
Course Content
A. Numbers and Counting
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A.01. Identify prime and composite numbers.
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A.02. Understand the definition of a square root and cube root.
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A.03. Add, subtract, multiply, and divide rational numbers proficiently.
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A.04. Estimate the values of square roots and cube roots without a calculator.
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A.05. Identify and differentiate between rational and irrational numbers.
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A.06. Compare and order rational numbers on a number line.
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A.07. Evaluate numerical expressions involving rational numbers using the order of operations.
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A.08. Express recurring decimals as fractions using algebraic methods.
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A.09. Explore the properties of rational and irrational numbers within the real number system.
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A.10. Apply the concept of significant figures when dealing with approximations of irrational numbers
B. Percents and Proportions
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B.01. Understand and calculate basic percentages of given quantities.
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B.02. Calculate the percent of change (increase or decrease).
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B.03. Solve multi-step problems involving successive percentage changes.
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B.04. Calculate sale prices and VAT (Value Added Tax) to find the original price of an item.
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B.05. Solve word problems involving percent of change, including finding the original amount.
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B.06. Apply percentages in real-world scenarios, such as discounts, taxes, and interest rates.
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B.07. Analyze and solve complex percentage problems involving multiple steps and variables.
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B.08. Solve reverse percentage problems, finding the original value after a percentage increase or decrease.
C. Expressions and Properties
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C.01. Understand and apply the commutative, associative, and distributive properties.
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C.02. Identify and combine like terms in algebraic expressions.
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C.03. Apply the distributive property to expand and simplify algebraic expressions.
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C.04. Write equivalent expressions using the properties of addition and multiplication.
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C.05. Simplify variable expressions involving like terms and the distributive property.
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C.06. Recognize and identify equivalent linear expressions through simplification.
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C.07. Use properties of operations to justify steps in simplifying expressions.
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C.08. Model algebraic expressions using manipulatives (e.g., algebra tiles) to enhance understanding.
D. Solving Linear Equations
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D.01. Solve one- and two-step linear equations using inverse operations.
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D.02. Rearrange multi-variable equations to solve for a specific variable.
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D.03. Solve advanced linear equations involving multiple steps and operations.
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D.04. Solve equations with variables on both sides of the equal sign.
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D.05. Determine the number of solutions (none, one, or infinite) for a linear equation.
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D.06. Solve linear equations presented in real-world word problems.
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D.07. Complete the steps to solve a given linear equation.
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D.08. Create equations with no solutions or infinitely many solutions, and explain why.
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D.09. Solve linear equations and check the validity of the solutions.
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D.10. Solve linear equations with fractional coefficients and constants.
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D.11. Analyze and solve complex word problems that require setting up and solving linear equations.
E. Problem Solving with Equations
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E.01. Apply linear equations to solve consecutive integer problems.
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E.02. Solve word problems involving rates of travel using distance, speed, and time relationships.
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E.03. Solve word problems involving weighted averages, such as mixtures or grades.
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E.04. Formulate and solve algebraic equations based on real-world scenarios.
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E.05. Use problem-solving strategies, such as making a table or drawing a diagram, to solve mathematical problems
F. Single-Variable Linear Inequalities
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F.01. Solve one- and two-step linear inequalities using inverse operations.
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F.02. Represent solutions to linear inequalities on a number line.
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F.03. Solve advanced linear inequalities, including those with variables on both sides.
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F.04. Solve compound inequalities involving “and” and “or” conditions.
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F.05. Graph the solutions to compound inequalities on a number line.
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F.06. Write compound inequalities from given graphs on a number line.
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F.07. Interpret the solution of an inequality in the context of a problem.
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F.08. Solve absolute value inequalities by splitting them into two separate inequalities.
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F.09. Solve linear inequalities and represent the solutions sets using interval notation.
G. Relations and Functions
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G.01. Define the terms “relation,” “domain,” and “range” in the context of functions.
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G.02. Identify the domain and range of a relation from various representations.
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G.03. Evaluate a function for a given input value using function notation.
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G.04. Find values using function graphs.
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G.05. Convert between tables, graphs, mappings, and lists of points for relations.
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G.06. Complete a function table from a graph or from an equation.
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G.07. Identify independent and dependent variables in a functional relationship.
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G.08. Determine if a given relation is a function using the vertical line test.
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G.09. Find solutions to equations using a table.
