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Curriculum (United States)

Mathematics — Grade 11

11th grade math according to the Common Core State Standards, usually Algebra II: polynomial division, rational expressions and equations, complex numbers, the binomial theorem, radian measure and periodic functions. Every topic comes with printable worksheets.

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What do students learn in 11th grade math?

In 11th grade students divide polynomials, simplify rational expressions and solve rational equations. They compute with complex numbers and solve quadratic equations with complex roots, expand powers with the binomial theorem, and transform graphs of functions. Radian measure and periodic functions prepare the trigonometry of precalculus.

About the standards: the Common Core high school standards are organized by conceptual category (Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability), not by grade. Assigning a topic to a grade is our decision, following the common course sequence Algebra I, Geometry, Algebra II and Precalculus. Standards marked (+) go beyond the college and career readiness core.

Page status: the topics of this grade are ready as plain exercises (instruction and formula); problems with diagrams and word problems are being added next.

Curriculum scope

  1. Curriculum point HSN-CN · Teaching content · checked against the act

    The Complex Number System

    CCSS Mathematics (2010), High School, domain The Complex Number System (HSN-CN)

  2. Curriculum point HSN-CN.A · Teaching content · checked against the act

    Perform arithmetic operations with complex numbers.

    CCSS Mathematics (2010), High School, The Complex Number System, cluster A

  3. Curriculum point HSN-CN.C · Teaching content · checked against the act

    Use complex numbers in polynomial identities and equations.

    CCSS Mathematics (2010), High School, The Complex Number System, cluster C

  4. Curriculum point HSN-CN.A.1 · Teaching content · checked against the act

    Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

    CCSS Mathematics (2010), High School, The Complex Number System, standard HSN-CN.A.1

    Adding, Multiplying, and Working with Complex Numbers (we teach in grade 11)

  5. Curriculum point HSN-CN.A.2 · Teaching content · checked against the act

    Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

    CCSS Mathematics (2010), High School, The Complex Number System, standard HSN-CN.A.2

    Adding, Multiplying, and Working with Complex Numbers (we teach in grade 11)

  6. Curriculum point HSN-CN.C.7 · Teaching content · checked against the act

    Solve quadratic equations with real coefficients that have complex solutions.

    CCSS Mathematics (2010), High School, The Complex Number System, standard HSN-CN.C.7

    Solving Quadratic Equations with Complex Roots (we teach in grade 11)

  7. Curriculum point HSN-CN.C.8 · Teaching content · checked against the act

    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).

    CCSS Mathematics (2010), High School, The Complex Number System, standard HSN-CN.C.8

    Solving Quadratic Equations with Complex Roots (we teach in grade 11)

  8. Curriculum point HSN-CN.C.9 · Teaching content · checked against the act

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

    CCSS Mathematics (2010), High School, The Complex Number System, standard HSN-CN.C.9

  9. Curriculum point HSA-SSE · Teaching content · checked against the act

    Seeing Structure in Expressions

    CCSS Mathematics (2010), High School, domain Seeing Structure in Expressions (HSA-SSE)

  10. Curriculum point HSA-SSE.A · Teaching content · checked against the act

    Interpret the structure of expressions

    CCSS Mathematics (2010), High School, Seeing Structure in Expressions, cluster A

  11. Curriculum point HSA-SSE.B · Teaching content · checked against the act

    Write expressions in equivalent forms to solve problems

    CCSS Mathematics (2010), High School, Seeing Structure in Expressions, cluster B

  12. Curriculum point HSA-SSE.A.1 · Teaching content · checked against the act

    Interpret expressions that represent a quantity in terms of its context.★ a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

    CCSS Mathematics (2010), High School, Seeing Structure in Expressions, standard HSA-SSE.A.1

  13. Curriculum point HSA-SSE.A.2 · Teaching content · checked against the act

    Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – ( y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

    CCSS Mathematics (2010), High School, Seeing Structure in Expressions, standard HSA-SSE.A.2

    Using Special Product Formulas (we teach in grade 9-11) · Factoring Polynomials with Grouping and Cubes (we teach in grade 9-11)

  14. Curriculum point HSA-SSE.B.4 · Teaching content · checked against the act

    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. For example, calculate mortgage payments.★

    CCSS Mathematics (2010), High School, Seeing Structure in Expressions, standard HSA-SSE.B.4

    Finding the nth Term and Sum of a Geometric Sequence (we teach in grade 9-11)

  15. Curriculum point HSA-APR · Teaching content · checked against the act

    Arithmetic with Polynomials and Rational Expressions

    CCSS Mathematics (2010), High School, domain Arithmetic with Polynomials and Rational Expressions (HSA-APR)

  16. Curriculum point HSA-APR.A · Teaching content · checked against the act

    Perform arithmetic operations on polynomials

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, cluster A

  17. Curriculum point HSA-APR.B · Teaching content · checked against the act

    Understand the relationship between zeros and factors of polynomials

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, cluster B

  18. Curriculum point HSA-APR.C · Teaching content · checked against the act

    Use polynomial identities to solve problems

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, cluster C

  19. Curriculum point HSA-APR.D · Teaching content · checked against the act

    Rewrite rational expressions

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, cluster D

  20. Curriculum point HSA-APR.A.1 · Teaching content · checked against the act

    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.

