Course Content
A. Numbers and Operations
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A.01. Understand basic arithmetic operations with integers.
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A.02. Apply order of operations to evaluate integer expressions.
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A.03. Convert between fractions, decimals, and percentages.
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A.04. Perform addition and subtraction of rational numbers.
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A.05. Perform multiplication and division of rational numbers.
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A.06. Simplify complex expressions involving rational numbers.
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A.07. Estimate and approximate values of irrational numbers.
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A.08. Explore the historical context and real-world applications of number systems.
B. Functions
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B.01. Identify functions from various representations.
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B.02. Determine the domain and range of a function.
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B.03. Evaluate functions using tables, graphs, and equations.
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B.04. Find the slope of a linear function and interpret its meaning.
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B.05. Graph linear functions and identify key features.
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B.06. Write the equation of a linear function given various information.
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B.07. Add, subtract, multiply, and divide functions.
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B.08. Analyze linear functions over unit intervals.
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B.09. Understand and apply function composition.
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B.10. Identify and find inverse functions.
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B.11. Analyze inverse functions graphically and numerically.
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B.12. Distinguish between continuous and discontinuous functions.
C. Families of Functions
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C.01. Describe translations of functions.
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C.02. Describe reflections of functions.
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C.03. Describe dilations of functions.
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C.04. Combine transformations of functions.
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C.05. Write transformation rules for functions.
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C.06. Analyze the effects of transformations on function graphs.
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C.07. Apply transformations to solve real-world problems.
D. Quadratic Relations
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D.01. Identify characteristics of quadratic functions (vertex, intercepts, axis of symmetry).
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D.02. Graph quadratic functions using various methods.
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D.03. Match quadratic functions to their graphs.
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D.04. Find the maximum or minimum value of a quadratic function.
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D.05. Solve quadratic equations using square roots.
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D.06. Solve quadratic equations by factoring.
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D.07. Solve quadratic equations by completing the square.
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D.08. Solve quadratic equations using the quadratic formula.
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D.09. Use the discriminant to determine the nature of quadratic equation solutions.
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D.10. Apply quadratic functions to model real-world situations.
E. Polynomials
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E.01. Find the roots of factored polynomials.
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E.02. Write a polynomial given its roots.
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E.03. Perform polynomial long division.
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E.04. Apply the rational root theorem.
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E.05. Apply the complex conjugate theorem.
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E.06. Use Descartes’ Rule of Signs.
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E.07. Understand the Fundamental Theorem of Algebra.
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E.08. Match polynomials to their graphs.
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E.09. Identify even and odd functions.
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E.10. Factor sums and differences of cubes.
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E.11. Solve equations involving sums and differences of cubes.
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E.12. Factor polynomials using quadratic patterns.
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E.13. Solve equations using quadratic patterns.
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E.14. Utilize Pascal’s Triangle and the Binomial Theorem.
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E.15. Apply the Binomial Theorem to expand expressions.
F. Rational Functions
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F.01. Identify asymptotes and excluded values of rational functions.
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F.02. Solve rational equations.
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F.03. Determine if two rational functions are inverses.
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F.04. Analyze the behavior of rational functions near asymptotes.
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F.05. Apply rational functions to model real-world problems.
G. Exponential and Logarithmic Functions
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G.01. Understand the relationship between exponential and logarithmic forms.
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G.02. Evaluate exponential and logarithmic expressions.
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G.03. Apply the change of base formula.
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G.04. Identify properties of logarithms.
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G.05. Apply the product, quotient, and power properties of logarithms.
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G.06. Solve exponential equations by rewriting the base.
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G.07. Solve exponential equations using logarithms.
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G.08. Solve logarithmic equations.
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G.09. Distinguish between linear and exponential growth/decay.
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G.10. Model real-world situations using exponential and logarithmic functions.
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G.11. Solve compound interest and continuously compounded interest problems.
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G.12. Analyze the domain and range of exponential and logarithmic functions.
H. Radical Functions
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H.01. Determine the domain and range of radical functions.
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H.02. Solve radical equations.
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H.03. Simplify radical expressions.
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H.04. Graph radical functions.
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H.05. Apply radical functions to model real-world problems.
I. Roots and Rational Exponents
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I.01. Find roots of integers and rational numbers.
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I.02. Use a calculator to find roots.
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I.03. Evaluate expressions with rational exponents.
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I.04. Perform operations with rational exponents.
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I.05. Simplify expressions involving rational exponents and variables.
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I.06. Understand nth roots and their properties.
J. Systems of Equations
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J.01. Solve systems of equations by graphing.
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J.02. Solve systems of equations using substitution.
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J.03. Solve systems of equations using elimination.
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J.04. Classify systems of equations (consistent/inconsistent, dependent/independent).
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J.05. Solve systems of equations in three variables.
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J.06. Model real-world problems using systems of equations.
K. Systems of Inequalities
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K.03. Apply linear programming techniques to solve optimization problems.
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K.01. Solve systems of inequalities by graphing.
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K.02. Find the vertices of a solution set.
L. Nonlinear Inequalities
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L.01. Graph solutions to quadratic inequalities.
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L.02. Solve quadratic inequalities algebraically.
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L.03. Graph solutions to higher-degree inequalities.
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L.04. Solve higher-degree inequalities algebraically.
M. Matrices
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M.01. Understand matrix vocabulary (dimensions, elements).
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M.02. Perform matrix addition and subtraction.
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M.03. Multiply a matrix by a scalar.
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M.04. Perform linear combinations of matrices.
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M.05. Multiply two matrices.
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M.06. Simplify matrix expressions.
