Polynomials and their graphs
Students work with longer expressions that have powers like squares and cubes. They add, multiply, and factor these expressions, then sketch how the matching graphs rise, fall, and cross zero.
What does a student learn in
This is the year math stretches beyond straight lines and simple curves into the full family of functions students will use in college work. Students graph and solve problems with polynomials, exponentials, logarithms, and trig functions, and they work with fractions that have variables in the denominator. They also use sample data to make careful claims about a larger group. By spring, students can sketch a curve like a sine wave or a logarithm and explain what its shape says about a real situation.
- Polynomial functions
- Rational expressions
- Exponential and logarithmic functions
- Trigonometry
- Statistical inference
- Modeling with functions
Year at a glance
How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.
- 1
- 2
Rational and radical expressions
Students move into fractions that have variables in them and equations with square roots. They learn what makes these expressions break down and how to solve them without getting fooled by false answers.
- 3
Exponential and logarithmic functions
Students study growth that doubles or decays over time, like interest on a loan or medicine leaving the body. Logarithms show up as the tool for solving when the unknown is stuck in an exponent.
- 4
Trigonometry and periodic patterns
Students use sine and cosine to describe things that repeat, like tides, sound waves, or a Ferris wheel. They graph these waves and use trig identities to rewrite and solve equations.
- 5
Statistics and sampling
Students learn how a small sample can speak for a much larger group. They look at how surveys and experiments are designed and what makes a conclusion about a population trustworthy.
Mastery Learning Standards
The required skills a student should display by the end of Grade 12.
Standards for Mathematical Practice
Standards for Mathematical Practice
- Algebra II
Make Sense of Problems
Students read a math problem carefully, figure out what it's actually asking, and keep working even when a solution isn't obvious. They check whether their answer makes sense before moving on.
- Algebra II
Reason Abstractly
Students move back and forth between the real situation and the math that models it, translating a word problem into symbols to solve it, then checking that the answer still makes sense in the original context.
- Algebra II
Construct Arguments
Students explain why their math steps make sense and point out where another student's reasoning breaks down. The work is less about getting the answer and more about defending how they got there.
- Algebra II
Model with Mathematics
Students take a real situation, like figuring out a loan payment or predicting a trend, and write a math equation or draw a graph that helps make sense of it.
- Algebra II
Use Tools Strategically
Students choose the right tool for the problem, whether that means a graphing calculator, a quick estimate, or working it out by hand. Knowing which tool fits is part of solving the problem.
- Algebra II
Attend to Precision
Students use the right math words, label their units (like miles or dollars), and check that their calculations are exact. Sloppy notation or a missing label can change what an answer actually means.
- Algebra II
Use Structure
Students spot patterns and hidden structure in equations, graphs, and expressions, then use what they notice to solve problems faster or see why a method works.
- Algebra II
Express Regularity
Students notice when the same steps keep appearing in a problem and use that pattern to find a shortcut or write a general rule. This is how formulas get built.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems Algebra II | Students read a math problem carefully, figure out what it's actually asking, and keep working even when a solution isn't obvious. They check whether their answer makes sense before moving on. | MD-MATH.MP.hs-algebra-2.1 |
| Reason Abstractly Algebra II | Students move back and forth between the real situation and the math that models it, translating a word problem into symbols to solve it, then checking that the answer still makes sense in the original context. | MD-MATH.MP.hs-algebra-2.2 |
| Construct Arguments Algebra II | Students explain why their math steps make sense and point out where another student's reasoning breaks down. The work is less about getting the answer and more about defending how they got there. | MD-MATH.MP.hs-algebra-2.3 |
| Model with Mathematics Algebra II | Students take a real situation, like figuring out a loan payment or predicting a trend, and write a math equation or draw a graph that helps make sense of it. | MD-MATH.MP.hs-algebra-2.4 |
| Use Tools Strategically Algebra II | Students choose the right tool for the problem, whether that means a graphing calculator, a quick estimate, or working it out by hand. Knowing which tool fits is part of solving the problem. | MD-MATH.MP.hs-algebra-2.5 |
| Attend to Precision Algebra II | Students use the right math words, label their units (like miles or dollars), and check that their calculations are exact. Sloppy notation or a missing label can change what an answer actually means. | MD-MATH.MP.hs-algebra-2.6 |
| Use Structure Algebra II | Students spot patterns and hidden structure in equations, graphs, and expressions, then use what they notice to solve problems faster or see why a method works. | MD-MATH.MP.hs-algebra-2.7 |
| Express Regularity Algebra II | Students notice when the same steps keep appearing in a problem and use that pattern to find a shortcut or write a general rule. This is how formulas get built. | MD-MATH.MP.hs-algebra-2.8 |
Algebra II
Algebra II
- Algebra II
Functions and Graphs
Students read graphs of advanced functions, spotting where they rise, fall, flatten, or repeat. This includes curves from exponential growth, logarithms, and wave patterns.