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.A.1

  21. Curriculum point HSA-APR.B.2 · Teaching content · checked against the act

    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).

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.B.2

    Dividing Polynomials and the Remainder Theorem (we teach in grade 11)

  22. Curriculum point HSA-APR.B.3 · Teaching content · checked against the act

    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.

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.B.3

  23. Curriculum point HSA-APR.C.4 · Teaching content · checked against the act

    Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = ( x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.C.4

  24. Curriculum point HSA-APR.C.5 · Teaching content · checked against the act

    (+) 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.

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.C.5

    Finding Coefficients in Binomial Expansions (we teach in grade 11)

  25. Curriculum point HSA-APR.D.6 · Teaching content · checked against the act

    Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.D.6

    Dividing Polynomials and the Remainder Theorem (we teach in grade 11) · Multiplying and Subtracting Rational Expressions (we teach in grade 11)

  26. Curriculum point HSA-APR.D.7 · Teaching content · checked against the act

    (+) 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.

    CCSS Mathematics (2010), High School, Arithmetic with Polynomials and Rational Expressions, standard HSA-APR.D.7

  27. Curriculum point HSA-CED · Teaching content · checked against the act

    Creating Equations★

    CCSS Mathematics (2010), High School, domain Creating Equations★ (HSA-CED)

  28. Curriculum point HSA-CED.A · Teaching content · checked against the act

    Create equations that describe numbers or relationships

    CCSS Mathematics (2010), High School, Creating Equations★, cluster A

  29. Curriculum point HSA-CED.A.1 · Teaching content · checked against the act

    Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

    CCSS Mathematics (2010), High School, Creating Equations★, standard HSA-CED.A.1

  30. Curriculum point HSA-CED.A.2 · Teaching content · checked against the act

    Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

    CCSS Mathematics (2010), High School, Creating Equations★, standard HSA-CED.A.2

  31. Curriculum point HSA-CED.A.3 · Teaching content · checked against the act

    Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

    CCSS Mathematics (2010), High School, Creating Equations★, standard HSA-CED.A.3

  32. Curriculum point HSA-CED.A.4 · Teaching content · checked against the act

    Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

    CCSS Mathematics (2010), High School, Creating Equations★, standard HSA-CED.A.4

  33. Curriculum point HSA-REI · Teaching content · checked against the act

    Reasoning with Equations and Inequalities

    CCSS Mathematics (2010), High School, domain Reasoning with Equations and Inequalities (HSA-REI)

  34. Curriculum point HSA-REI.A · Teaching content · checked against the act

    Understand solving equations as a process of reasoning and explain the reasoning

    CCSS Mathematics (2010), High School, Reasoning with Equations and Inequalities, cluster A

  35. Curriculum point HSA-REI.C · Teaching content · checked against the act

    Solve systems of equations

    CCSS Mathematics (2010), High School, Reasoning with Equations and Inequalities, cluster C

  36. Curriculum point HSA-REI.D · Teaching content · checked against the act

    Represent and solve equations and inequalities graphically

    CCSS Mathematics (2010), High School, Reasoning with Equations and Inequalities, cluster D

  37. Curriculum point HSA-REI.A.2 · Teaching content · checked against the act

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

    CCSS Mathematics (2010), High School, Reasoning with Equations and Inequalities, standard HSA-REI.A.2

    Solving Rational and Radical Equations (we teach in grade 11)

  38. Curriculum point HSA-REI.D.11 · Teaching content · checked against the act

    Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions appr oximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★

    CCSS Mathematics (2010), High School, Reasoning with Equations and Inequalities, standard HSA-REI.D.11

  39. Curriculum point HSF-IF · Teaching content · checked against the act

    Interpreting Functions

    CCSS Mathematics (2010), High School, domain Interpreting Functions (HSF-IF)

  40. Curriculum point HSF-IF.B · Teaching content · checked against the act

    Interpret functions that arise in applications in terms of the context

    CCSS Mathematics (2010), High School, Interpreting Functions, cluster B

  41. Curriculum point HSF-IF.C · Teaching content · checked against the act

    Analyze functions using different representations

    CCSS Mathematics (2010), High School, Interpreting Functions, cluster C

  42. Curriculum point HSF-IF.B.4 · Teaching content · checked against the act

    For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negat ive; relative maximums and minimums; symmetries; end behavior; and periodicity .★

