Course Content
A. Numbers and Operations
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A.01. Understand integers and their properties (addition, subtraction, multiplication, division).
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A.02. Simplify numerical expressions with integers using order of operations.
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A.03. Convert between decimals and fractions.
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A.04. Perform operations with rational numbers (addition, subtraction, multiplication, division).
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A.05. Simplify complex numerical expressions involving rational and irrational numbers.
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A.06. Estimate and approximate values of irrational numbers.
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A.07. Explore real-world applications of rational and irrational numbers.
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A.08. Understand and apply absolute value.
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A.09. Represent numbers on a number line.
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A.10. Compare and order rational numbers.
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A.11. Identify factors, prime factors, GCF, and LCM.
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A.12. Solve word problems using GCF and LCM.
B. Exponents
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B.01. Understand and apply powers with integer bases.
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B.02. Evaluate expressions using properties of exponents.
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B.03. Perform multiplication and division with exponents.
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B.04. Apply the power rule.
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B.05. Simplify expressions involving exponents.
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B.06. Work with powers having decimal and fractional bases.
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B.07. Understand and apply negative exponents.
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B.08. Identify equivalent expressions involving exponents.
C. Scientific Notation
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C.01. Convert between standard and scientific notation.
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C.02. Compare numbers in scientific notation.
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C.03. Multiply and divide numbers in scientific notation.
D. Radicals and Rational Exponents
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D.01. Understand square and cube roots.
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D.02. Simplify radical expressions.
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D.03. Simplify radical expressions by rationalizing the denominator.
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D.04. Perform operations (addition, subtraction, multiplication) with radical expressions.
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D.05. Simplify expressions using the distributive property.
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D.06. Evaluate rational exponents.
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D.07. Perform operations (multiplication, division) with rational exponents.
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D.08. Apply the power rule with rational exponents.
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D.09. Simplify complex expressions involving rational exponents.
E. Coordinate Plane
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E.01. Understand and utilize the coordinate plane.
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E.02. Find the midpoint between two points.
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E.03. Calculate the distance between two points.
F. Solving Equations and Inequalities
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F.01. Solve one-step linear equations.
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F.02. Solve two-step linear equations.
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F.03. Solve linear equations with variables on both sides.
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F.04. Solve advanced linear equations.
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F.05. Determine the number of solutions to a linear equation.
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F.06. Create equations with no solutions or infinitely many solutions.
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F.07. Solve linear equations in word problems.
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F.08. Graph inequalities.
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F.09. Write inequalities from graphs.
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F.10. Identify solutions to inequalities.
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F.11. Solve one-step linear inequalities.
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F.12. Solve two-step linear inequalities.
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F.13. Solve advanced linear inequalities.
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F.14. Graph solutions to linear inequalities (one-step, two-step, advanced, compound).
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F.15. Write and solve compound inequalities.
G. Data Analysis and Graphs
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G.01. Interpret bar graphs, line graphs, and histograms.
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G.02. Create bar graphs, line graphs, and histograms.
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G.03. Interpret circle graphs, stem-and-leaf plots, and box-and-whisker plots.
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G.04. Interpret and analyze scatter plots, including lines of best fit.
H. Relations and Functions
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H.01. Understand relations and represent them in various forms (tables, graphs, mappings, lists).
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H.02. Identify the domain and range of a relation.
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H.03. Differentiate between independent and dependent variables.
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H.04. Identify functions using the vertical line test.
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H.05. Evaluate functions and complete function tables.
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H.06. Interpret function graphs in word problems.
I. Direct and Inverse Variation
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I.01. Identify proportional relationships.
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I.02. Find the constant of variation.
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I.03. Graph proportional relationships.
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I.04. Write and solve direct variation equations.
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I.05. Identify direct and inverse variation.
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I.06. Write and solve inverse variation equations.
J. Linear Functions
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J.06. Write linear equations in slope-intercept form from graphs, tables, and word problems.
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J.07. Solve linear equations for y.
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J.08. Write linear equations in standard form.
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J.09. Find x- and y-intercepts from standard form.
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J.10. Graph linear equations in standard form.
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J.11. Write equations of horizontal and vertical lines.
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J.12. Graph horizontal and vertical lines.
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J.13. Use point-slope form to graph and write equations.
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J.14. Understand slopes of parallel and perpendicular lines.
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J.15. Write equations for parallel or perpendicular lines.
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J.16. Find the distance between a point and a line, and between two parallel lines.
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J.17. Understand transformations of linear functions.
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J.18. Solve word problems involving linear functions.
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J.01. Identify linear functions from graphs, tables, and equations.
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J.02. Find the slope of a line from a graph or two points.
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J.03. Find a missing coordinate using slope.
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J.04. Use slope-intercept form to find the slope and y-intercept.
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J.05. Graph linear equations using slope-intercept form.
K. Systems of Linear Equations
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K.01. Determine if a point is a solution to a system of equations.
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K.02. Solve systems of equations by graphing.
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K.03. Solve systems of equations using substitution.
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K.04. Solve systems of equations using elimination.
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K.05. Solve systems of equations using any appropriate method.
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K.06. Determine the number of solutions to a system of equations.
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K.07. Classify systems of equations.
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K.08. Solve systems of equations in word problems.
L. Polynomials and Factoring
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L.01. Identify monomials and polynomials.
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L.02. Multiply and divide monomials.
