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Grade 11

What Math Does a 11th Grader Learn? All 30 Topics, in Order

By Knomi Learning · Updated

The short answer

A 11th grader learns 30 math topics, in 6 units: Polynomials; Rational and Radical; Exponentials, Logs and Series; Functions and Modeling; Trigonometry; and Inferences from Data. That is 120 smaller skills in all, taught in the order below, each building on earlier ones.

  • The earlier topics 11th grade leans on most: Exponent Rules (Grade 8), Square and Cube Roots (Grade 8), Multi-Step Equations (Grade 8), Integer Exponents (Grade 8) and Linear Expressions (Grade 7).
  • All 120 skills are matched to a Common Core standard.
  • Every one of them has a full lesson on Knomi.

Unit 1: Polynomials

1

Polynomial Arithmetic

Polynomials behave like the integers of algebra: add, subtract or multiply two and you get another. The kid names degree and terms, then works with longer polynomials than in Grade 9. Writing (x + 3)^2 as x^2 + 9 sends the tutor back to the four-cell area model.

What it covers

  • Polynomials and Their Degree
  • Adding and Subtracting Polynomials
  • Multiplying Polynomials

Builds on

  • Grade 9: Parts of an Expression
  • Grade 9: Multiplying Binomials
  • Grade 8: Multiplying and Dividing Powers
  • Grade 7: Like Terms with Negatives
  • Grade 7: Adding and Subtracting Expressions
  • Grade 7: Expanding Expressions
  • and 2 more
Polynomial Arithmetic on the 11th grade map
2

Complex Numbers

A new number i with i^2 = −1 gives every quadratic equation a solution. The kid simplifies roots of negatives, computes with a + bi, plots it on the complex plane and solves quadratics whose graphs miss the x-axis. Leaving i^2 in an answer sends the tutor back to the definition.

What it covers

  • The Imaginary Unit
  • Complex Numbers and the Complex Plane
  • Adding and Subtracting Complex Numbers
  • Multiplying Complex Numbers
  • Quadratics with Complex Solutions

Builds on

  • Grade 9: Simplifying Square Roots
  • Grade 9: Using the Formula
  • Grade 9: Features of a Parabola
  • Grade 8: Equations with Squares and Cubes
  • Grade 8: Rational or Irrational
  • Grade 7: Subtracting Rational Numbers
  • and 4 more
Complex Numbers on the 11th grade map
3

Polynomial Identities

Some products are worth knowing on sight: squares of binomials, differences of squares, sums of cubes, the rows of Pascal's triangle. The kid proves identities and uses them to find Pythagorean triples. Writing (a + b)^2 = a^2 + b^2 sends the tutor back to the area model.

What it covers

  • Special Products
  • Proving Identities
  • Pascal's Triangle and Binomial Powers

Builds on

  • Grade 10: Combinations
  • Grade 9: Special Products
  • Grade 8: Cube Roots
  • Grade 8: Converse of the Theorem
  • Grade 8: Powers of Powers and Products
Polynomial Identities on the 11th grade map
4

Factoring Polynomials

Factoring runs multiplication backwards, now for cubics and quartics. The kid pulls out common factors, groups four terms, spots squares and cubes in disguise and keeps going until nothing factors. Stopping at (x^2 − 1)(x^2 − 4) sends the tutor back to the special products.

What it covers

  • Common Factors
  • Factoring by Grouping
  • Quadratic Patterns in Disguise
  • Sums and Differences of Cubes
  • Factoring Completely

Builds on

  • Grade 9: Factoring x² + bx + c
  • Grade 9: Factoring by Structure
  • Grade 8: Multiplying and Dividing Powers
  • Grade 8: Powers of Powers and Products
  • Grade 8: Cube Roots
  • Grade 7: Factoring Expressions
  • and 2 more
Factoring Polynomials on the 11th grade map
5

Polynomial Division

Dividing polynomials is long division with x in place of ten, and the leftover says something: dividing by x − a leaves p(a). The kid divides, uses the Remainder and Factor Theorems and splits a cubic once one zero is known. A missing placeholder term sends the tutor back to long division.

What it covers

  • Dividing by a Monomial
  • Dividing by a Linear Factor
  • Synthetic Division
  • The Remainder Theorem
  • The Factor Theorem

Builds on

  • Grade 9: Factoring x² + bx + c
  • Grade 8: Multiplying and Dividing Powers
  • Grade 8: Variables on Both Sides
  • Grade 7: Signs of Products and Powers
  • Grade 6: Remainders and Estimates
  • Grade 6: Long Division
Polynomial Division on the 11th grade map
6

Polynomial Graphs

A polynomial's graph crosses the x-axis at its zeros and heads up or down at each end. The kid reads zeros and multiplicity from factored form, predicts end behavior, sketches the curve and solves inequalities from it. Reading the zero of (x + 3) as 3 sends the tutor back to solving x + 3 = 0.