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G.10. Approximate solutions using a table.
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G.11. Interpret functions using everyday language and real-world contexts.
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G.12. Calculate and interpret the rate of change from tables and graphs.
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G.13. Analyze and model real-world situations using functional relationships.
H. Direct and Inverse Variation
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H.01. Recognize proportional relationships from equations, tables, and graphs.
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H.02. Calculate the constant of variation in a direct or inverse variation.
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H.03. Write direct variation equations to model proportional relationships.
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H.04. Graph direct variation relationships on the coordinate plane.
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H.05. Write and solve direct variation equations to find unknown values.
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H.06. Write inverse variation equations to represent inversely proportional relationships.
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H.07. Write and solve inverse variation equations to solve problems.
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H.08. Differentiate between direct and inverse variation relationships.
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H.09. Apply direct and inverse variation concepts to real-world problems involving scaling and rates.
I. Linear Functions: Slope-Intercept Form
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I.01. Identify linear functions from equations, graphs, and tables.
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I.02. Understand and interpret points on the graph of a linear function in context.
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I.03. Calculate the gradient (slope) of a line from a graph or two points.
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I.04. Find a missing coordinate on a line given its gradient and another point.
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I.05. Determine the gradient and y-intercept of a linear equation in slope-intercept form (y = mx + c).
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I.06. Graph a linear equation in slope-intercept form.
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I.07. Find the equation of a line given its slope and y-intercept.
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I.08. Determine the equation of a line from its graph in slope-intercept form.
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I.09. Convert linear equations to slope-intercept form.
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I.10. Write the equation of a line in slope-intercept form from a table of values.
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I.11. Write the equation of a line in slope-intercept form from a word problem.
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I.12. Find x- and y-intercepts for equations in ax + by = c form.
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I.13. Graph an equation in ax + by = c form.
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I.14. Understand and apply the equations of horizontal and vertical lines.
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I.15. Write linear functions to solve word problems.
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I.16. Complete a table and graph a linear function
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I.17. Compare linear functions: graphs, tables and equations.
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I.18. Write an equation for a parallel line
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I.19. Write an equation for a perpendicular line
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I.20. Write an equation for a parallel or perpendicular line
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I.21. Transformations of linear functions
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I.22. Apply the point-gradient form to graph an equation
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I.23. Apply the point-gradient form to write an equation
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I.24. Apply the point-gradient form to write an equation from a graph
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I.25. Investigate the properties of the gradients of parallel and perpendicular lines
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I.26. Develop an understanding of how slope impacts real world situations
J. Systems of Linear Equations
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J.01. Determine if an ordered pair (x, y) is a solution to a system of linear equations.
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J.02. Solve systems of linear equations graphically by finding the point of intersection.
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J.03. Apply graphing methods to solve simultaneous equations word problems
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J.04. Determine the number of solutions (none, one, or infinite) of a system of linear equations graphically.
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J.05. Determine the number of solutions to simultaneous equations by algebraic methods
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J.06. Solve systems of linear equations using the substitution method.
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J.07. Apply the substitution method to solve simultaneous equations word problems
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J.08. Solve systems of linear equations using the elimination method (addition/subtraction).
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J.09. Apply the elimination method to solve simultaneous equations word problems
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J.10. Choose the most efficient method (graphing, substitution, or elimination) to solve a system of equations.
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J.11. Solve a system of equations using any method
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J.12. Solve a system of equations using any method: word problems
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J.13. Create and solve systems of linear equations to model and solve real-world problems.
K. Linear Inequalities in Two Variables
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K.01. Determine if an ordered pair (x, y) satisfies a given linear inequality.
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K.02. Solve a linear inequality for y to express it in slope-intercept form.
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K.03. Graph a linear inequality in the coordinate plane, indicating the solution region.
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K.04. Solve word problems involving linear inequalities by graphing.
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K.05. Determine if an ordered pair (x, y) is a solution to a system of linear inequalities.
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K.06. Solve systems of linear inequalities graphically by identifying the region of intersection.
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K.07. Formulate linear inequalities to represent real-world constraints and optimize solutions graphically.
L. Indices and Exponents
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L.01. Review basic index laws (product, quotient, power of a power).
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L.02. Simplify expressions involving negative indices.
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L.03. Apply index laws to simplify expressions with multiplication.
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L.04. Apply index laws to simplify expressions with division.