    CCSS Mathematics (2010), High School, Interpreting Functions, standard HSF-IF.B.4

  43. Curriculum point HSF-IF.B.5 · Teaching content · checked against the act

    Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. ★

    CCSS Mathematics (2010), High School, Interpreting Functions, standard HSF-IF.B.5

  44. Curriculum point HSF-IF.B.6 · Teaching content · checked against the act

    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. ★

    CCSS Mathematics (2010), High School, Interpreting Functions, standard HSF-IF.B.6

    Finding the Average Rate of Change (we teach in grade 9-11)

  45. Curriculum point HSF-IF.C.7 · Teaching content · checked against the act

    Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. (+) Graph rational functions, identifying zeros and asymptotes when suitable f actorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

    CCSS Mathematics (2010), High School, Interpreting Functions, standard HSF-IF.C.7

  46. Curriculum point HSF-IF.C.8 · Teaching content · checked against the act

    Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

    CCSS Mathematics (2010), High School, Interpreting Functions, standard HSF-IF.C.8

    Finding the Vertex and Using Vertex Form (we teach in grade 9-11)

  47. Curriculum point HSF-IF.C.9 · Teaching content · checked against the act

    Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

    CCSS Mathematics (2010), High School, Interpreting Functions, standard HSF-IF.C.9

  48. Curriculum point HSF-BF · Teaching content · checked against the act

    Building Functions

    CCSS Mathematics (2010), High School, domain Building Functions (HSF-BF)

  49. Curriculum point HSF-BF.A · Teaching content · checked against the act

    Build a function that models a relationship between two quantities

    CCSS Mathematics (2010), High School, Building Functions, cluster A

  50. Curriculum point HSF-BF.B · Teaching content · checked against the act

    Build new functions from existing functions

    CCSS Mathematics (2010), High School, Building Functions, cluster B

  51. Curriculum point HSF-BF.A.1 · Teaching content · checked against the act

    Write a function that describes a relationship between two quantities.★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

    CCSS Mathematics (2010), High School, Building Functions, standard HSF-BF.A.1

    Writing Equations of Lines and Parallel Lines (we teach in grade 9-11) · Combining Functions by Composition (we teach in grade 9-11)

  52. Curriculum point HSF-BF.B.3 · Teaching content · checked against the act

    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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

    CCSS Mathematics (2010), High School, Building Functions, standard HSF-BF.B.3

    Shifting Graphs Horizontally and Vertically (we teach in grade 9-11)

  53. Curriculum point HSF-BF.B.4 · Teaching content · checked against the act

    Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1. b. (+) Verify by composition that one function is the inverse of another. c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. d. (+) Produce an invertible function from a non-invertible function by restricting the domain.

    CCSS Mathematics (2010), High School, Building Functions, standard HSF-BF.B.4

    Finding the Inverse of a Linear Function (we teach in grade 9-11)

  54. Curriculum point HSF-LE · Teaching content · checked against the act

    Linear, Quadratic, and Exponential Models★

    CCSS Mathematics (2010), High School, domain Linear, Quadratic, and Exponential Models★ (HSF-LE)

  55. Curriculum point HSF-LE.A · Teaching content · checked against the act

    Construct and compare linear, quadratic, and exponential models and solve problems

    CCSS Mathematics (2010), High School, Linear, Quadratic, and Exponential Models★, cluster A

  56. Curriculum point HSF-LE.A.4 · Teaching content · checked against the act

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

    CCSS Mathematics (2010), High School, Linear, Quadratic, and Exponential Models★, standard HSF-LE.A.4

  57. Curriculum point HSF-TF · Teaching content · checked against the act

    Trigonometric Functions

    CCSS Mathematics (2010), High School, domain Trigonometric Functions (HSF-TF)

  58. Curriculum point HSF-TF.A · Teaching content · checked against the act

    Extend the domain of trigonometric functions using the unit circle

    CCSS Mathematics (2010), High School, Trigonometric Functions, cluster A

  59. Curriculum point HSF-TF.B · Teaching content · checked against the act

    Model periodic phenomena with trigonometric functions

    CCSS Mathematics (2010), High School, Trigonometric Functions, cluster B

  60. Curriculum point HSF-TF.C · Teaching content · checked against the act

    Prove and apply trigonometric identities

    CCSS Mathematics (2010), High School, Trigonometric Functions, cluster C

  61. Curriculum point HSF-TF.A.1 · Teaching content · checked against the act

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

    CCSS Mathematics (2010), High School, Trigonometric Functions, standard HSF-TF.A.1

    Converting Between Degrees and Radians (we teach in grade 11)

  62. Curriculum point HSF-TF.A.2 · Teaching content · checked against the act

    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.

