G.19Solve a system of equations using augmented matrices: word problems

## Complex numbers

## Factoring

## Quadratic functions

- J.1Characteristics of quadratic functions
- J.2Complete a function table: quadratic functions
- J.3Find a quadratic function
- J.4Graph a quadratic function
- J.5Match quadratic functions and graphs
- J.6Solve a quadratic equation using square roots
- J.7Solve a quadratic equation using the zero product property
- J.8Solve a quadratic equation by factoring
- J.9Complete the square
- J.10Solve a quadratic equation using the quadratic formula
- J.11Using the discriminant

## Polynomials

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

## Radical functions and expressions

- L.1Roots of integers
- L.2Roots of rational numbers
- L.3Find roots using a calculator
- L.4Nth roots
- L.5Simplify radical expressions with variables I
- L.6Simplify radical expressions with variables II
- L.7Multiply radical expressions
- L.8Divide radical expressions
- L.9Add and subtract radical expressions
- L.10Simplify radical expressions using the distributive property
- L.11Simplify radical expressions using conjugates
- L.12Domain and range of radical functions
- L.13Solve radical equations

## Rational exponents

## Rational functions and expressions

## Function operations

- O.1Add and subtract functions
- O.2Multiply functions
- O.3Divide functions
- O.4Composition of linear functions
- O.5Composition of linear and quadratic functions
- O.6Identify inverse functions
- O.7Find values of inverse functions from tables
- O.8Find values of inverse functions from graphs
- O.9Find inverse functions and relations

## Families of functions

## Variation

## Logarithms

- R.1Convert between exponential and logarithmic form: rational bases
- R.2Convert between natural exponential and logarithmic form
- R.3Convert between exponential and logarithmic form: all bases
- R.4Evaluate logarithms
- R.5Evaluate natural logarithms
- R.6Change of base formula
- R.7Identify properties of logarithms
- R.8Product property of logarithms
- R.9Quotient property of logarithms
- R.10Power property of logarithms
- R.11Properties of logarithms: mixed review
- R.12Evaluate logarithms: mixed review

## Exponential and logarithmic functions

- S.1Domain and range of exponential and logarithmic functions
- S.2Evaluate exponential functions
- S.3Match exponential functions and graphs
- S.4Solve exponential equations using factoring
- S.5Solve exponential equations using common logarithms
- S.6Solve exponential equations using natural logarithms
- S.7Solve logarithmic equations I
- S.8Solve logarithmic equations II
- S.9Identify linear and exponential functions
- S.10Exponential functions over unit intervals
- S.11Describe linear and exponential growth and decay
- S.12Exponential growth and decay: word problems
- S.13Compound interest: word problems
- S.14Continuously compounded interest: word problems

## Parabolas

- T.1Identify the direction a parabola opens
- T.2Find the vertex of a parabola
- T.3Find the focus or directrix of a parabola
- T.4Find the axis of symmetry of a parabola
- T.5Write equations of parabolas in vertex form from graphs
- T.6Write equations of parabolas in vertex form using properties
- T.7Convert equations of parabolas from general to vertex form
- T.8Find properties of a parabola from equations in general form
- T.9Graph parabolas

## Circles

- U.1Find the center of a circle
- U.2Find the radius or diameter of a circle
- U.3Write equations of circles in standard form from graphs
- U.4Write equations of circles in standard form using properties
- U.5Convert equations of circles from general to standard form
- U.6Find properties of circles from equations in general form
- U.7Graph circles

## Ellipses

- V.1Find the center, vertices, or co-vertices of an ellipse
- V.2Find the length of the major or minor axes of an ellipse
- V.3Find the foci of an ellipse
- V.4Write equations of ellipses in standard form from graphs
- V.5Write equations of ellipses in standard form using properties
- V.6Convert equations of ellipses from general to standard form
- V.7Find properties of ellipses from equations in general form

## Hyperbolas

- W.1Find the center of a hyperbola
- W.2Find the vertices of a hyperbola
- W.3Find the length of the transverse or conjugate axes of a hyperbola
- W.4Find the equations for the asymptotes of a hyperbola
- W.5Find the foci of a hyperbola
- W.6Write equations of hyperbolas in standard form from graphs
- W.7Write equations of hyperbolas in standard form using properties
- W.8Convert equations of hyperbolas from general to standard form
- W.9Find properties of hyperbolas from equations in general form

## Angle measures

## Trigonometry

- Y.1Pythagorean Theorem and its converse
- Y.2Special right triangles
- Y.3Trigonometric ratios: sin, cos, and tan
- Y.4Trigonometric ratios: csc, sec, and cot
- Y.5Trigonometric ratios in similar right triangles
- Y.6Find trigonometric ratios using the unit circle
- Y.7Sin, cos, and tan of special angles
- Y.8Csc, sec, and cot of special angles
- Y.9Find trigonometric functions using a calculator
- Y.10Inverses of sin, cos, and tan
- Y.11Inverses of csc, sec, and cot
- Y.12Solve trigonometric equations I
- Y.13Solve trigonometric equations II
- Y.14Trigonometric ratios: find a side length
- Y.15Trigonometric ratios: find an angle measure
- Y.16Solve a right triangle
- Y.17Law of Sines
- Y.18Law of Cosines
- Y.19Solve a triangle
- Y.20Area of a triangle: sine formula
- Y.21Area of a triangle: Law of Sines

## Trigonometric functions

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

## Trigonometric identities

## Sequences and series

- BB.1Classify formulas and sequences
- BB.2Find terms of an arithmetic sequence
- BB.3Find terms of a geometric sequence
- BB.4Find terms of a recursive sequence
- BB.5Evaluate formulas for sequences
- BB.6Write a formula for an arithmetic sequence
- BB.7Write a formula for a geometric sequence
- BB.8Write a formula for a recursive sequence
- BB.9Sequences: mixed review
- BB.10Introduction to sigma notation
- BB.11Identify arithmetic and geometric series
- BB.12Find the sum of a finite arithmetic or geometric series
- BB.13Introduction to partial sums
- BB.14Partial sums of arithmetic series
- BB.15Partial sums of geometric series
- BB.16Partial sums: mixed review
- BB.17Convergent and divergent geometric series
- BB.18Find the value of an infinite geometric series
- BB.19Write a repeating decimal as a fraction

## Probability

- CC.1Introduction to probability
- CC.2Calculate probabilities of events
- CC.3Counting principle
- CC.4Combinations and permutations
- CC.5Find probabilities using combinations and permutations
- CC.6Find probabilities using two-way frequency tables
- CC.7Identify independent events
- CC.8Probability of independent and dependent events
- CC.9Find conditional probabilities
- CC.10Independence and conditional probability
- CC.11Find conditional probabilities using two-way frequency tables
- CC.12Find probabilities using the addition rule
- CC.13Identify discrete and continuous random variables
- CC.14Write a discrete probability distribution
- CC.15Graph a discrete probability distribution
- CC.16Expected values of random variables
- CC.17Write the probability distribution for a game of chance
- CC.18Expected values for a game of chance
- CC.19Choose the better bet
- CC.20Find probabilities using the binomial distribution
- CC.21Find probabilities using the normal distribution