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L.05. Apply both multiplication and division index laws to simplify expressions.
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L.06. Apply the power rule (power of a power) to simplify expressions.
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L.07. Evaluate expressions using properties of indices (exponents).
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L.08. Identify equivalent expressions involving indices through simplification.
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L.09. Extend the understanding of indices to include rational exponents.
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L.10. Use scientific notation to perform calculations with very large or very small numbers.
M. Number Sequences
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M.01. Recognize and classify arithmetic and geometric sequences.
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M.02. Determine the common difference in an arithmetic sequence.
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M.03. Determine the common ratio in a geometric sequence.
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M.04. Evaluate variable expressions for number sequences
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M.05. Evaluate variable expressions for number sequences.
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M.06. Determine the nth term in an arithmetic sequence.
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M.07. Determine the nth term in a geometric sequence.
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M.08. Write variable expressions for arithmetic sequences.
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M.09. Write variable expressions for geometric sequences.
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M.10. Recognize and continue sequences of square and cube numbers.
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M.11. Identify and generate terms in Fibonacci-type sequences.
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M.12. Apply knowledge of sequences to solve mixed review problems.
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M.13. Model patterns with recursive formulas and understand their relationship to explicit formulas
N. Standard Form (Scientific Notation)
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N.01. Convert between ordinary numbers and standard form (scientific notation).
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N.02. Compare numbers written in standard form.
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N.03. Add and subtract numbers written in standard form.
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N.04. Multiply and divide numbers written in standard form.
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N.05. Apply standard form to solve real-world problems involving very large or very small quantities.
O. Exponential Functions
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O.01. Evaluate exponential functions for given input values.
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O.02. Write exponential functions to model real-world scenarios, such as population growth or decay.
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O.03. Match exponential functions to their corresponding graphs.
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O.04. Graph exponential functions.
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O.05. Identify the domain and range of exponential functions.
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O.06. Solve exponential growth and decay word problems.
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O.07. Apply exponential functions to calculate compound interest.
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O.08. Analyze and interpret the parameters of exponential functions in context.
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O.09. Model and analyse compound interest and depreciation problems
P. Monomials
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P.01. Define and identify monomials.
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P.02. Multiply monomials using the product of powers rule.
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P.03. Divide monomials using the quotient of powers rule.
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P.04. Multiply and divide monomials combining the product and quotient rules.
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P.05. Raise monomials to a power using the power of a power rule.
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P.06. Simplify expressions involving monomials using the rules of exponents.
Q. Polynomials
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Q.01. Define polynomial vocabulary, including terms like degree, coefficient, and constant.
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Q.02. Add and subtract polynomials using algebra tiles.
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Q.03. Add and subtract polynomials algebraically.
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Q.04. Multiply a polynomial by a monomial.
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Q.05. Multiply two polynomials using algebra tiles.
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Q.06. Multiply two binomials using the distributive property (FOIL method).
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Q.07. Identify and multiply two binomials that represent special cases (difference of squares, perfect square trinomials).
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Q.08. Multiply polynomials of various degrees.
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Q.09. Apply polynomial operations to solve geometric problems, such as finding the perimeter of a shape.
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Q.10. Express geometric shapes using polynomial expressions
R. Factorising Polynomials
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R.09. Apply the null factor law to solve polynomial equations.
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R.01. Find the highest common factor (HCF) of monomials.
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R.02. Factorise out a monomial from a polynomial expression.
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R.03. Factorise quadratic expressions using algebra tiles.
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R.04. Factorise quadratic expressions with a leading coefficient of 1.
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R.05. Factorise quadratic expressions with leading coefficients other than 1.
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R.06. Factorise quadratic expressions that are special cases (difference of squares, perfect square trinomials).
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R.07. Factorise polynomials by grouping.
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R.08. Factorise polynomials of various degrees using a combination of techniques.
S. Quadratic Equations and Inequalities
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S.01. Identify the key characteristics of quadratic functions from their graphs (vertex, axis of symmetry, intercepts).
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S.02. Identify the key characteristics of quadratic functions from their equations.
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S.03. Complete a function table for a quadratic function.
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S.04. Match quadratic functions to their corresponding graphs.
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S.05. Graph a quadratic function by finding its vertex, intercepts, and axis of symmetry.
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S.06. Solve a quadratic equation using square roots.
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S.07. Solve a quadratic equation using the zero product property (factorising).