    CCSS Mathematics (2010), High School, Trigonometric Functions, standard HSF-TF.A.2

  63. Curriculum point HSF-TF.B.5 · Teaching content · checked against the act

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

    CCSS Mathematics (2010), High School, Trigonometric Functions, standard HSF-TF.B.5

    Finding the Period and Amplitude of a Sine Curve (we teach in grade 11)

  64. Curriculum point HSF-TF.C.8 · Teaching content · checked against the act

    Prove the Pythagorean identity sin2(θ) + cos2(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.

    CCSS Mathematics (2010), High School, Trigonometric Functions, standard HSF-TF.C.8

  65. Curriculum point HSF-TF.C.9 · Teaching content · checked against the act

    (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them t o solve problems.

    CCSS Mathematics (2010), High School, Trigonometric Functions, standard HSF-TF.C.9

  66. Curriculum point HSG-GPE · Teaching content · checked against the act

    Expressing Geometric Properties with Equations

    CCSS Mathematics (2010), High School, domain Expressing Geometric Properties with Equations (HSG-GPE)

  67. Curriculum point HSG-GPE.A · Teaching content · checked against the act

    Translate between the geometric description and the equation for a conic section

    CCSS Mathematics (2010), High School, Expressing Geometric Properties with Equations, cluster A

  68. Curriculum point HSG-GMD · Teaching content · checked against the act

    Geometric Measurement and Dimension

    CCSS Mathematics (2010), High School, domain Geometric Measurement and Dimension (HSG-GMD)

  69. Curriculum point HSG-GMD.A · Teaching content · checked against the act

    Explain volume formulas and use them to solve problems

    CCSS Mathematics (2010), High School, Geometric Measurement and Dimension, cluster A

  70. Curriculum point HSS-ID · Teaching content · checked against the act

    Interpreting Categorical and Quantitative Data

    CCSS Mathematics (2010), High School, domain Interpreting Categorical and Quantitative Data (HSS-ID)

  71. Curriculum point HSS-ID.A · Teaching content · checked against the act

    Summarize, represent, and interpret data on a single count or measurement variable

    CCSS Mathematics (2010), High School, Interpreting Categorical and Quantitative Data, cluster A

  72. Curriculum point HSS-ID.A.4 · Teaching content · checked against the act

    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.

    CCSS Mathematics (2010), High School, Interpreting Categorical and Quantitative Data, standard HSS-ID.A.4

  73. Curriculum point HSS-IC · Teaching content · checked against the act

    Making Inferences and Justifying Conclusions

    CCSS Mathematics (2010), High School, domain Making Inferences and Justifying Conclusions (HSS-IC)

  74. Curriculum point HSS-IC.A · Teaching content · checked against the act

    Understand and evaluate random processes underlying statistical experiments

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, cluster A

  75. Curriculum point HSS-IC.B · Teaching content · checked against the act

    Make inferences and justify conclusions from sample surveys, experiments, and observational studies

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, cluster B

  76. Curriculum point HSS-IC.A.1 · Teaching content · checked against the act

    Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, standard HSS-IC.A.1

  77. Curriculum point HSS-IC.A.2 · Teaching content · checked against the act

    Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, standard HSS-IC.A.2

  78. Curriculum point HSS-IC.B.3 · Teaching content · checked against the act

    Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, standard HSS-IC.B.3

  79. Curriculum point HSS-IC.B.4 · Teaching content · checked against the act

    Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, standard HSS-IC.B.4

  80. Curriculum point HSS-IC.B.5 · Teaching content · checked against the act

    Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, standard HSS-IC.B.5

  81. Curriculum point HSS-IC.B.6 · Teaching content · checked against the act

    Evaluate reports based on data.

    CCSS Mathematics (2010), High School, Making Inferences and Justifying Conclusions, standard HSS-IC.B.6

  82. Curriculum point HSS-MD · Teaching content · checked against the act

    Using Probability to Make Decisions

    CCSS Mathematics (2010), High School, domain Using Probability to Make Decisions (HSS-MD)

  83. Curriculum point HSS-MD.B · Teaching content · checked against the act

    Use probability to evaluate outcomes of decisions

    CCSS Mathematics (2010), High School, Using Probability to Make Decisions, cluster B

  84. Curriculum point HSS-MD.B.6 · Teaching content · checked against the act

    (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number gener ator).

    CCSS Mathematics (2010), High School, Using Probability to Make Decisions, standard HSS-MD.B.6

  85. Curriculum point HSS-MD.B.7 · Teaching content · checked against the act

    (+) Analyze decisions and strategies using probability concepts (e.g., product t esting, medical testing, pulling a hockey goalie at the end of a game).