What it covers

  • Zeros from Factored Form
  • Zeros and Multiplicity
  • End Behavior
  • Sketching Polynomial Graphs
  • Polynomial Inequalities

Builds on

  • Grade 9: Using the Formula
  • Grade 9: Features of a Parabola
  • Grade 9: Maxima and Minima
  • Grade 8: Intercepts
  • Grade 8: Powers with Negative Bases
  • Grade 8: Linear or Nonlinear
  • and 3 more
Polynomial Graphs on the 11th grade map
7

Polynomial Equations

The polynomial unit comes together: the kid solves cubic and quartic equations, writes a polynomial with given zeros, finds complex zeros and models a box's volume. Dividing both sides by x and losing x = 0 sends the tutor back to factoring out the common factor.

What it covers

  • Solving by Factoring
  • Writing Polynomials from Zeros
  • Complex Zeros
  • Modeling with Polynomials

Builds on

  • Grade 9: Quadratic Word Problems
  • Grade 6: Substituting Values
Polynomial Equations on the 11th grade map

Unit 2: Rational and Radical

8

Rational Expressions

A rational expression is a fraction of polynomials and follows the rules of 3/4: factor, cancel common factors, find a common denominator. The kid simplifies and combines them and keeps track of excluded values. Cancelling a term, as in (x + 3)/3 = x, sends the tutor back to factors.

What it covers

  • Simplifying Rational Expressions
  • Multiplying and Dividing
  • Adding and Subtracting
  • Quotient and Remainder Form

Builds on

  • Grade 7: Negative Signs in Fractions
  • Grade 7: Multiplying Rational Numbers
  • Grade 7: Adding and Subtracting Expressions
  • Grade 6: Greatest Common Factor
  • Grade 6: Reciprocals and Mixed Numbers
  • Grade 6: Least Common Multiple
  • and 1 more
Rational Expressions on the 11th grade map
9

Rational Equations

An equation with x in a denominator is solved by multiplying through by a common denominator, a step that can invent an answer. The kid clears denominators, checks every candidate and models shared work. Keeping a value that makes a denominator zero sends the tutor back to excluded values.

What it covers

  • Solving Rational Equations
  • Extraneous Solutions
  • Rational Equation Word Problems

Builds on

  • Grade 9: Using the Formula
  • Grade 9: Reasoning Step by Step
  • Grade 8: Fraction and Decimal Coefficients
  • Grade 8: One, None or Infinitely Many
  • Grade 7: Solving Proportions
  • Grade 7: Fraction Rate Problems
  • and 1 more
Rational Equations on the 11th grade map
10

Rational Exponents

A fractional exponent is a root: 8^(1/3) is the cube root of 8 and 8^(2/3) is that root squared. The kid rewrites between roots and powers, combines radicals and solves 2^(x + 1) = 8^x. Reading 8^(1/3) as 8 ÷ 3 sends the tutor back to the power rule.

What it covers

  • Rational Exponents and Radicals
  • Exponent Properties with Fractions
  • Combining Radicals and Conjugates
  • Equations with a Common Base

Builds on

  • Grade 9: Rational Exponents
  • Grade 9: Simplifying Square Roots
  • Grade 8: Cube Roots
  • Grade 8: Powers of Powers and Products
  • Grade 8: Negative Exponents
  • Grade 8: Rules with Integer Exponents
  • and 2 more
Rational Exponents on the 11th grade map
11

Radical Equations

To undo a square root the kid squares both sides, and squaring can smuggle in a false answer. Isolate, square or cube, solve, then check every candidate. Accepting x = 10 for √(x − 1) = −3 sends the tutor back to what √ promises: a root that is never negative.

What it covers

  • Square-Root Equations
  • Extraneous Solutions from Squaring
  • Cube-Root Equations

Builds on

  • Grade 9: Using the Formula
  • Grade 9: Reasoning Step by Step
  • Grade 8: Square Roots of Perfect Squares
  • Grade 8: Cube Roots
  • Grade 8: Volume of Spheres
Radical Equations on the 11th grade map

Unit 3: Exponentials, Logs and Series

12

Exponential Models

Anything that grows or shrinks by the same percent each step follows an exponential model. The kid reads growth and decay factors, builds models from a rate or two points, changes the time unit and meets e. Writing 7% growth as × 0.07 sends the tutor back to percent change as a multiplier.