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S.08. Solve a quadratic equation with leading coefficient 1 by factorising.
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S.09. Solve a quadratic equation with other leading coefficients by factorising.
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S.10. Complete the square to rewrite a quadratic expression in vertex form.
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S.11. Solve a quadratic equation by completing the square.
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S.12. Solve a quadratic equation using the quadratic formula.
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S.13. Solve simultaneous quadratic and linear equations graphically.
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S.14. Solve simultaneous quadratic and linear equations algebraically.
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S.15. Graph solutions to quadratic inequalities on a number line.
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S.16. Solve quadratic inequalities algebraically.
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S.17. Apply the discriminant to determine the nature and number of roots in a quadratic equation.
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S.18. Solve quadratic equations arising from real-world applications, such as projectile motion or area optimization.
T. Function Types: Linear, Quadratic, and Exponential
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T.01. Identify linear, quadratic, and cubic functions from their graphs.
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T.02. Identify linear, quadratic, cubic, and exponential functions from their graphs.
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T.03. Identify linear, quadratic, and exponential functions from tables of values.
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T.04. Write linear, quadratic, and exponential functions to model given data.
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T.05. Calculate linear functions over unit intervals and interpret the rate of change.
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T.06. Calculate exponential functions over unit intervals and interpret the growth or decay factor.
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T.07. Describe linear and exponential growth and decay in context.
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T.08. Analyze the long-term behavior of linear, quadratic, and exponential functions.
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T.09. Compare and contrast the characteristics of linear, quadratic, and exponential functions.
U. Function Operations: Composition and Inverses
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U.01. Evaluate the composition of linear functions for a given value.
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U.02. Find the equation of the composition of two linear functions.
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U.03. Evaluate the composition of linear and quadratic functions for a given value.
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U.04. Find the equation of the composition of linear and quadratic functions.
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U.05. Identify inverse functions from their equations, graphs, or tables.
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U.06. Find values of inverse functions from tables.
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U.07. Find values of inverse functions from graphs.
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U.08. Find inverse functions and relations algebraically.
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U.09. Determine the domain and range of inverse functions.
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U.10. Verify inverse functions using composition.
V. Function Transformations
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V.01. Understand and apply translation and reflection rules.
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V.02. Apply vertical and horizontal translations to functions.
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V.03. Reflect functions across the x-axis and y-axis.
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V.04. Apply combinations of translations and reflections to functions.
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V.05. Apply vertical and horizontal stretches and compressions to functions.
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V.06. Predict the effect of transformations on key features of functions, such as intercepts and turning points.
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V.07. Express transformations using function notation (e.g., f(x) + a, f(x – b)).
W. Radical Expressions
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W.01. Simplify radical expressions by factoring out perfect squares or cubes.
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W.02. Simplify radical expressions involving fractions by rationalizing the denominator.
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W.03. Multiply radical expressions using the distributive property.
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W.04. Add and subtract radical expressions by combining like terms.
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W.05. Simplify radical expressions using the distributive property.
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W.06. Simplify radical expressions using conjugates.
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W.07. Simplify radical expressions: mixed review
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W.08. Convert between radicals and rational exponents.
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W.09. Solve equations involving radical expressions.
X. Fractional Indices (Rational Exponents)
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X.01. Evaluate expressions with fractional indices (rational exponents).
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X.02. Apply the product rule to simplify expressions with fractional indices.
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X.03. Apply the quotient rule to simplify expressions with fractional indices.
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X.04. Apply the power rule to simplify expressions with fractional indices.
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X.05. Simplify expressions involving fractional indices I
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X.06. Simplify expressions involving fractional indices II
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X.07. Express fractional indices as radical expressions and vice versa.
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X.08. Apply fractional indices to solve equations and problems involving roots.
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X.09. Use fractional indices to simplify surds
Y. Rational Functions and Expressions
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Y.01. Identify asymptotes and excluded values of rational functions.
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Y.02. Simplify complex fractions by multiplying by the reciprocal of the denominator.
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Y.03. Simplify rational expressions by factorising and cancelling common factors.
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Y.04. Multiply and divide rational expressions.
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Y.05. Divide polynomials using long division or synthetic division.
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Y.06. Add and subtract rational expressions with like and unlike denominators.
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Y.07. Solve rational equations by clearing fractions and solving the resulting equation.
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Y.08. Identify and address extraneous solutions in rational equations.
