GOZUNTA
Try it now
All courses
Algebra II

Algebra 2 Practice Problems

Complex numbers, polynomial and rational expressions, advanced functions, logarithms, trigonometry, and inference.

55 objectives
Try free problems
Objective 001 N-CN.1

Understand i as a number with i^2=-1 and represent complex numbers as a+bi.

Number and Quantity The Complex Number System
Objective 002 N-CN.2

Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.

Number and Quantity The Complex Number System
Objective 003 N-CN.7

Solve real-coefficient quadratic equations that have complex solutions.

Number and Quantity The Complex Number System
Objective 004 N-CN.8

Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.

Number and Quantity The Complex Number System
Objective 005 N-CN.9

Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.

Number and Quantity The Complex Number System
Objective 006 N-CN.8

Extend polynomial identities to complex numbers for higher-degree polynomial work.

Number and Quantity The Complex Number System
Objective 007 N-CN.9

Know the Fundamental Theorem of Algebra and connect it to polynomial roots.

Number and Quantity The Complex Number System
Objective 008 A-APR.1

Add, subtract, and multiply polynomials beyond quadratic cases.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 009 A-APR.2

Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 010 A-APR.3

Identify zeros from factorizations and use them to sketch polynomial graphs.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 011 A-APR.4

Prove polynomial identities and use them to solve or describe numerical relationships.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 012 A-APR.5

Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 013 A-APR.6

Rewrite rational expressions using inspection, polynomial division, or technology.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 014 A-APR.7

Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.

Algebra Arithmetic with Polynomials and Rational Expressions
Objective 015 A-SSE.1.a

Interpret terms, factors, and coefficients in polynomial and rational expressions.

Algebra Seeing Structure in Expressions
Objective 016 A-SSE.1.b

Interpret complex polynomial/rational expressions by treating parts as single units.

Algebra Seeing Structure in Expressions
Objective 017 A-SSE.2

Use expression structure to find useful rewrites.

Algebra Seeing Structure in Expressions
Objective 018 A-SSE.4

Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.

Algebra Seeing Structure in Expressions
Objective 019 A-CED.1

Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.

Algebra Creating Equations
Objective 020 A-CED.2

Create equations in two or more variables, graph them, and interpret relationships with labels and scales.

Algebra Creating Equations
Objective 021 A-CED.3

Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.

Algebra Creating Equations
Objective 022 A-CED.4

Rearrange formulas to highlight a chosen quantity across the expression types studied.

Algebra Creating Equations
Objective 023 A-REI.3.1

Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.

Algebra Reasoning with Equations and Inequalities
Objective 024 A-REI.11

Solve f(x)=g(x) approximately using intersections of polynomial, rational, radical, absolute-value, exponential, and logarithmic graphs.

Algebra Reasoning with Equations and Inequalities
Objective 025 A-REI.2

Solve simple rational and radical equations and identify extraneous solutions.

Algebra Reasoning with Equations and Inequalities
Objective 026 F-BF.1.b

Combine studied function types arithmetically to build models.

Functions Building Functions
Objective 027 F-BF.3

Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.

Functions Building Functions
Objective 028 F-BF.4.a

Find inverse functions for simple invertible functions, including rational examples.

Functions Building Functions
Objective 029 F-IF.4

Interpret key features of rational, square-root, cube-root, and other function models in context.

Functions Interpreting Functions
Objective 030 F-IF.5

Relate a function's domain to its equation, graph, and context, especially when model choice matters.

Functions Interpreting Functions
Objective 031 F-IF.6

Calculate, estimate, and interpret average rate of change for advanced function types.

Functions Interpreting Functions
Objective 032 F-IF.7.b

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.

Functions Interpreting Functions
Objective 033 F-IF.7.c

Graph polynomial functions using zeros, factorizations, and end behavior.

Functions Interpreting Functions
Objective 034 F-IF.7.e

Graph exponential, logarithmic, and trigonometric functions with key features.

Functions Interpreting Functions
Objective 035 F-IF.8

Rewrite functions in equivalent forms to reveal and explain useful properties.

Functions Interpreting Functions
Objective 036 F-IF.9

Compare functions represented algebraically, graphically, numerically, or verbally.

Functions Interpreting Functions
Objective 037 F-LE.4

Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.

Functions Linear, Quadratic, and Exponential Models
Objective 038 F-LE.4.1

Prove simple logarithm laws.

Functions Linear, Quadratic, and Exponential Models
Objective 039 F-LE.4.2

Use the definition of logarithms to translate among logarithms in any base.

Functions Linear, Quadratic, and Exponential Models
Objective 040 F-LE.4.3

Use logarithm properties to simplify numeric logarithmic expressions and estimate values.

Functions Linear, Quadratic, and Exponential Models
Objective 041 F-TF.8

Prove and use sin^2(theta)+cos^2(theta)=1 to find trig values with quadrant information.

Functions Trigonometric Functions
Objective 042 F-TF.1

Understand radian measure as arc length on the unit circle.

Functions Trigonometric Functions
Objective 043 F-TF.2

Use the unit circle to extend trig functions to all real-number radian measures.

Functions Trigonometric Functions
Objective 044 F-TF.2.1

Graph all six basic trigonometric functions.

Functions Trigonometric Functions
Objective 045 F-TF.5

Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.

Functions Trigonometric Functions
Objective 046 G-GPE.3.1

Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.

Geometry Expressing Geometric Properties with Equations
Objective 047 S-ID.4

Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.

Statistics and Probability Interpreting Categorical and Quantitative Data
Objective 048 S-IC.1

Understand statistics as inference about population parameters from random samples.

Statistics and Probability Making Inferences and Justifying Conclusions
Objective 049 S-IC.2

Use simulation to decide whether data are consistent with a proposed model.

Statistics and Probability Making Inferences and Justifying Conclusions
Objective 050 S-IC.3

Distinguish sample surveys, experiments, and observational studies; explain randomization in each.

Statistics and Probability Making Inferences and Justifying Conclusions
Objective 051 S-IC.4

Use sample data to estimate population means/proportions and develop margins of error using simulation.

Statistics and Probability Making Inferences and Justifying Conclusions
Objective 052 S-IC.5

Use randomized-experiment data and simulations to compare treatments and judge significance.

Statistics and Probability Making Inferences and Justifying Conclusions
Objective 053 S-IC.6

Evaluate reports based on data.

Statistics and Probability Making Inferences and Justifying Conclusions
Objective 054 S-MD.6

Use probabilities to make fair decisions in more complex settings.

Statistics and Probability Using Probability to Make Decisions
Objective 055 S-MD.7

Analyze decisions and strategies using probability concepts in more complex settings.

Statistics and Probability Using Probability to Make Decisions