What it covers

  • Growth and Decay Factors
  • Constructing Exponential Models
  • Changing the Time Unit
  • The Number e

Builds on

  • Grade 9: Linear or Exponential
  • Grade 9: Percent Growth and Decay
  • Grade 9: Building Exponential Models
  • Grade 9: Geometric Sequences
  • Grade 9: Rewriting Exponential Expressions
  • Grade 8: Rational or Irrational
  • and 2 more
Exponential Models on the 11th grade map
13

Logarithms

A logarithm answers 'the base to what power?': log₂ 32 = 5. The kid moves between exponential and log form, evaluates logs, uses the product, quotient and power rules and changes base. Writing log(a + b) as log a + log b sends the tutor back to the exponent rules the log rules come from.

What it covers

  • Meaning of a Logarithm
  • Evaluating Logarithms
  • Product, Quotient and Power Rules
  • Expanding and Condensing Logarithms
  • Change of Base

Builds on

  • Grade 8: Zero Exponents
  • Grade 8: Negative Exponents
  • Grade 8: Multiplying and Dividing Powers
  • Grade 8: Powers of Powers and Products
  • Grade 7: Adding the Opposite
  • Grade 6: Meaning of Exponents
Logarithms on the 11th grade map
14

Exponential Equations

When the unknown sits in an exponent and no common base appears, a logarithm brings it down. The kid solves exponential and log equations and answers 'how long until it doubles?'. Taking the log before isolating the power sends the tutor back to the product rule for logs.

What it covers

  • Solving with Logarithms
  • Solving Logarithmic Equations
  • Exponential Model Problems

Builds on

  • Grade 8: Variables on Both Sides
Exponential Equations on the 11th grade map
15

Finite Series

Adding up a sequence has a formula. The kid sums arithmetic series by pairing terms, derives the geometric series formula from a polynomial identity, and prices savings plans and loans. Using n − 1 where the formula wants n terms sends the tutor back to counting the terms.

What it covers

  • Arithmetic Series
  • The Geometric Series Formula
  • Geometric Series Word Problems
  • Compound Interest and Annuities

Builds on

  • Grade 9: Arithmetic Sequences
  • Grade 9: Geometric Sequences
  • Grade 9: Simple and Compound Interest
  • Grade 8: Variables on Both Sides
  • Grade 8: Rules with Integer Exponents
  • Grade 7: Percent Change as a Multiplier
  • and 1 more
Finite Series on the 11th grade map

Unit 4: Functions and Modeling

16

Transformations of Functions

Whatever the function, adding to the output lifts its graph, changing the input slides it, multiplying stretches it and a minus sign flips it. The kid applies and combines these moves and spots even and odd symmetry. Moving f(x + 2) right sends the tutor back to which input gives the old output.

What it covers

  • Shifting Functions
  • Reflecting Functions
  • Scaling Functions
  • Combining Transformations
  • Even and Odd Functions

Builds on

  • Grade 9: Shifting and Stretching Parabolas
  • Grade 9: Evaluating with Function Notation
  • Grade 8: Translations
  • Grade 8: Functions on Graphs
  • Grade 8: Reflections
  • Grade 8: Dilations with Coordinates
  • and 5 more
Transformations of Functions on the 11th grade map
17

Graphs of Function Families

Algebra 2 fills the family album: root, absolute value, piecewise, rational, exponential and log graphs. The kid sketches each parent graph and its transformations and reads intercepts and asymptotes. Drawing y = √x left of the y-axis sends the tutor back to which inputs a square root takes.

What it covers

  • Square Root and Cube Root Functions
  • Piecewise and Absolute Value Functions
  • Rational Function Graphs
  • Graphs of Exponential Functions
  • Graphs of Logarithmic Functions

Builds on

  • Grade 9: Square Root and Cube Root Graphs
  • Grade 9: Piecewise Functions
  • Grade 9: Inverse Variation
  • Grade 9: Graphs of Exponential Growth
  • Grade 8: Negative Exponents
  • Grade 6: Graphing Inequalities
Graphs of Function Families on the 11th grade map
18

Inverse Functions

An inverse runs a function backwards, from output to input. The kid solves f(x) = c, writes inverses of cubic, root, rational and exponential functions, and reflects graphs across y = x. Reading f^(−1)(x) as 1/f(x) sends the tutor back to what an inverse undoes.