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Y.09. Formulate rational functions to model real-world relationships and solve related problems.
Z. Midpoints and Distance in Coordinate Geometry
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Z.01. Calculate the midpoint of a line segment given the coordinates of its endpoints.
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Z.02. Calculate the distance between two points in the coordinate plane using the distance formula.
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Z.03. Calculate the distance from a point to the origin in three dimensions.
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Z.04. Apply the midpoint and distance formulas to solve geometric problems.
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Z.05. Connect the distance formula to Pythagoras’ Theorem and demonstrate the relationship
AA. Transformations in Geometry
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AA.01. Recognize and identify translations, reflections, and rotations.
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AA.02. Perform translations on geometric figures and graph the image.
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AA.03. Determine the coordinates of the image after a translation.
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AA.04. Write the rule for a given translation.
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AA.05. Reflect geometric figures across the x-axis, y-axis, and other lines, and graph the image.
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AA.06. Determine the coordinates of the image after a reflection.
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AA.07. Rotate polygons about a point by specified angles.
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AA.08. Perform rotations on geometric figures and graph the image.
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AA.09. Determine the coordinates of the image after a rotation.
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AA.10. Describe transformations that map one figure onto another.
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AA.11. Reflections and rotations: write the rule
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AA.12. Sequences of translations, reflections and rotations: graph the image
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AA.13. Sequences of congruence transformations: choose the sequence
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AA.14. Transformations that carry a polygon onto itself
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AA.15. Translations, reflections and rotations: mixed review
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AA.16. Perform dilations on geometric figures and graph the image.
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AA.17. Determine the coordinates of the image after a dilation.
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AA.18. Determine length, perimeter and area following dilations
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AA.19. Dilations: scale factor and classification
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AA.20. Dilations: find the scale factor and center of the dilation
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AA.21. Dilations and parallel lines
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AA.22. Classify transformations as isometric or non-isometric.
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AA.23. Explore tessellations and their relationship to transformations.
BB. Congruence in Geometry
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BB.01. Identify congruent figures based on visual inspection.
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BB.02. Write congruence statements and identify corresponding parts of congruent figures.
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BB.03. Solve problems involving corresponding parts of congruent figures.
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BB.04. Determine if two figures are congruent and justify the answer using congruence postulates and theorems.
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BB.05. Apply the Side-Side-Side (SSS) congruence theorem.
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BB.06. Apply the Side-Angle-Side (SAS) congruence theorem.
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BB.07. Apply the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) congruence theorems.
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BB.08. Apply SSS, SAS, ASA and AAS Theorems to solve geometric problems
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BB.09. Apply the SSS Theorem in the coordinate plane.
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BB.10. Prove congruency in isosceles and equilateral triangles.
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BB.11. Apply the Hypotenuse-Leg (HL) congruence theorem for right triangles.
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BB.12. Use congruence criteria to prove geometric constructions are valid.
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BB.13. Determine what minimum criteria can be used to show that triangles are congruent.
CC. Similarity in Geometry
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CC.01. Identify similar figures based on visual inspection and proportional reasoning.
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CC.02. Determine the ratios of corresponding sides in similar figures.
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CC.03. Write similarity statements for similar figures.
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CC.04. Determine side lengths and angle measures in similar figures using proportionality.
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CC.05. Apply similar triangles to solve problems using indirect measurement.
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CC.06. Determine the relationship between perimeters of similar figures.
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CC.07. Apply similarity rules for triangles (AA, SSS, SAS).
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CC.08. Relate similar triangles to transformations (dilations).
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CC.09. Determine the relationship between areas of similar figures.
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CC.10. Use similarity theorems to prove geometric relationships.
DD. Right Triangles: Pythagoras’ Theorem and Special Triangles
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DD.01. Apply Pythagoras’ Theorem to find missing side lengths in right triangles.
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DD.02. Solve word problems involving Pythagoras’ Theorem.
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DD.03. Apply the converse of Pythagoras’ Theorem to determine if a triangle is a right triangle.
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DD.04. Apply Pythagoras’ Inequality Theorems to classify triangles as acute or obtuse.
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DD.05. Determine side length ratios in special right triangles (30-60-90 and 45-45-90).
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DD.06. Apply right triangle relationships to solve problems in trigonometry and geometry.
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DD.07. Generalise Pythagoras’ Theorem to Pythagoras’ Theorem in 3D.