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L.03. Add, subtract, and multiply polynomials.
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L.04. Find the GCF of monomials.
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L.05. Factor out a monomial.
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L.06. Factor quadratics (leading coefficient 1 and other leading coefficients).
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L.07. Factor quadratics using special cases and by grouping.
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L.08. Factor polynomials completely.
M. Quadratic Equations and Parabolas
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M.01. Understand characteristics of quadratic functions.
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M.02. Complete function tables for quadratic functions.
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M.03. Solve quadratic equations using square roots, the zero product property, and factoring.
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M.04. Complete the square to solve quadratic equations.
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M.05. Solve quadratic equations using the quadratic formula.
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M.06. Use the discriminant.
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M.07. Identify the direction a parabola opens.
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M.08. Find the vertex and axis of symmetry of a parabola.
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M.09. Write equations of parabolas in vertex form from graphs and properties.
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M.10. Graph parabolas.
N. Functions: Linear, Quadratic, Exponential
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N.01. Identify linear, quadratic, and exponential functions from graphs and tables.
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N.02. Write linear, quadratic, and exponential functions.
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N.03. Analyze linear and exponential functions over unit intervals.
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N.04. Describe linear and exponential growth and decay.
O. Rational Functions and Expressions
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O.01. Understand asymptotes and excluded values in rational functions.
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O.02. Simplify complex fractions and rational expressions.
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O.03. Multiply, divide, add, and subtract rational expressions.
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O.04. Divide polynomials.
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O.05. Solve rational equations.
P. Circles in the Coordinate Plane
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P.01. Find the center and radius/diameter of a circle.
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P.02. Write equations of circles in standard form from graphs and properties.
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P.03. Graph circles.
Q. Logic and Reasoning
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Q.01. Identify hypotheses and conclusions.
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Q.02. Understand counterexamples.
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Q.03. Construct and interpret truth tables.
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Q.04. Determine truth values of statements.
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Q.05. Work with conditionals, negations, converses, inverses, and contrapositives.
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Q.06. Understand biconditionals.
R. Measurement and Geometry
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R.01. Estimate and convert metric and imperial measurements (length, area, volume).
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R.02. Work with unit rates and unit prices.
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R.03. Solve problems involving scale drawings.
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R.04. Perform geometric constructions (angle bisector, congruent angle).
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R.05. Understand polygon vocabulary and properties.
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R.06. Calculate perimeter, area, and circumference of various shapes (triangles, quadrilaterals, circles).
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R.07. Find area and perimeter in the coordinate plane.
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R.08. Calculate area of compound figures and area between shapes.
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R.09. Understand properties of similar figures (area and perimeter).
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R.10. Classify quadrilaterals and understand their properties.
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R.11. Graph quadrilaterals.
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R.12. Understand three-dimensional figure vocabulary and nets.
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R.13. Calculate surface area and volume of prisms, cylinders, pyramids, cones, and spheres.
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R.14. Understand similar solids and their surface area and volume.
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R.15. Understand cross-sections and solids of revolution.
S. Congruence and Similarity
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S.01. Understand congruent line segments and figures.
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S.02. Understand congruence statements and corresponding parts.
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S.03. Solve problems using congruent figures.
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S.04. Apply SSS, SAS, ASA, and AAS theorems.
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S.05. Apply the Hypotenuse-Leg theorem.
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S.06. Understand congruence in isosceles and equilateral triangles.
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S.07. Apply congruence in the coordinate plane.
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S.08. Identify similar figures.
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S.09. Understand ratios and similarity statements in similar figures.
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S.10. Apply similarity rules for triangles.
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S.11. Use similar triangles for indirect measurement.
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S.12. Understand perimeters and areas of similar figures.
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S.13. Apply the Triangle Proportionality Theorem.
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S.14. Understand similarity transformations.
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S.15. Understand similarity of circles.
T. Right Triangles and Trigonometry
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T.01. Apply the Pythagorean theorem and its converse.
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T.02. Apply the Pythagorean Inequality Theorems.
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T.03. Work with special right triangles (30-60-90 and 45-45-90).
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T.04. Understand and use trigonometric ratios (sin, cos, tan, csc, sec, cot).
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T.05. Find trigonometric functions of special angles.
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T.06. Use a calculator to find trigonometric functions.
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T.07. Use inverse trigonometric functions.
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T.08. Find side lengths and angle measures using trigonometry.
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T.09. Solve right triangles.
U. Transformations
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U.01. Perform and analyze translations, reflections, and rotations.
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U.02. Find coordinates after transformations.
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U.03. Write rules for transformations.
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U.04. Classify congruence transformations.
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U.05. Perform compositions of congruence transformations.
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U.06. Identify transformations that carry a polygon onto itself.
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U.07. Perform and analyze dilations.
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U.08. Find coordinates after dilations.
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U.09. Understand scale factors and classifications of dilations.
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U.10. Understand dilations and parallel lines.
V. Probability and Statistics
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V.01. Calculate theoretical and experimental probability.
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V.02. Understand compound events, including independent and dependent events.
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V.03. Calculate factorials, permutations, and combinations.
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V.04. Apply the counting principle.
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V.05. Understand geometric probability.
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V.06. Calculate mean, median, mode, and range.
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V.07. Understand quartiles.
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V.08. Identify biased samples.
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V.09. Calculate mean absolute deviation, variance, and standard deviation.