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M.07. Solve matrix equations.
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M.08. Find the determinant of a matrix.
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M.09. Determine if a matrix is invertible.
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M.10. Find the inverse of a 2×2 and 3×3 matrix.
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M.11. Solve matrix equations using inverses.
N. Trigonometry
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N.01. Convert between radians and degrees.
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N.02. Understand radians and arc length.
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N.03. Identify quadrants and understand their properties.
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N.04. Find coterminal and reference angles.
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N.05. Find trigonometric ratios using right triangles.
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N.06. Find trigonometric ratios using the unit circle.
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N.07. Find trigonometric ratios using reference angles.
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N.08. Understand inverse trigonometric functions.
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N.09. Solve trigonometric equations.
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N.10. Solve right triangles using trigonometric ratios.
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N.11. Apply the Law of Sines.
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N.12. Apply the Law of Cosines.
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N.13. Solve general triangles.
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N.14. Find the area of a triangle using sine or Heron’s formula.
O. Trigonometric Functions
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O.01. Identify properties of sine and cosine functions (period, amplitude, phase shift).
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O.02. Write equations of sine and cosine functions from graphs and properties.
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O.03. Graph sine and cosine functions.
P. Trigonometric Identities
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P.01. Understand and apply complementary angle identities.
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P.02. Understand symmetry and periodicity of trigonometric functions.
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P.03. Use Pythagorean and reciprocal identities to find trigonometric ratios.
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P.04. Use multiple identities to find trigonometric ratios.
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P.05. Apply trigonometric sum and difference identities.
Q. Conic Sections
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Q.01. Identify and find properties of parabolas.
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Q.02. Write equations of parabolas in vertex form.
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Q.03. Graph parabolas.
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Q.04. Identify and find properties of circles.
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Q.05. Write equations of circles in standard form.
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Q.06. Graph circles.
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Q.07. Identify and find properties of ellipses.
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Q.08. Find the eccentricity of an ellipse.
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Q.09. Write equations of ellipses in standard form.
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Q.10. Identify and find properties of hyperbolas.
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Q.11. Find the eccentricity of a hyperbola.
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Q.12. Write equations of hyperbolas in standard form.
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Q.13. Convert equations of conic sections between general and standard forms.
R. Complex Numbers
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R.01. Understand the concept of complex numbers.
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R.02. Add, subtract, multiply, and divide complex numbers.
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R.03. Understand complex conjugates.
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R.04. Find the absolute value of complex numbers.
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R.05. Understand powers of i.
S. Complex Plane
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S.01. Understand the complex plane.
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S.02. Graph complex numbers in the complex plane.
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S.03. Perform addition and subtraction of complex numbers graphically.
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S.04. Graph complex conjugates.
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S.05. Find the absolute value of complex numbers graphically.
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S.06. Find midpoints and distances in the complex plane.
T. Polar Form
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T.01. Find the modulus and argument of a complex number.
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T.02. Convert between rectangular and polar forms of complex numbers.
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T.03. Match polar equations to their graphs.
U. Two-Dimensional Vectors
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U.01. Find the magnitude and direction of a vector.
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U.02. Find the component form of a vector.
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U.03. Find a unit vector.
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U.04. Add and subtract vectors.
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U.05. Multiply a vector by a scalar.
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U.06. Find the magnitude and direction of a vector sum.
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U.07. Perform linear combinations of vectors.
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U.08. Graph resultant vectors using the triangle and parallelogram methods.
V. Three-Dimensional Vectors
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V.01. Find the magnitude and component form of a 3D vector.
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V.02. Find a 3D unit vector.
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V.03. Add, subtract, and find scalar multiples of 3D vectors.
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V.04. Perform linear combinations of 3D vectors.
W. Sequences and Series
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W.01. Find terms of sequences (explicit and recursive).
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W.02. Identify arithmetic and geometric sequences.
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W.03. Find recursive and explicit formulas for sequences.
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W.04. Convert between explicit and recursive formulas.
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W.05. Understand sigma notation.
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W.06. Find the sum of finite arithmetic and geometric series.
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W.07. Understand partial sums.
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W.08. Identify convergent and divergent geometric series.
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W.09. Find the value of an infinite geometric series.
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W.10. Write repeating decimals as fractions.
X. Logic
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X.01. Identify hypotheses and conclusions.
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X.02. Understand counterexamples.
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X.03. Understand conditionals, negations, converses, inverses, and contrapositives.
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X.04. Understand biconditionals.
Y. Probability
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Y.01. Understand basic probability concepts.
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Y.02. Calculate probabilities of events.
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Y.03. Understand combinations and permutations.
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Y.04. Find probabilities using combinations and permutations.
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Y.05. Find probabilities using two-way frequency tables.
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Y.06. Identify and analyze independent events.
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Y.07. Find conditional probabilities.
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Y.08. Use the addition rule to find probabilities.
Z. Probability Distributions
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Z.01. Identify discrete and continuous random variables.
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Z.02. Write and graph discrete probability distributions.
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Z.03. Find expected values and variances of random variables.
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Z.04. Write probability distributions for games of chance.
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Z.05. Find probabilities using binomial and normal distributions.
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Z.06. Understand the Central Limit Theorem.
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Z.07. Use normal distributions to approximate binomial distributions.
AA. Statistics
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AA.01. Identify biased samples.
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AA.02. Understand variance and standard deviation.
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AA.03. Identify and analyze outliers.
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AA.04. Match correlation coefficients to scatter plots.
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AA.05. Calculate correlation coefficients.
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AA.06. Find and interpret regression lines.
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AA.07. Find confidence intervals for population means and proportions.