EE. Trigonometry
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EE.01. Define the primary trigonometric ratios (sin, cos, tan) in terms of right triangles.
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EE.02. Define the reciprocal trigonometric ratios (csc, sec, cot).
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EE.03. Find trigonometric functions of special angles: sin, cos and tan.
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EE.04. Find trigonometric functions of special angles: csc, sec and cot.
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EE.05. Use a calculator to find trigonometric functions of angles in degrees or radians.
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EE.06. Understand and apply the inverses of trigonometric functions (arcsin, arccos, arctan).
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EE.07. Use trigonometric ratios to find a side length in a right triangle.
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EE.08. Use trigonometric ratios to find an angle measure in a right triangle.
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EE.09. Solve a right triangle by finding all missing side lengths and angle measures.
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EE.10. Apply the Law of Sines to solve non-right triangles.
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EE.11. Apply the Law of Cosines to solve non-right triangles.
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EE.12. Solve a triangle by using Law of Sines and Law of Cosines
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EE.13. Calculate the area of a triangle using the sine formula.
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EE.14. Graph sine functions
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EE.15. Graph cosine functions
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EE.16. Graph sine and cosine functions
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EE.17. Apply trigonometric functions to solve real-world problems involving angles, heights, and distances.
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EE.18. Relate trigonometric functions to the unit circle.
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EE.19. Model periodic phenomena using sine and cosine functions.
FF. Perimeter, Area, and Volume
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FF.01. Calculate the perimeter of various geometric shapes.
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FF.02. Calculate the area of triangles and quadrilaterals.
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FF.03. Calculate area and perimeter in the coordinate plane I
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FF.04. Calculate area and perimeter in the coordinate plane II
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FF.05. Calculate the area and circumference of circles.
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FF.06. Calculate the area of compound figures by dividing them into simpler shapes.
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FF.07. Determine the area between two shapes by subtraction.
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FF.08. Determine area and perimeter of similar figures
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FF.09. Apply area formulas to solve real-world problems involving surface coverage and design.
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FF.10. Extend area and perimeter concepts to irregular and composite shapes.
GG. Three-Dimensional Figures
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GG.01. Identify parts of three-dimensional figures (faces, edges, vertices).
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GG.02. Learn and apply three-dimensional figure vocabulary.
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GG.03. Draw and interpret front, side, and top views of three-dimensional figures.
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GG.04. Interpret and create base plans of three-dimensional structures.
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GG.05. Draw and construct nets of three-dimensional figures.
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GG.06. Describe and sketch cross-sections of three-dimensional figures.
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GG.07. Visualise and describe solids of revolution formed by rotating two-dimensional shapes.
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GG.08. Use orthogonal views to construct 3-D objects and determine their volume and surface area.
HH. Surface Area and Volume of Solids
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HH.01. Calculate the surface area and volume of cuboids (rectangular prisms).
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HH.02. Calculate the surface area of prisms and cylinders.
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HH.03. Calculate the surface area of pyramids and cones.
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HH.04. Calculate the surface area of spheres.
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HH.05. Apply surface area formulas to solve mixed review problems.
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HH.06. Calculate the volume of prisms and cylinders.
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HH.07. Calculate the volume of pyramids and cones.
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HH.08. Calculate the volume of spheres.
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HH.09. Calculate the volume of compound figures by addition or subtraction.
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HH.10. Apply volume formulas to solve mixed review problems.
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HH.11. Analyse similar solids
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HH.12. Analyse surface area of similar solids
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HH.13. Analyse volume of similar solids
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HH.14. Analyse surface area and volume of similar solids
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HH.15. Apply surface area and volume formulas to solve real-world problems involving packaging, construction, and design.
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HH.16. Model and design optimal shapes for minimal surface area or maximal volume.
II. Circles: Geometry and Equations
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II.01. Identify and define the parts of a circle (center, radius, diameter, chord, secant, tangent).
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II.02. Define and measure central angles in a circle.
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II.03. Understand arc length and sector area of a circle
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II.04. Calculate arc measure and arc length.
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II.05. Calculate the area of sectors.
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II.06. Apply circle measurement formulas to solve mixed review problems.