    CCSS Mathematics (2010), High School, Using Probability to Make Decisions, standard HSS-MD.B.7

Skills step by step

Factoring Polynomials with Grouping and Cubes

Students learn to break down complex algebraic expressions by pulling out common factors, grouping terms, and using patterns for the sum and difference of cubes.

Curriculum point HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – ( y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

In 11th grade, students use the structure of an algebraic expression to break it into simpler factors. Instead of relying solely on basic quadratic methods, students examine multi-term expressions to locate greatest common factors, group terms with shared characteristics, and recognize expressions made of two perfect cubes.

A common error occurs with negative signs when factoring by grouping or using cube patterns. When grouping four terms, students often forget to distribute a negative sign out of the second pair, leaving mismatched binomials that prevent them from finishing the problem. With sum and difference of cubes, students frequently mix up the positive and negative signs in the linear and quadratic parts of the factored form.

Worksheet tasks reinforce these skills through three main formats:

  • Factoring out a monomial: identifying and extracting the greatest common factor shared by all terms in an expression.
  • Factoring by grouping: splitting four-term polynomials into pairs to reveal and pull out a common binomial factor.
  • Sum and difference of cubes: identifying cubed terms and applying the appropriate cube formula to rewrite the expression.
Create a worksheet for this skill

Task types: Factoring out a monomial · Factoring by grouping · Sum and difference of cubes

Adding, Multiplying, and Working with Complex Numbers

Students learn to add, subtract, and multiply complex numbers in the form a + bi and simplify powers of i using the rule that i² equals –1.

Curriculum point HSN-CN.A.1 Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.
Curriculum point HSN-CN.A.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

In Grade 11, students work with complex numbers written in standard a + bi form, where a and b are real numbers. By applying familiar algebraic rules—including the commutative, associative, and distributive properties—alongside the core definition that i² = –1, students learn to add, subtract, and multiply complex numbers, as well as evaluate positive powers of i.

A frequent error occurs during multiplication when students treat i simply as a regular variable like x. They often forget to substitute –1 for i², which causes a sign error in the final real part of the number. Another common mistake happens during subtraction, where students forget to distribute the negative sign across both the real and imaginary parts of the second number.

Practice tasks cover three clear formats based on these skills. In adding and subtracting complex numbers, students combine real terms with real terms and imaginary terms with imaginary terms. In multiplying complex numbers, students expand expressions like (3 + 2i)(1 – 4i) and simplify the result into standard a + bi form. Finally, tasks on powers of i require students to simplify higher exponents down to 1, –1, i, or –i by applying the rule that i² = –1.

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Task types: Adding and subtracting complex numbers · Powers of i · Multiplying complex numbers

Finding the nth Term and Sum of a Geometric Sequence

Students learn to write formulas to find any term in a geometric sequence and use the sum formula to calculate the total of a finite series.

Curriculum point 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. For example, calculate mortgage payments.★
Curriculum point 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. ★
Curriculum point 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).

In Grade 11, students work with geometric sequences where each value is multiplied by a constant common ratio (other than 1). Students write explicit rules to calculate any specific term—known as the nth term—and use the finite geometric series formula to add up a set number of terms quickly.

A frequent error occurs when evaluating exponents and signs. When finding the nth term, students often mistakenly multiply the first term by the common ratio before applying the power, or they forget to use n − 1 in the exponent. When evaluating sums, negative common ratios often lead to sign errors in the denominator, where subtracting a negative value should result in addition.

Worksheet practice focuses on two main task templates:

  • Geometric sequence — nth term: Students identify the first term and common ratio from a list or table to calculate a specific later term, such as the 8th or 12th term.
  • Geometric sequence — sum of terms: Students apply the sum formula to find the total of the first n terms of a sequence without adding each value by hand.
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Task types: Geometric sequence — nth term · Geometric sequence — sum of terms

Using Special Product Formulas

Students learn to use algebraic patterns to quickly expand the square of a sum or difference and the product of a sum and a difference.

Curriculum point HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – ( y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

At this level, students learn to recognize the structure of an algebraic expression rather than multiplying every term by hand. They identify expressions that match standard patterns and apply shortcut formulas to find the expanded form directly, working with sums and differences of terms containing variables and constants.

A very common mistake occurs when students square a binomial. Many forget the middle term entirely, incorrectly assuming that squaring a sum means simply squaring each individual term. This happens because they try to distribute the exponent over addition or subtraction instead of applying the complete multiplication pattern.

