Course Content
A. Numbers and Counting
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A.01. Classify different types of numbers (e.g., natural, integer, rational, irrational).
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A.02. Represent numbers on a number line.
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A.03. Convert between decimals, fractions, and percentages.
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A.04. Compare and order rational numbers.
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A.05. Estimate and approximate square roots and cube roots.
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A.06. Understand and apply the concept of absolute value.
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A.07. Explore the properties of real numbers and their applications in real-world scenarios.
B. Operations with Rational Numbers
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B.01. Add, subtract, multiply, and divide integers.
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B.02. Add and subtract rational numbers.
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B.03. Multiply and divide rational numbers.
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B.04. Evaluate numerical expressions involving integers using the order of operations (PEMDAS/BODMAS).
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B.05. Evaluate numerical expressions involving rational numbers.
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B.06. Evaluate variable expressions involving integers.
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B.07. Evaluate variable expressions involving rational numbers.
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B.08. Apply the distributive property to simplify expressions with rational numbers.
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B.09. Solve real-world problems involving operations with rational numbers.
C. Ratios, Rates, and Proportions
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C.01. Identify equivalent ratios.
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C.02. Write an equivalent ratio.
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C.03. Calculate unit rates.
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C.04. Determine unit prices.
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C.05. Solve proportions.
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C.06. Solve proportion word problems.
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C.07. Apply proportions to scale drawings and word problems.
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C.08. Use proportions to solve problems involving similar figures.
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C.09. Apply ratio and proportion concepts to solve real-world scaling problems.
D. Percents
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D.01. Convert between percents, fractions, and decimals.
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D.02. Solve basic percent equations.
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D.03. Solve percent word problems.
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D.04. Calculate percent of change.
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D.05. Solve percent of change word problems.
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D.06. Calculate simple interest.
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D.07. Calculate compound interest.
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D.08. Calculate the percent of a number, including GST and discounts.
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D.09. Find the percent, including discount and mark-up.
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D.10. Solve multi-step problems involving percents.
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D.11. Analyze the impact of different interest rates and compounding periods.
E. Measurement
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E.01. Convert rates and measurements within and between systems.
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E.02. Determine the precision of a measurement.
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E.03. Calculate the greatest possible error in a measurement.
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E.04. Determine the minimum and maximum possible area and volume given measurement errors.
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E.05. Calculate percent error.
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E.06. Calculate percent error in area and volume measurements.
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E.07. Apply measurement concepts to solve problems involving scale and accuracy.
F. Properties
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F.01. Identify and apply the properties of addition and multiplication (commutative, associative, identity, inverse, distributive).
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F.02. Apply the distributive property to simplify expressions.
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F.03. Simplify variable expressions using properties.
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F.04. Identify and apply the properties of equality (addition, subtraction, multiplication, division).
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F.05. Use properties to justify steps in solving equations.
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F.06. Extend the understanding of properties to more complex algebraic manipulations.
G. Coordinate Plane
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G.01. Review the basics of the coordinate plane (axes, quadrants, ordered pairs).
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G.02. Calculate the midpoint of a line segment.
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G.03. Calculate the distance between two points.
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G.04. Apply the distance formula to solve geometric problems.
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G.05. Explore transformations of geometric shapes on the coordinate plane.
H. Geometry
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H.01. Calculate the perimeter of various shapes.
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H.02. Calculate the area of basic geometric figures.
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H.03. Calculate the area of compound figures.
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H.04. Calculate interior angles of polygons.
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H.05. Identify angle relationships formed by a transversal of parallel lines.
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H.06. Calculate the volume of basic solids.
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H.07. Calculate the surface area of basic solids.
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H.08. Identify congruent figures and their corresponding side lengths and angle measures.
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H.09. Identify similar figures and their corresponding side lengths and angle measures.
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H.10. Apply similar triangles to solve indirect measurement problems.
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H.11. Understand and apply dilations and scale factors.
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H.12. Determine the relationship between area and perimeter of similar figures.
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H.13. Calculate the area between two shapes.
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H.14. Identify similar solids.
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H.15. Calculate the volume and surface area of similar solids.
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H.16. Analyze the effect of changes in scale on perimeter, area, and volume.
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H.17. Apply Pythagoras’ theorem.
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H.18. Solve Pythagoras’ theorem word problems.
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H.19. Apply the converse of Pythagoras’ theorem to determine if a triangle is a right triangle.
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H.20. Apply relationships in special right triangles (30-60-90 and 45-45-90).
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H.21. Use geometric principles to solve design and construction problems.
I. Variable Expressions and Equations
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I.01. Write variable expressions to represent real-world situations.
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I.02. Simplify variable expressions involving like terms and the distributive property.
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I.03. Identify equivalent linear expressions.
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I.04. Write variable equations to represent relationships.
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I.05. Determine if a given value satisfies an equation.
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I.06. Solve equations using the order of operations.
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I.07. Translate word problems into algebraic equations.
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I.08. Model relationships using variables and equations to analyze scenarios.
J. Solving Equations
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J.01. Model and solve equations using algebra tiles.
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J.02. Write and solve equations that represent diagrams.