What it covers

  • Finding an Input from an Output
  • Writing an Inverse Function
  • Inverses on Graphs and Tables

Builds on

  • Grade 9: Inverses of Linear Functions
  • Grade 9: Inputs from Outputs
  • Grade 9: Restricting the Domain
  • Grade 8: Rearranging Formulas
  • Grade 6: Reflections Across the Axes
Inverse Functions on the 11th grade map
19

Features of Functions

Whatever its family, a graph tells a story: where it rises, peaks, turns positive and what it does far out. The kid reads features in context, picks a sensible domain, finds rates of change and compares functions. 'Increasing' read as 'above the axis' sends the tutor back to direction.

What it covers

  • Key Features in Context
  • Domain in Context
  • Average Rate of Change
  • Comparing Functions in Different Forms
  • Sketching from a Description

Builds on

  • Grade 9: Increasing and Decreasing
  • Grade 9: Domain in Context
  • Grade 9: Average Rate of Change
  • Grade 9: Comparing Functions in Different Forms
  • Grade 8: Describing Graphs
  • Grade 8: Slope from Two Points
  • and 2 more
Features of Functions on the 11th grade map
20

Building Functions

Real situations are often simple functions glued together: profit is revenue minus cost, cooling tea is room temperature plus a fading exponential. The kid combines functions and fits families to data. Cooling modeled as decay to 0 sends the tutor back to the limiting value.

What it covers

  • Combining Functions
  • Modeling with Two Variables
  • Choosing a Model

Builds on

  • Grade 9: Two-Variable Equations from Situations
  • Grade 9: Fitting Other Functions
  • Grade 9: Residuals
  • Grade 8: Describing Association
  • Grade 6: Graphs of Relationships
Building Functions on the 11th grade map
21

Equations as Models

Modeling means turning a situation into equations and inequalities, solving them and asking whether the answers are allowed. The kid writes richer equations, constraints and formulas. Reporting a negative length sends the tutor back to the situation's domain.

What it covers

  • Equations and Inequalities
  • Constraints and Systems
  • Rearranging Formulas
  • Expressions with Several Variables

Builds on

  • Grade 10: Lines and Circles Intersecting
  • Grade 9: Quadratic Equations in Context
  • Grade 9: Constraints in Context
  • Grade 9: Substituting into the Quadratic
  • Grade 9: Multi-Step Formulas
  • Grade 9: Parts of an Expression
Equations as Models on the 11th grade map
22

Solving by Graphing

Any equation f(x) = g(x) can be solved by graphing both sides and reading where they cross, which is how a kid solves 2^x = x + 3 when no algebra works. Reporting the y-coordinate of the crossing sends the tutor back to what a solution of a system is.

What it covers

  • Solutions as Intersections
  • Approximating Solutions
  • Graphical Solutions in Context

Builds on

  • Grade 9: Solving with Graphs and Tables
  • Grade 8: Solutions of a System
  • Grade 8: Estimating Square Roots
Solving by Graphing on the 11th grade map

Unit 5: Trigonometry

23

Unit Circle

The unit circle lets sine and cosine take any angle, not just the acute ones of right triangles. The kid measures angles in radians, reads cos θ and sin θ as coordinates and solves sin θ = 1/2. A wrong sign outside the first quadrant sends the tutor back to which way x points.

What it covers

  • Radians on the Unit Circle
  • Angles Around the Circle
  • Sine and Cosine as Coordinates
  • Special Angle Values
  • Trig Equations on an Interval

Builds on

  • Grade 10: Radians
  • Grade 10: Sine, Cosine and Tangent
  • Grade 10: 30-60-90 Triangles
  • Grade 10: 45-45-90 Triangles
  • Grade 9: Solving by Factoring
  • Grade 8: Rotations
  • and 3 more
Unit Circle on the 11th grade map
24

Trigonometric Identities

Every point on the unit circle satisfies x^2 + y^2 = 1, so sin^2 θ + cos^2 θ = 1 for every angle. The kid proves it, finds one ratio from another, meets sec, csc and cot, and proves short identities. Dropping the ± the quadrant decides sends the tutor back to the signs on the circle.

What it covers

  • The Pythagorean Identity
  • Values from One Ratio
  • Reciprocal and Quotient Identities
  • Symmetry and Periodicity

Builds on

  • Grade 10: Equation from Center and Radius
  • Grade 8: Finding the Hypotenuse
  • Grade 8: Equations with Squares and Cubes
  • Grade 8: Reflections
  • Grade 6: Reciprocals and Mixed Numbers
Trigonometric Identities on the 11th grade map
25

Graphs of Sine and Cosine

Walk around the unit circle and plot your height against the distance walked: the sine wave appears. The kid graphs sine and cosine and reads midline, amplitude and period from graphs and equations. Giving sin(3x) a longer period sends the tutor back to horizontal scaling.