Practice tasks for this skill typically focus on two formats:

  • Product of a sum and a difference, where students multiply conjugate pairs, such as (x + 5)(x – 5), to arrive directly at a difference of squares.
  • Square of a sum or difference, where students expand expressions like (x + 3) squared or (2x – 7) squared by including the doubled middle term alongside the squared end terms.
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Task types: Product of a sum and a difference · Square of a sum or difference

Dividing Polynomials and the Remainder Theorem

Students learn to divide polynomials by linear factors like x − a and find the remainder directly using the Remainder Theorem.

Curriculum point 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).
Curriculum point HSA-APR.D.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

In Grade 11, students learn to divide a polynomial by a linear binomial of the form x − a using long division. They write their answers in the form q(x) + r/(x − a), where q(x) is the quotient and r is the constant remainder. Alongside division, students use the Remainder Theorem to find this remainder quickly: by calculating p(a), they can determine the remainder without completing the full division, confirming that x − a is an exact factor whenever p(a) = 0.

A frequent error is mixing up the sign of a. When dividing by a binomial such as x − 3, students often evaluate p(−3) instead of p(3) because they carry the minus sign into the calculation. In polynomial long division, students also tend to make sign errors when subtracting rows, especially when subtracting terms that already have negative coefficients.

Worksheet tasks for this skill center on two main formats. In Dividing a polynomial by a binomial, students work through polynomial division step by step to find the quotient and any leftover remainder. In Remainder of polynomial division, students use the Remainder Theorem to quickly calculate the remainder or check whether a given binomial divides evenly into the polynomial.

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Task types: Remainder of polynomial division · Dividing a polynomial by a binomial

Multiplying and Subtracting Rational Expressions

Students learn to multiply and subtract rational expressions formed by polynomials, simplifying the results into a single algebraic fraction.

Curriculum point HSA-APR.D.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

In 11th grade, students work with rational expressions—fractions where both the numerator and the denominator are polynomials. Students rewrite and combine these algebraic fractions using multiplication and subtraction to produce a single, simplified rational expression.

A common mistake during subtraction is forgetting to distribute the negative sign across every term in the numerator of the second fraction after finding a common denominator. When multiplying, students often attempt to cancel individual terms separated by addition or subtraction signs instead of factoring the polynomials first to divide out shared factors.

Practice tasks focus on two main formats: multiplying rational expressions and subtracting rational expressions. In subtraction problems, students identify a shared polynomial denominator and combine like terms in the numerator. In multiplication problems, students factor polynomial numerators and denominators completely to reduce the final product to its simplest form.

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Task types: Multiplying rational expressions · Subtracting rational expressions

Solving Rational and Radical Equations

Students learn to solve simple rational and radical equations in one variable and identify extraneous solutions that do not work in the original equation.

Curriculum point HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Students learn to solve simple one-variable equations that contain rational expressions (fractions with variables in the denominator) or radical expressions (roots containing variables). They apply algebraic techniques such as clearing denominators by multiplying by a common term or clearing roots by raising both sides of the equation to an appropriate power.

A common stumbling block is identifying extraneous solutions. Because algebraic steps like squaring both sides or multiplying by an expression containing the variable can create values that do not satisfy the original problem, students often forget to check their results. This leads to accepting invalid answers, such as values that make a denominator equal to zero or require a principal square root to equal a negative number.

Worksheets and practice tasks focus on two formats:

  • Radical equation: Tasks where students isolate a root, eliminate it by powering both sides, solve for the variable, and test for valid answers.
  • Rational equation: Tasks where students clear denominators, solve the remaining linear or polynomial equation, and check that no solutions cause division by zero.
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Task types: Radical equation · Rational equation

Writing Equations of Lines and Parallel Lines

Students learn to determine explicit linear functions given two coordinate points or a single point and a parallel line.

Curriculum point HSF-BF.A.1 Write a function that describes a relationship between two quantities.★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

Students write explicit linear functions to describe the relationship between two quantities. They determine the slope between two given coordinates or identify the matching slope needed to write the equation of a parallel line passing through a target point.

A frequent error happens when working with parallel lines: students sometimes alter the slope—such as inverting or negating it—instead of keeping it identical. Another common mistake arises during the slope calculation itself, where students reverse the ratio by placing changes in x over changes in y, or swap the coordinate values when substituting them into the equation.

Practice tasks include Parallel line through a point, where students use an existing linear equation and a given coordinate to write a new parallel line, and Linear function through two points, where they find the rate of change between two coordinates to build the complete linear equation.

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Task types: Linear function through two points · Parallel line through a point

Finding the Vertex and Using Vertex Form

Students learn to rewrite quadratic equations into vertex form to identify a parabola's vertex, line of symmetry, and maximum or minimum values.

Curriculum point HSF-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

In Grade 11, students use algebraic methods such as completing the square to rewrite quadratic functions into vertex form, y = a(x − h)2 + k. Converting to this form allows them to directly pinpoint the parabola's vertex at (h, k), determine the axis of symmetry, and state the function's extreme values (whether the graph opens up to a minimum or down to a maximum).