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J.03. Solve one-step linear equations.
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J.04. Solve two-step linear equations.
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J.05. Solve advanced linear equations (multi-step).
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J.06. Solve equations with variables on both sides.
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J.07. Complete the solution to a given equation.
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J.08. Determine the number of solutions to a linear equation (none, one, infinite).
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J.09. Create equations with no solutions or infinitely many solutions.
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J.10. Solve linear equations word problems.
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J.11. Solve linear equations mixed review.
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J.12. Analyze and solve equations arising from geometric contexts.
K. Single-Variable Inequalities
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K.06. Solve one-step linear inequalities (mixed).
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K.07. Graph solutions to one-step linear inequalities.
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K.08. Solve two-step linear inequalities.
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K.09. Graph solutions to two-step linear inequalities.
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K.10. Solve advanced linear inequalities.
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K.11. Graph solutions to advanced linear inequalities.
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K.12. Apply inequalities to represent and solve real-world constraints.
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K.01. Graph inequalities on a number line.
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K.02. Write inequalities from graphs.
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K.03. Identify solutions to inequalities.
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K.04. Solve one-step linear inequalities using addition and subtraction.
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K.05. Solve one-step linear inequalities using multiplication and division.
L. Relations and Functions
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L.01. Represent relations using tables, graphs, mappings, and lists of points.
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L.02. Identify independent and dependent variables in a relationship.
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L.03. Identify functions.
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L.04. Identify functions using the vertical line test.
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L.05. Find values using function graphs.
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L.06. Evaluate a function given an input.
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L.07. Evaluate a function by plugging in an expression.
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L.08. Complete a function table from a graph.
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L.09. Complete a function table from an equation.
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L.10. Interpret the graph of a function in word problems.
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L.11. Determine the domain and range of a function from its graph or equation.
M. Linear Functions
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M.01. Identify linear functions from equations, graphs, and tables.
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M.02. Find the gradient (slope) of a line from its graph.
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M.03. Find the gradient from two points.
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M.04. Find a missing coordinate using the gradient.
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M.05. Find the gradient and y-intercept of a linear equation.
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M.06. Graph an equation in slope-intercept form (y = mx + c).
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M.07. Write an equation in slope-intercept form from a graph.
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M.08. Write an equation in slope-intercept form given slope and y-intercept.
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M.09. Write an equation in slope-intercept form from a table.
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M.10. Write an equation in slope-intercept form from a word problem.
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M.11. Solve linear equations for y to express them in slope-intercept form.
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M.12. Write linear functions to solve word problems.
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M.13. Complete a table and graph a linear function.
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M.14. Compare linear functions represented as graphs, tables, and equations.
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M.15. Write equations in standard form (Ax + By = C).
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M.16. Find x- and y-intercepts from standard form.
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M.17. Graph an equation in standard form.
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M.18. Write equations of horizontal and vertical lines.
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M.19. Graph horizontal and vertical lines.
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M.20. Graph an equation in point-slope form.
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M.21. Write an equation in point-slope form.
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M.22. Write an equation in point-slope form from a graph.
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M.23. Determine gradients of parallel and perpendicular lines.
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M.24. Write an equation for a parallel or perpendicular line.
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M.25. Describe transformations of linear functions (shifts, stretches, reflections).
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M.26. Model real-world situations using linear functions and analyze their graphs.
N. Direct Variation
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N.01. Identify proportional relationships from tables, graphs, and equations.
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N.02. Find the constant of variation (k).
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N.03. Graph a proportional relationship.
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N.04. Write direct variation equations (y = kx).
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N.05. Write and solve direct variation equations.
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N.06. Apply direct variation to solve problems involving scaling and proportions.
O. Linear Inequalities
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O.01. Determine if a point (x, y) satisfies a linear inequality.
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O.02. Solve linear inequalities for y.
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O.03. Graph a linear inequality in the coordinate plane.
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O.04. Solve linear inequality word problems.
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O.05. Determine if a point (x, y) is a solution to a system of linear inequalities.
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O.06. Use linear inequalities to represent constraints in real-world optimization problems.
P. Simultaneous Equations (Systems of Linear Equations)
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P.01. Determine if a point (x, y) is a solution to a system of linear equations.
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P.02. Solve systems of linear equations by graphing.
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P.03. Solve systems of linear equations by graphing word problems.
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P.04. Determine the number of solutions to a system of linear equations by graphing.
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P.05. Determine the number of solutions to a system of linear equations without graphing.
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P.06. Solve systems of linear equations using substitution.
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P.07. Solve systems of linear equations using substitution word problems.
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P.08. Solve systems of linear equations using elimination.
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P.09. Solve systems of linear equations using elimination word problems.
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P.10. Choose the most efficient method (graphing, substitution, or elimination) for solving a system of equations.
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P.11. Model and solve real-world problems using systems of linear equations.
Q. Exponents
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Q.01. Evaluate powers with integer bases.
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Q.02. Evaluate powers with decimal and fractional bases.
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Q.03. Understand and apply negative exponents.
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Q.04. Apply the product of powers property (multiplication with exponents).
