Polynomials and their graphs
Students work with longer expressions that involve powers like x cubed and higher. They add, subtract, multiply, and divide these expressions, then sketch the curves and find where the graph crosses zero.
What does a student learn in
This is the year math expands beyond straight lines and simple curves into the full family of functions students will see in college. Students graph and work with polynomials, rational expressions, exponentials, logarithms, and the sine and cosine waves that describe things like tides and sound. Statistics also gets serious, with students using a sample to make claims about a whole population. By spring, students can solve an equation involving an exponent or a logarithm and explain what the answer means.
- Polynomial functions
- Rational expressions
- Exponentials and logarithms
- Trigonometry
- Statistical inference
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 handle fractions that have variables on the top and bottom, along with expressions under square roots. They simplify them, solve equations that use them, and learn to spot answers that look right but do not actually work.
- 3
Exponential and logarithmic functions
Students study patterns that grow or shrink quickly, like savings with interest or a population over time. They learn logarithms as the tool that undoes exponents and use both to solve real problems.
- 4
Trigonometry and periodic patterns
Students extend sine and cosine beyond triangles to describe things that repeat, such as tides, sound, and daylight hours. They graph these waves and use identities to rewrite and solve equations.
- 5
Statistics and sampling
Students use data from a smaller group to make careful claims about a larger one. They look at how samples are collected, what margin of error means, and when a result is strong enough to trust.
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 all the way through before jumping to calculations, then keep working even when the path isn't obvious. They check whether their answer actually fits the question they were asked.
- Algebra II
Reason Abstractly
Students take a real situation, turn it into an equation or expression to solve it, then translate the answer back into what it means in context.
- Algebra II
Construct Arguments
Students build a math argument by showing why their answer works, then explain where a classmate's reasoning goes wrong. The focus is on justifying steps, not just getting the right answer.
- Algebra II
Model with Mathematics
Students take a real situation, like comparing loan options or splitting costs, and write an equation or draw a graph to figure out what happens. Math becomes a tool for answering actual questions, not just solving textbook problems.
- Algebra II
Use Tools Strategically
Students choose the right tool for the problem, whether that means a calculator, a quick estimate, or working it out by hand. The goal is knowing when each one helps.
- Algebra II
Attend to Precision
Students use the right math words, label their units correctly, and calculate without cutting corners. Precision in algebra means a misplaced negative sign or a dropped unit changes the answer.
- 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 as a shortcut or rule. Instead of starting from scratch each time, they ask why the pattern works and write it down as a general method.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems Algebra II | Students read a math problem all the way through before jumping to calculations, then keep working even when the path isn't obvious. They check whether their answer actually fits the question they were asked. | DC-MATH.MP.hs-algebra-2.1 |
| Reason Abstractly Algebra II | Students take a real situation, turn it into an equation or expression to solve it, then translate the answer back into what it means in context. | DC-MATH.MP.hs-algebra-2.2 |
| Construct Arguments Algebra II | Students build a math argument by showing why their answer works, then explain where a classmate's reasoning goes wrong. The focus is on justifying steps, not just getting the right answer. | DC-MATH.MP.hs-algebra-2.3 |
| Model with Mathematics Algebra II | Students take a real situation, like comparing loan options or splitting costs, and write an equation or draw a graph to figure out what happens. Math becomes a tool for answering actual questions, not just solving textbook problems. | DC-MATH.MP.hs-algebra-2.4 |
| Use Tools Strategically Algebra II | Students choose the right tool for the problem, whether that means a calculator, a quick estimate, or working it out by hand. The goal is knowing when each one helps. | DC-MATH.MP.hs-algebra-2.5 |
| Attend to Precision Algebra II | Students use the right math words, label their units correctly, and calculate without cutting corners. Precision in algebra means a misplaced negative sign or a dropped unit changes the answer. | DC-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. | DC-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 as a shortcut or rule. Instead of starting from scratch each time, they ask why the pattern works and write it down as a general method. | DC-MATH.MP.hs-algebra-2.8 |
Algebra II
Algebra II
- Algebra II
Functions and Graphs
Reading a graph tells students whether a function rises, falls, levels off, or repeats. Students identify these patterns across five function types, from curved polynomials to wave-shaped trig graphs.
- Algebra II
Polynomial and Rational
Students add, subtract, multiply, and divide expressions with variables and exponents, then solve equations built from those expressions. This shows up in physics, engineering, and any field where relationships between quantities aren't simple straight lines.
- Algebra II
Trigonometry
Students use sine and cosine functions to describe patterns that repeat on a regular cycle, like sound waves or seasonal temperatures. 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 larger population. This includes choosing the right summary numbers and deciding how confident they can be that the sample reflects the whole group.
| Standard | Definition | Code |
|---|---|---|
| Functions and Graphs Algebra II | Reading a graph tells students whether a function rises, falls, levels off, or repeats. Students identify these patterns across five function types, from curved polynomials to wave-shaped trig graphs. | DC-MATH.A2.hs-algebra-2.1 |
| Polynomial and Rational Algebra II | Students add, subtract, multiply, and divide expressions with variables and exponents, then solve equations built from those expressions. This shows up in physics, engineering, and any field where relationships between quantities aren't simple straight lines. | DC-MATH.A2.hs-algebra-2.2 |
| Trigonometry Algebra II | Students use sine and cosine functions to describe patterns that repeat on a regular cycle, like sound waves or seasonal temperatures. They apply trig identities to simplify and solve those models. | DC-MATH.A2.hs-algebra-2.3 |
| Statistics and Probability Algebra II | Students use data collected from a sample group to draw conclusions about a larger population. This includes choosing the right summary numbers and deciding how confident they can be that the sample reflects the whole group. | DC-MATH.A2.hs-algebra-2.4 |
Assessments
The state tests students at this grade and subject take.
DC CAPE: High School (Algebra I, English II)
End-of-course CAPE assessments in Algebra I and English II for high school accountability.
- When given:
- spring
- 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