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II.07. Analyse arcs and chords
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II.08. Analyse tangent lines
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II.09. Apply angles formed by chords, secants, and tangents
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II.10. Apply segments formed by chords, secants, and tangents
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II.11. Analyse perimeter of polygons with an inscribed circle
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II.12. Analyse inscribed angles
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II.13. Analyse angles in inscribed right triangles
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II.14. Analyse angles in inscribed quadrilaterals I
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II.15. Analyse angles in inscribed quadrilaterals II
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II.16. Write equations of circles centered at the origin from graphs
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II.17. Write equations of circles centered at the origin from properties
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II.18. Analyse properties of circles from equations
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II.19. Graph circles centered at the origin
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II.20. Apply circle theorems to solve geometric problems.
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II.21. Construct tangent lines to a circle from a point outside the circle.
JJ. Vectors in Two Dimensions
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JJ.01. Use compass directions and vectors
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JJ.02. Calculate the magnitude of a vector.
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JJ.03. Find the component form of a vector.
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JJ.04. Find the component form of a vector given its magnitude and direction angle.
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JJ.05. Graph a resultant vector using the triangle method.
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JJ.06. Graph a resultant vector using the parallelogram method.
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JJ.07. Add vectors by adding their components.
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JJ.08. Subtract vectors by subtracting their components.
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JJ.09. Multiply a vector by a scalar.
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JJ.10. Find the magnitude of a vector scalar multiple
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JJ.11. Determine the direction of a vector scalar multiple
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JJ.12. Find linear combinations of vectors
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JJ.13. Resolve vectors into horizontal and vertical components.
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JJ.14. Use vectors to solve problems involving forces, velocities, and displacements.
KK. Measurement and Units
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KK.01. Convert rates and measurements: metric units
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KK.02. Metric mixed units
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KK.03. Convert rates and measurements: imperial units
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KK.04. Imperial mixed units
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KK.05. Convert between metric and imperial units
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KK.06. Understand and apply the concept of precision in measurement.
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KK.07. Calculate the greatest possible error in a measurement.
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KK.08. Determine the minimum and maximum possible area and volume based on measurement precision.
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KK.09. Calculate percent error in a measurement.
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KK.10. Calculate percent error: area and volume
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KK.11. Perform unit analysis to check the validity of calculations.
LL. Data Representation and Interpretation
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LL.08. Choose the best type of graph to represent a given data set.
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LL.09. Interpret and create box plots to display data distributions.
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LL.10. Critically evaluate the effectiveness and potential biases of different graphical representations.
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LL.01. Interpret information presented in tables.
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LL.02. Interpret information presented in line graphs.
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LL.03. Create line graphs from data sets.
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LL.04. Interpret bar graphs for grouped data.
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LL.05. Create bar graphs for grouped data.
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LL.06. Interpret information presented in pie charts.
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LL.07. Interpret information presented in stem-and-leaf plots.
MM. Descriptive Statistics
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MM.01. Calculate the mean, median, mode, and range of a data set.
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MM.02. Determine quartiles and interquartile range (IQR) of a data set.
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MM.03. Calculate variance and standard deviation of a data set.
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MM.04. Describe distributions in line plots
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MM.05. Populations and samples
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MM.06. Identify biased samples
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MM.07. Create scatter plots to display the relationship between two variables.
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MM.08. Identify trends (positive, negative, or no correlation) using scatter plots.
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MM.09. Make predictions based on trends observed in scatter plots.
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MM.10. Identify outliers in scatter plots and discuss their potential impact on analysis.
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MM.11. Write an equation for a line of best fit to model the relationship between variables in a scatter plot.
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MM.12. Understand the difference between correlation and causation.
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MM.13. Use statistical software and tools to analyze and visualize data sets.
NN. Probability
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NN.01. Calculate theoretical probability of simple events.
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NN.02. Determine experimental probability based on observed outcomes.
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NN.03. Make predictions based on probabilities.
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NN.04. Determine the number of outcomes in compound events.
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NN.05. Calculate the probability of compound events.
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NN.06. Solve probability problems involving compound events.
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NN.07. Find probabilities using two-way frequency tables.
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NN.08. Identify independent and dependent events.
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NN.09. Calculate the probability of independent and dependent events.
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NN.10. Find conditional probabilities.
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NN.11. Identify independence and conditional probability
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NN.12. Find conditional probabilities using two-way frequency tables
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NN.13. Determine geometric probability
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NN.14. Design and conduct probability experiments to test theoretical predictions.
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NN.15. Analyse and compare simulations of events with theoretical outcomes.