A frequent error occurs with the horizontal shift inside the squared term. Because the template contains a subtraction sign, students often misread the signs and identify the vertex of y = (x − 4)2 + 3 as (−4, 3) instead of (4, 3). Errors also happen when the leading coefficient a is not 1, where students forget to factor it out before completing the square or fail to balance the equation properly.

Worksheet tasks focus on Vertex form of a quadratic function and finding the Vertex of a parabola. Students practice converting equations from standard form to vertex form step by step, extracting the coordinates of the vertex, and interpreting what that turning point represents.

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Task types: Vertex of a parabola · Vertex form of a quadratic function

Converting Between Degrees and Radians

Students learn to understand radians as arc lengths on a unit circle and convert angle measurements between degrees and radians.

Curriculum point HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

In 11th grade, students learn that the radian measure of an angle is the length of the arc it cuts out on a unit circle. Using this definition, they connect their prior knowledge of degree turns to this new measurement system and learn to translate angle sizes back and forth between degrees and radians.

A typical error occurs when students invert the conversion fraction, multiplying by π/180° when they need to multiply by 180°/π. Learners also frequently assume that an angle is only in radians if it includes the symbol π, which causes confusion about what radians actually represent on the circle.

Tasks for this skill focus on two distinct worksheet templates: Degrees to radians, where students rewrite angles given in degrees as exact radian measures, and Radians to degrees, where they convert radian measures back into degree values.

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Task types: Degrees to radians · Radians to degrees

Finding the Period and Amplitude of a Sine Curve

Students learn to identify the period and find the maximum or amplitude of a sine curve to model periodic patterns.

Curriculum point HSF-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. ★

In 11th grade, students examine the graphs of periodic functions to model repeating cycles. They identify the key geometric features of a sine curve, determining its period—the horizontal length of one full cycle—and locating the curve's maximum value to determine its amplitude.

A common error is confusing the total vertical height of the wave with its amplitude. Students often measure from the lowest trough all the way to the crest, forgetting that amplitude is measured from the center midline to the peak. Another frequent slip occurs when measuring the period: students often take the distance between two consecutive zero-crossings, which captures only half of a wave rather than a complete cycle.

Worksheet tasks focus directly on these visual features. Under Maximum of a sine curve, students read a graphed wave to find the highest value it reaches along the vertical axis. In Period of a sine curve, students inspect the horizontal axis to measure the exact distance from one wave peak to the next.

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Task types: Maximum of a sine curve · Period of a sine curve

Finding Coefficients in Binomial Expansions

Students learn to find specific coefficients in expressions of the form (x + c)ⁿ for positive whole-number powers using the Binomial Theorem or Pascal’s Triangle.

Curriculum point 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.

Students learn to determine terms in expressions of the form (x + c)n, where n is a positive integer and c is a constant number. Using the Binomial Theorem or rows of Pascal’s Triangle, they find the numerical coefficient of any designated power of x without needing to multiply the binomial repeatedly by hand.

A common error happens when students overlook the constant value c. They often correctly identify the combinatoric number from Pascal’s Triangle but forget to raise c to its corresponding power, or they mishandle negative signs when c is negative, leading to an incorrect final product for the coefficient.

Worksheet tasks focus directly on finding a single coefficient in a binomial expansion. For example, a student may be given an expression like (x + 3)5 and asked to calculate the coefficient of the x2 term.

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Shifting Graphs Horizontally and Vertically

Students learn to shift function graphs up, down, left, and right by changing the equation, and find the shift value given a graph.

Curriculum point 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

In 11th grade, students connect changes in an equation to physical movements of its graph on the coordinate plane. By working with specific positive and negative values of k, they learn that replacing f(x) with f(x) + k shifts the curve vertically up or down, while replacing it with f(x + k) shifts the curve horizontally left or right. They also analyze graphs to determine the exact numerical value of k.

A frequent mistake happens with horizontal shifts. Students routinely assume that f(x + 3) moves a graph three units to the right toward positive numbers, rather than three units to the left. Students also mix up operations applied inside the function's input, like f(x + k), with operations applied to the entire output, like f(x) + k.

Practice with Translating a graph worksheets presents students with a base curve alongside a shifted curve. Students count the units moved along the x- or y-axis to identify the value of k and write the new function formula, or they take a given formula and sketch the resulting shift.

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Finding the Average Rate of Change

Students learn to calculate and interpret the average rate of change of a function from an equation or table over a given interval, and estimate it from a graph.

