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

## Functions

- D.1 Domain and range
- D.2 Identify functions
- D.3 Evaluate functions
- D.4 Find values using function graphs
- D.5 Complete a table for a function graph
- D.6 Find the slope of a linear function
- D.7 Graph a linear function
- D.8 Write the equation of a linear function
- D.9 Linear functions over unit intervals
- D.10 Average rate of change

## Systems of equations

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

## Systems of inequalities

## Matrices

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

## Complex numbers

## Factoring

## Quadratic functions

- J.1 Characteristics of quadratic functions
- J.2 Complete a function table: quadratic functions
- J.3 Graph a quadratic function
- J.4 Solve a quadratic equation using square roots
- J.5 Solve a quadratic equation using the zero product property
- J.6 Solve a quadratic equation by factoring
- J.7 Complete the square
- J.8 Solve a quadratic equation by completing the square
- J.9 Solve a quadratic equation using the quadratic formula
- J.10 Using the discriminant
- J.11 Match quadratic functions and graphs
- J.12 Write a quadratic function from its zeros

## Polynomials

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

## Radical functions and expressions

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

## Rational exponents

## Rational functions and expressions

## Function operations

- O.1 Add and subtract functions
- O.2 Multiply functions
- O.3 Divide functions
- O.4 Composition of linear functions: find a value
- O.5 Composition of linear functions: find an equation
- O.6 Composition of linear and quadratic functions: find a value
- O.7 Composition of linear and quadratic functions: find an equation
- O.8 Identify inverse functions
- O.9 Find values of inverse functions from tables
- O.10 Find values of inverse functions from graphs
- O.11 Find inverse functions and relations

## Families of functions

## Variation

## Logarithms

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

## Exponential and logarithmic functions

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

## Parabolas

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

## Circles

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

## Ellipses

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

## Hyperbolas

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

## Angle measures

## Trigonometry

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

## Trigonometric functions

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

## Trigonometric identities

## Sequences and series

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

## Probability

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

## Statistics

- DD.1 Identify biased samples
- DD.2 Variance and standard deviation
- DD.3 Identify an outlier
- DD.4 Identify an outlier and describe the effect of removing it
- DD.5 Outliers in scatter plots
- DD.6 Find the equation of a regression line
- DD.7 Interpret regression lines
- DD.8 Analyze a regression line of a data set
- DD.9 Experiment design