- Algebra II
Polynomial and Rational
Students add, subtract, multiply, and divide expressions that include variables with exponents, then solve equations built from those expressions. This covers the algebra behind curves and graphs seen in advanced math and science classes.
- Algebra II
Trigonometry
Students use sine and cosine functions to describe things that repeat on a cycle, like a ferris wheel's height or a sound wave's pressure. They apply trig identities to simplify and solve those models.
- Algebra II
Statistics and Probability
Students use data collected from a sample group to draw conclusions about a much larger population. This is the math behind surveys and polls.
| Standard | Definition | Code |
|---|---|---|
| Functions and Graphs Algebra II | Students read graphs of advanced functions, spotting where they rise, fall, flatten, or repeat. This includes curves from exponential growth, logarithms, and wave patterns. | MD-MATH.A2.hs-algebra-2.1 |
| Polynomial and Rational Algebra II | Students add, subtract, multiply, and divide expressions that include variables with exponents, then solve equations built from those expressions. This covers the algebra behind curves and graphs seen in advanced math and science classes. | MD-MATH.A2.hs-algebra-2.2 |
| Trigonometry Algebra II | Students use sine and cosine functions to describe things that repeat on a cycle, like a ferris wheel's height or a sound wave's pressure. They apply trig identities to simplify and solve those models. | MD-MATH.A2.hs-algebra-2.3 |
| Statistics and Probability Algebra II | Students use data collected from a sample group to draw conclusions about a much larger population. This is the math behind surveys and polls. | MD-MATH.A2.hs-algebra-2.4 |
Assessments
The state tests students at this grade and subject take.
MCAP: Algebra I (End-of-Course)
End-of-course assessment in Algebra I, administered upon completion of the course in high school.
- When given:
- by course completion
- Frequency:
- by course completion
NAEP (National Assessment of Educational Progress)
Federally administered sample-based assessment in reading, mathematics, science, and writing. NAEP results inform state-by-state comparisons rather than individual student or school accountability.
- When given:
- biennial in winter
- Frequency:
- every two years
Common Questions
What does Algebra II look like across the year?
Students study families of functions, including polynomials, rational expressions, exponentials, logarithms, and trig. They learn to graph each family, solve equations built from them, and use them to describe real situations like growth, decay, and repeating patterns. The year also includes a unit on statistics and sampling.
How can I help at home if my child gets stuck on a problem?
Ask them to explain what the problem is asking and what they already tried. Most stuck moments come from skipping a step or missing a definition, not from a missing talent for math. A five minute conversation at the kitchen table often unsticks more than another worked example.
Does my child still need to know algebra and geometry from earlier years?
Yes, and a lot of it. Factoring, fractions, solving for a variable, and reading a graph all show up constantly. If those feel rusty, a quick warm up on Khan Academy or a few old practice problems before homework helps more than re reading the textbook.
How should I sequence the function families across the year?
Most teachers build from polynomial and rational functions in the fall, move into exponentials and logarithms midyear, and finish with trig and statistics. Keeping graphing behavior, solving, and modeling together inside each unit tends to stick better than teaching all the graphing first and all the solving later.
Which topics usually need the most reteaching?
Rational expressions and logarithms are the classic trouble spots. Students often lose fractions skills from earlier grades, and logs feel unfamiliar because they undo something rather than build it. Plan extra practice days for both, and revisit them in later units instead of teaching them once and moving on.
My child says they will never use this. What do I say?
Exponentials describe interest on a loan and how medicine leaves the body. Trig describes anything that repeats, like tides or sound. Statistics shows up every time a poll or medical study makes the news. The point is not the formulas, it is learning to read situations that behave in predictable ways.
What is a good way to study for an Algebra II test at home?
Redo two or three problems from the homework without looking at the answers, then check. If a problem feels easy, skip it and pick a harder one. Twenty focused minutes of redoing problems beats an hour of rereading notes.
How do I know if students are ready for Precalculus?
By June, students should be able to graph a function from its equation, solve polynomial and rational equations without a calculator on simple cases, and switch between exponential and logarithmic form. They should also be able to set up a trig equation for a repeating situation and explain what their answer means.
How much should students rely on a graphing calculator?
Calculators are useful for checking work, exploring a graph, and handling messy numbers. Students still need to solve clean problems by hand so they understand what the calculator is doing. A good rule is pencil first, calculator second, then compare.