flagPennsylvania

Algebra II

Master Algebra II

Watch algebra videos, practice with step-by-step solutions

students image

Exponential functions were killing me. The video lessons made everything click. Went from D to B+ in one semester.

Jordan Martinez

pug

Why Algebra II Students Choose StudyPug

The complete learning system to master Algebra II

Search with Photo

Search with Photo

Snap a photo of any problem and get the exact lesson

Expert Video Teaching

Expert Video Teaching

Certified teachers explain every concept with clear examples

Unlimited Practice

Unlimited Practice

Thousands of practice questions with step-by-step solutions

How Pennsylvania Students Use StudyPug

1

Select Grade Level
Select Grade Level

Choose your Pennsylvania grade (K-12) and current math topics.

2

Get Unstuck
Get Unstuck

Upload homework problems or browse curriculum-aligned lessons.

3

Practice & Master
Practice & Master

Work through similar problems until concepts stick.

4

See Results
See Results

Track progress and watch grades improve week by week.

Pennsylvania Algebra II Help: Master Concepts FastHelp

Print

ID

Standard

StudyPug Topic

CC.HSN.RN.A.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

CC.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

CC.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

CC.HSF.IF.A.3

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

CC.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

CC.HSF.IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

CC.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

CC.HSF.BF.A.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

CC.HSF.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

CC.HSF.LE.A.1

Distinguish between situations that can be modeled with linear functions and with exponential functions.

CC.HSF.LE.A.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

CC.HSA.APR.A.1

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

CC.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

CC.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

CC.HSA.APR.C.4

Prove polynomial identities and use them to describe numerical relationships.

CC.HSA.APR.C.5

Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.

CC.HSA.APR.D.6

Rewrite simple rational expressions in different forms.

CC.HSA.APR.D.7

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

CC.HSA.REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

CC.HSF.LE.A.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

CC.HSF.LE.A.4

For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

CC.HSF.TF.A.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

CC.HSF.TF.A.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

CC.HSF.TF.A.3

Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.

CC.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

CC.HSF.TF.B.6

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

CC.HSF.TF.B.7

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

CC.HSF.TF.C.8

Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

CC.HSF.TF.C.9

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

CC.HSG.SRT.D.9

Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

CC.HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

CC.HSG.SRT.D.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

CC.HSA.SSE.B.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

CC.HSN.CN.A.1

Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real.

CC.HSN.CN.A.2

Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

CC.HSN.CN.A.3

Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

CC.HSN.CN.B.4

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

CC.HSN.CN.B.5

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

CC.HSN.CN.B.6

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

CC.HSN.CN.C.9

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

CC.HSA.REI.C.8

Represent a system of linear equations as a single matrix equation in a vector variable.

CC.HSA.REI.C.9

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

CC.HSN.VM.C.6

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

CC.HSN.VM.C.7

Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

CC.HSN.VM.C.8

Add, subtract, and multiply matrices of appropriate dimensions.

CC.HSN.VM.C.9

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

CC.HSN.VM.C.10

Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

CC.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

CC.HSG.GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

CC.HSS.ID.A.4

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

CC.HSS.ID.B.5

Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

CC.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

CC.HSS.CP.A.2

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

CC.HSS.CP.A.3

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

CC.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems.
Complete Pennsylvania Algebra II Coverage

Algebra II Lessons

217

Video Explanations

1413

Practice Problems

2354

Pennsylvania Standards

100% Aligned

Why Pennsylvania Algebra II Students Love StudyPug

Keystone Exam Preparation

Keystone Exam Preparation

Practice with real Keystone-style questions—be ready for exam day

Certified Teachers

Certified Teachers

Learn from expert Pennsylvania teachers who know exactly what you need for Algebra II

Learn Anywhere

Learn Anywhere

Desktop, tablet, or phone—your Algebra II lessons sync across all devices

Get Started Today

Success Stories

I was struggling with polynomial identities until StudyPug. The step-by-step videos saved my grade. Aced my Keystone exam.

Alex Chen

Homework took hours every night. The AI finds exact lessons instantly. Cut my study time in half and my grades went up.

Taylor Rodriguez

Read More

Frequently Asked Questions

Everything you need to know about Algebra II on StudyPug

What does Algebra II coverage include?

Complete Algebra II curriculum with video lessons on polynomials, exponential functions, logarithms, trigonometry, and complex numbers. Includes practice problems, step-by-step solutions, and progress tracking.

How does photo search work?

Take a photo of any algebra problem, and StudyPug finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need.

Are the teachers certified Pennsylvania educators?

Yes! Our teachers are certified Pennsylvania educators who understand Algebra II curriculum and create lessons specifically for Pennsylvania standards and Keystone exam preparation.

Can I use StudyPug on my phone or tablet?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can study for Algebra II anywhere, anytime.

How will StudyPug help me prepare for the Keystone Exam?

We include Keystone-style practice questions for every Algebra II topic and teach the exact concepts tested on the exam. Students report significantly improved scores and confidence on exam day.

How StudyPug Works
Get Started

Practice Smart, See Real Progress

Unlimited Targeted Practice
Unlimited Targeted Practice

10,000+ questions adjust to your exact skill level. Never run out of problems that challenge you.

Visual Progress Tracking
Visual Progress Tracking

See mastery percentage for every topic. Parents get weekly progress emails automatically.

Achievement System
Achievement System

Earn badges for consistency and improvement. Build learning streaks that motivate daily practice

Detailed Analytics
Detailed Analytics

Time spent, problems solved, concepts mastered. Identify exactly where more practice is needed.

student
CallToActionContent

End Math Struggles Today

Pennsylvania standard-aligned help that actually works

Get Started
mathImage