Examples for

Common Core Math: High School

The Common Core Standards for high school math are organized into five major topics: Algebra, Functions, Geometry, Number and Quantity, and Statistics and Probability. Individual schools or districts may choose to sequence the content as they see fit. The two most common pathways through high school mathematics, as defined by the Common Core, are "integrated" and "traditional." In an integrated model, students take courses that combine content across all topics simultaneously. In a traditional model, high school math courses are organized by topic and may include, for example, Algebra I, Algebra II and Geometry. For any sequencing of the content, Wolfram|Alpha is a great tool for exploring high school math.

Algebra

Solve and manipulate expressions with variables.

Rewrite algebraic expressions (CCSS.Math.Content.HSA-SSE.A.2):

simplify x^2 + x * (3y + 4) - x * y + 2x^2
factor by grouping x^3 + 5 x^2 + 6 x + 30

Solve linear equations and inequalities (CCSS.Math.Content.HSA-REI.B.3):

4x – 6 = 2x + 8 solution
solve for x if 4 - x <= 2

Solve a system of linear equations (CCSS.Math.Content.HSA-REI.C.5):

solve 3x + y = 2 and x - y = 10

Perform polynomial division (CCSS.Math.Content.HSA-APR.D.6):

(x^2 + 5x + 6)/(x + 3)
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Geometry

Prove and apply geometric facts about shapes and solids.

Solve for unknown measurements in triangles (CCSS.Math.Content.HSG-SRT.C.8):

Pythagorean theorem a = 10, b = 24

Compute arc lengths and sector areas (CCSS.Math.Content.HSG-C.B.5):

arc length for r = 3 and 120 degrees
radius 0.75, angle Pi/5 sector area

Find equations for ellipses and hyperbolas (CCSS.Math.Content.HSG-GPE.A.3):

ellipse with foci at (-2, 5) and (9, 5) and major axis 16
((x - 2)^2)/4 - ((y - 2)^2)/8 = 1
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Functions

Use functions to define and interpret mathematical relationships.

Determine the domain and range of a function (CCSS.Math.Content.HSF-IF.A.1):

domain and range of y = x^2 + 4x + 3

Construct functions (CCSS.Math.Content.HSF-LE.A.2):

line with slope 5 and y-intercept 2
exponential function through (1, 3) and (2, 9)

Determine intervals on which a function has a given behavior (CCSS.Math.Content.HSF-IF.B.4):

where is f(x) = 3x^2 + 9x increasing?
x^2 + x - 20 < 0

Analyze properties of trigonometric functions (CCSS.Math.Content.HSF-TF.B.5):

period of 6 sin(x/3) - 7
maximum of 8 cos(2t) - 1
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Number & Quantity

Compute with real numbers, complex numbers, vectors and matrices.

Compute with rational exponents (CCSS.Math.Content.HSN-RN.A.2):

16^(1/4) + 9^(1/2)

Evaluate powers of complex numbers (CCSS.Math.Content.HSN-CN.B.5):

(6i + 5)^2
3(1 + 2i)^3

Find reasonable estimates for real-world quantities (CCSS.Math.Content.HSN-Q.A.2):

pennies to cover 2 square feet
1000000 characters

Add, subtract and multiply matrices (CCSS.Math.Content.HSN-VM.C.8):

{{1, 2}, {3, 4}} + {{2, -1}, {-1, 2}}
{{2, 5}, {6, 0}} * {{3, 4, 5}, {0, 5, 1}}
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RELATED EXAMPLES

  • Algebra
  • Common Core Math: Grade 8
  • Numbers
  • Probability
  • Statistics
  • Trigonometry
    • Statistics & Probability

    Analyze datasets and compute probabilities.

    Represent data in plots (CCSS.Math.Content.HSS-ID.A.1):

    histogram {121, 142, 136, 142, 128, 238, 125, 354, 122, 232}

    Find a curve to approximate data (CCSS.Math.Content.HSS-ID.B.6):

    linear fit 2.2, 5.8, 10.2, 11.8, 12.5

    Calculate probabilities using the addition rule (CCSS.Math.Content.HSS-CP.B.7):

    P(A) = 3/4, P(B) = 1/5, P(A and B) = 0, what is P(A or B)?
    P(A) if P(A and B) = 0.2, P(A or B) = 0.4, P(B) = 0.333

    Determine expected payoffs (CCSS.Math.Content.HSS-MD.B.5):

    8:5 odds, bet $10
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