Curriculum point 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. ★

In Grade 11, students find how fast a function increases or decreases over a specific interval. They calculate the average rate of change using functions given as algebraic formulas (symbolically) or as tables of values, and they estimate this rate visually by reading points from a graph. They also learn to interpret what this rate of change represents in real-world contexts.

A frequent error occurs when students invert the calculation by dividing the change in inputs by the change in outputs, rather than dividing the change in function values by the interval length. Another common issue is finding only the total change between the two endpoints and forgetting to divide by the difference in the input values.

Worksheet tasks from the Average rate of change template present students with a specified interval alongside a function equation, a data table, or a graphed curve. Students determine the function values at the endpoints of the interval, divide the vertical change by the horizontal change, and write the final rate as a simplified value or rate with units.

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Combining Functions by Composition

Students learn to evaluate and write composite functions by using the output of one function as the input for another.

Curriculum point HSF-BF.A.1 Write a function that describes a relationship between two quantities.★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

In 11th grade, students learn to combine two mathematical rules so that the output of one function serves as the input for the next, written as f(g(x)). They build explicit expressions for these combined functions and interpret them in practical models, such as linking time to temperature through a changing height.

A common difficulty is getting the sequence backward: students frequently evaluate the outer function first, calculating g(f(x)) instead of f(g(x)), or confuse function composition with multiplication by treating (f ∘ g)(x) as f(x) · g(x). When substituting an algebraic expression into the outer formula, learners also commonly forget to wrap the inner expression in parentheses, causing sign and exponent errors.

Tasks generated from the Composition of functions template provide pairs of formulas—such as linear, quadratic, or rational equations—and ask students to find the combined expression f(g(x)) or evaluate the composite function at a specific numerical value.

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Finding the Inverse of a Linear Function

Students learn to find the algebraic inverse of a linear function by reversing its operations and solving for the input variable.

Curriculum point HSF-BF.B.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1. b. (+) Verify by composition that one function is the inverse of another. c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. d. (+) Produce an invertible function from a non-invertible function by restricting the domain.

Students work with linear equations written in function notation, such as f(x) = 3x + 4 or f(x) = -2x - 7. At this stage, they learn to undo the operations applied to the input variable by setting the function equal to an output value and solving for x. This allows them to write a clear formula for the inverse function, typically expressed as f⁻¹(x).

A common error is confusing an inverse function with a reciprocal, leading students to mistakenly treat f⁻¹(x) as 1/f(x). Another frequent misstep occurs during multi-step algebraic isolation: when dividing by the slope coefficient, students often divide only one term rather than the entire side of the equation, writing x/3 + 4 instead of (x - 4)/3.

On printable worksheets for the Inverse of a linear function template, tasks present a linear rule with integer or fractional coefficients and ask students to find the corresponding inverse equation. Students practice swapping the roles of the input and output variables and isolating the new dependent variable using inverse operations.

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Solving Quadratic Equations with Complex Roots

Students learn to solve quadratic equations with real coefficients that have complex solutions using the imaginary unit.

Curriculum point HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
Curriculum point HSN-CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).

In Grade 11, students solve quadratic equations with real coefficients where the solutions are not real numbers. When working with equations such as x2 + 4 = 0 or using the quadratic formula on equations with a negative discriminant, they express the square roots of negative numbers using the imaginary unit i. They can also use complex numbers to factor expressions that do not factor over real numbers, rewriting forms like x2 + 4 as (x + 2i)(x – 2i).

A frequent mistake happens when simplifying the square root of a negative value under the radical. Students often drop the negative sign entirely or treat it like a regular negative result—for example, writing the square root of –16 as –4 instead of 4i. Another common hurdle is forgetting that complex roots always appear in conjugate pairs when solving quadratic equations with real coefficients.

Worksheet tasks from the Quadratic equation with complex roots template present students with equations such as x2 + 2x + 5 = 0. Students apply algebraic methods like the quadratic formula or completing the square to find both complex solutions, writing their final answers in standard a ± bi form.

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Task templates to print

Every task type, grouped by skill. Clicking one opens the worksheet generator with it already selected.

Factoring Polynomials with Grouping and Cubes

Adding, Multiplying, and Working with Complex Numbers

Finding the nth Term and Sum of a Geometric Sequence

Using Special Product Formulas

Dividing Polynomials and the Remainder Theorem

Multiplying and Subtracting Rational Expressions

Solving Rational and Radical Equations

Writing Equations of Lines and Parallel Lines

Finding the Vertex and Using Vertex Form

Converting Between Degrees and Radians

Finding the Period and Amplitude of a Sine Curve

Finding Coefficients in Binomial Expansions

Shifting Graphs Horizontally and Vertically

Finding the Average Rate of Change

Combining Functions by Composition

Finding the Inverse of a Linear Function

Solving Quadratic Equations with Complex Roots

Other task types

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