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Q.05. Apply the quotient of powers property (division with exponents).
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Q.06. Simplify expressions involving multiplication and division with exponents.
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Q.07. Apply the power of a power rule.
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Q.08. Evaluate expressions using properties of exponents.
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Q.09. Identify equivalent expressions involving exponents.
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Q.10. Apply the properties of exponents to simplify complex expressions.
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Q.11. Connect exponential notation to repeated multiplication and division.
R. Standard Form (Scientific Notation)
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R.01. Convert between ordinary numbers and standard form.
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R.02. Compare numbers written in standard form.
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R.03. Multiply numbers written in standard form.
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R.04. Divide numbers written in standard form.
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R.05. Perform calculations involving numbers in standard form.
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R.06. Apply scientific notation to solve problems in science and engineering.
S. Monomials
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S.01. Identify monomials.
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S.02. Multiply monomials.
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S.03. Divide monomials.
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S.04. Multiply and divide monomials.
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S.05. Raise monomials to a power.
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S.06. Simplify expressions involving monomials using exponent rules.
T. Polynomials
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T.01. Understand polynomial vocabulary (degree, leading coefficient, constant term).
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T.02. Model polynomials with algebra tiles.
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T.03. Add and subtract polynomials using algebra tiles.
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T.04. Add and subtract polynomials algebraically.
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T.05. Add polynomials to find perimeter.
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T.06. Multiply a polynomial by a monomial.
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T.07. Multiply two polynomials using algebra tiles.
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T.08. Multiply two binomials (FOIL method).
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T.09. Multiply two binomials in special cases (difference of squares, perfect square trinomials).
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T.10. Multiply polynomials of higher degree.
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T.11. Apply polynomial operations to solve geometric and algebraic problems.
U. Factorising
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U.01. Find the highest common factor (HCF) of monomials.
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U.02. Factorise out a monomial from a polynomial.
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U.03. Factorise quadratics with a leading coefficient of 1.
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U.04. Factorise quadratics with leading coefficients other than 1.
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U.05. Factorise quadratics in special cases (difference of squares, perfect square trinomials).
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U.06. Factorise quadratics using algebra tiles.
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U.07. Factorise polynomials by grouping.
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U.08. Factorise polynomials completely.
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U.09. Connect factoring to the distributive property and polynomial multiplication.
V. Radical Expressions
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V.01. Simplify radical expressions.
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V.02. Simplify radical expressions with variables.
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V.03. Simplify radical expressions involving fractions.
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V.04. Multiply radical expressions.
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V.05. Add and subtract radical expressions.
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V.06. Simplify radical expressions using the distributive property.
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V.07. Divide radical expressions (rationalize the denominator).
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V.08. Simplify radical expressions: mixed review.
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V.09. Apply radical expressions to solve geometric and algebraic problems.
W. Rational Exponents
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W.04. Apply the power of a power rule with rational exponents.
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W.05. Simplify expressions involving rational exponents I.
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W.06. Simplify expressions involving rational exponents II.
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W.07. Convert between radical expressions and expressions with rational exponents.
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W.01. Evaluate rational exponents.
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W.02. Apply the product of powers property with rational exponents.
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W.03. Apply the quotient of powers property with rational exponents.
X. Rational Functions and Expressions
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X.01. Simplify complex fractions.
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X.02. Simplify rational expressions.
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X.03. Multiply and divide rational expressions.
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X.04. Divide polynomials.
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X.05. Add and subtract rational expressions.
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X.06. Solve rational equations.
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X.07. Identify restrictions on variables in rational expressions and equations.
Y. Data and Graphs
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Y.01. Interpret bar graphs, line graphs, and histograms.
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Y.02. Create bar graphs, line graphs, and histograms.
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Y.03. Interpret circle graphs (pie charts).
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Y.04. Interpret stem-and-leaf plots.
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Y.05. Interpret box-and-whisker plots.
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Y.06. Interpret scatter plots.
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Y.07. Draw a line of best fit on a scatter plot.
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Y.08. Analyze data distributions and identify trends.
Z. Statistics
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Z.01. Calculate mean, median, mode, and range.
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Z.02. Interpret charts to find mean, median, mode, and range.
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Z.03. Find the missing number given the mean, median, mode, or range.
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Z.04. Determine quartiles.
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Z.05. Identify biased samples.
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Z.06. Compare and contrast different measures of central tendency.
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Z.07. Assess the validity and reliability of statistical claims.
AA. Probability
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AA.01. Calculate theoretical probability.
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AA.02. Calculate experimental probability.
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AA.03. Determine the number of outcomes in compound events.
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AA.04. Identify independent and dependent events.
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AA.05. Calculate the probability of independent and dependent events.
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AA.06. Use probability to make predictions and informed decisions.
BB. Problem Solving
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BB.01. Solve word problems: mixed review.
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BB.02. Solve word problems involving money.
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BB.03. Solve consecutive integer problems.
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BB.04. Solve rate of travel word problems.
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BB.05. Solve weighted averages word problems.
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BB.06. Develop problem-solving strategies and apply them to diverse contexts.