What it covers

  • Unwrapping the Unit Circle
  • Midline, Amplitude and Period
  • Features from the Equation
  • Graphing Sinusoidal Functions

Builds on

  • Grade 8: Functions on Graphs
  • Grade 6: Mean
Graphs of Sine and Cosine on the 11th grade map
26

Sinusoidal Models

Tides, Ferris wheels and daylight hours repeat, and a sine wave models each one. The kid reads midline, amplitude and period in context, builds a model from the highest and lowest values and answers 'when?' questions. Using 365 as b for a yearly cycle sends the tutor back to period = 2π/b.

What it covers

  • Interpreting Periodic Graphs
  • Building a Sinusoidal Model
  • Answering Questions with a Model
Sinusoidal Models on the 11th grade map

Unit 6: Inferences from Data

27

Normal Distributions

Heights, test scores and measurement errors often pile up in a bell shape, and then the mean and standard deviation say almost everything. The kid uses the 68–95–99.7 rule, z-scores and areas under the curve. Fitting the bell to skewed data sends the tutor back to the shape of the data.

What it covers

  • When Data Are Normal
  • The Empirical Rule
  • Z-Scores
  • Areas Under the Normal Curve

Builds on

  • Grade 9: Standard Deviation
  • Grade 9: Choosing Center and Spread
  • Grade 7: Sum and Difference Word Problems
  • Grade 7: Quotients of Integers
  • Grade 7: Likelihood from 0 to 1
  • Grade 6: Shape of a Distribution
  • and 2 more
Normal Distributions on the 11th grade map
28

Sampling and Study Design

How data were collected decides what they can show. The kid tells a parameter from a statistic, spots biased samples, and sorts surveys, experiments and observational studies, knowing only random assignment shows cause. Trusting a huge voluntary poll sends the tutor back to random sampling.

What it covers

  • Populations and Parameters
  • Random Sampling and Bias
  • Types of Studies
  • Designing an Experiment

Builds on

  • Grade 9: Correlation and Causation
  • Grade 7: Populations and Samples
  • Grade 7: Sample Variability
  • Grade 7: Random Sampling
  • Grade 7: Simulations
  • Grade 6: Statistical Questions
Sampling and Study Design on the 11th grade map
29

Inference from Samples

One sample can't give the exact truth about a population, but simulation shows how far off it is likely to be. The kid tests a model by simulation and turns sample-to-sample spread into a margin of error. Thinking the margin covers a biased sample sends the tutor back to how it was chosen.

What it covers

  • Testing a Model by Simulation
  • Sample-to-Sample Variability
  • Margin of Error
  • Estimating a Population Mean

Builds on

  • Grade 7: Simulations
  • Grade 7: Probability of Compound Events
  • Grade 7: Estimating from a Sample
  • Grade 7: Inferences About Two Populations
  • Grade 6: Mean
Inference from Samples on the 11th grade map
30

Comparing Treatments

Did the treatment really work, or did the luck of who got it make the difference? The kid compares two groups, re-randomizes the results to see what chance alone does and reads reports critically. Treating any difference in means as real sends the tutor back to the spread within the groups.

What it covers

  • Differences Between Groups
  • Re-randomizing Groups
  • Statistical Significance
  • Evaluating Reports Based on Data

Builds on

  • Grade 7: Comparing Centers and Spreads
  • Grade 7: Overlap of Distributions
Comparing Treatments on the 11th grade map

Questions parents ask

How many math topics are in 11th grade?

On Knomi's map, 11th grade math has 30 topics in 6 units, made of 120 smaller skills.

What should a student know before starting 11th grade math?

The earlier topics 11th grade leans on most are Exponent Rules (Grade 8), Square and Cube Roots (Grade 8), Multi-Step Equations (Grade 8), Integer Exponents (Grade 8) and Linear Expressions (Grade 7). A student who is quick and sure with those is ready. Each topic below lists exactly what it builds on.

Is this 11th grade math list aligned to Common Core?

Common Core is the spine. All 120 skills carry a Common Core reference, and the order follows the usual US course.

Does Knomi teach 11th grade math?

Every one of them has a full lesson on Knomi. The 11th grade map is open to anyone, with no account needed to look around.

See 11th grade math as a map.

Every topic above, with lines to what it needs first. Open it and look around, no account needed.

Open the Grade 11 map

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