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Scope and Sequence AM™ CC Math 2 Library The Accelerated Math™ scope and sequence is based on extensive mathematics and standards research and consultation from mathematics educators, mathematicians, and university researchers. You're sure to find objectives that reinforce the skills you are teaching, regardless of what instructional materials you use. Accelerated Math makes it easy to select and organize objectives to suit your textbook and your own teaching approach. This Accelerated Math library provides the following scope and sequence of objectives Topic 1 - Extending the Number System • • • • • • • • • • • • • • • • • • • • • • Apply the product of powers property to a monomial algebraic expression Apply the power of a power property to a monomial algebraic expression Apply the power of a product property to a monomial algebraic expression Apply the quotient of powers property to monomial algebraic expressions Apply the power of a quotient property to monomial algebraic expressions Apply properties of exponents to monomial algebraic expressions Convert between radical notation and rational exponent notation Simplify a numerical expression that includes fractional exponents Simplify a monomial numerical expression involving the square root of a whole number Simplify a monomial algebraic radical expression Add and/or subtract numerical radical expressions Add or subtract algebraic radical expressions Multiply monomial numerical expressions involving radicals Multiply monomial algebraic radical expressions Divide monomial numerical expressions involving radicals Divide monomial algebraic radical expressions Represent an imaginary number in bi form Add or subtract complex numbers in a + bi form Add or subtract complex numbers using the relation i^2 = -1 Multiply complex numbers Add quadratic polynomials Subtract quadratic polynomials • • • • Multiply two binomials of the form (x +/- a)(x +/- b) Multiply two binomials of the form (ax +/- b)(cx +/- d) Multiply two binomials of the form (ax +/- by)(cx +/- dy) Square a binomial Topic 2 - Expressions and Equations • • • • • • • • • • • • • • Factor the GCF from a quadratic expression Factor a quadratic expression that results in factors of the form (x +/a)(x +/- b) Factor a quadratic expression that results in factors of the form (ax +/b)(cx +/- d) Factor a quadratic expression that results in factors of the form (ax +/by)(cx +/- dy) Factor a perfect-square trinomial Factor the difference of two squares Factor a quadratic expression that has a GCF and two linear binomial factors Solve a quadratic equation that can be written in x^2 = b form and has rational solutions, no solution, or nonsimplified radical solutions Solve a quadratic equation that can be written in x^2 = b form and has a simplified radical solution or no solution Solve a quadratic equation by taking square roots Determine the solution(s) of an equation given in factored form Solve a quadratic equation by factoring Determine the value needed to make a quadratic expression a perfect square trinomial Determine an expression of the form (x + b)^2 + c that is equivalent to the given expression P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 1 of 5 R57259.140114 Scope and Sequence • • • • • • • • • • • • Solve a quadratic equation by completing the square Solve a quadratic equation using the quadratic formula Factor a quadratic expression that has complex roots Solve a quadratic equation that has complex solutions Rearrange a formula to isolate a variable of interest where the formula is quadratic in that variable WP: Represent a situation using a 1variable quadratic equation WP: Solve a problem that can be represented by a 1-variable quadratic equation WP: Represent a situation using a 2variable quadratic equation Determine a quadratic equation using given information Determine the graph of a quadratic equation Determine the solution(s) to a system of equations represented graphically, consisting of a linear equation and an equation in quadratic form Determine the solution(s) to a system of equations consisting of a linear equation and an equation in quadratic form algebraically Topic 3 - Quadratic Functions and Modeling • • • • • • WP: Determine the graph of a quadratic function that represents a situation WP: Determine a reasonable domain for a quadratic function in a given situation using a representative graph WP: Determine a reasonable domain for a quadratic function in a given situation WP: Calculate the average rate of change of a quadratic function over a specified interval given a table or an equation WP: Estimate the average rate of change of a quadratic function over a specified interval given a graph Determine the graph of a quadratic function showing its intercepts and maximum or minimum AM™ CC Math 2 Library • • • • • • • • • • • • • • • Factor a quadratic function to determine the zeros of the function Complete the square of a quadratic function to determine the vertex Determine the quadratic function for a given graph Determine the graph of a piecewisedefined function Determine the graph of a step function Determine the graph of a 2-variable absolute value equation Compare the properties of two quadratic functions, each represented in a different way WP: Represent a situation using a quadratic function WP: Determine a recursive process for calculating the values in a situation that leads to a quadratic function Combine a quadratic function with a linear or a quadratic function using addition or subtraction WP: Combine a quadratic function with a linear or a quadratic function using addition or subtraction Determine the effect of replacing f(x) with f(x) + k or f(x + k) on the graph of a quadratic function Determine the effect of replacing f(x) with kf(x) or f(kx) on the graph of a quadratic function Determine the quadratic function resulting from a transformation given the parent function and graphs of the parent and transformed functions Determine the equation of the inverse of a linear function Topic 4 - Applications of Probability • • • • • Determine the probability of independent events Represent data using a two-way frequency table Approximate conditional probabilities using a two-way table as a sample space Determine the conditional probability of an event A given an event B Determine the probability of an event using the addition rule of probability, P(A or B) = P(A) + P(B) - P(A and B) P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 2 of 5 R57259.140114 Scope and Sequence • • • • • • • • Determine the probability of an event using the multiplication rule of probability, P(A and B) = P(A)P(B|A) = P(B)P(A|B) WP: Determine the number of permutations possible in a given situation Determine a probability using permutations WP: Solve a probability problem involving permutations WP: Determine the number of combinations possible in a given situation Determine a probability using combinations WP: Solve a probability problem involving combinations Analyze a decision or a strategy using simple probability concepts Topic 5 - Similarity, Right Triangle Trigonometry, and Proof • • • • • • • • • • Determine the midpoint of a line segment given the coordinates of the endpoints Solve a problem involving the midpoint formula Determine the point on a line segment that divides the segment into a given ratio Solve a problem using inequalities in a triangle Identify similar triangles using triangle similarity postulates or theorems Determine the length of a side or the measure of an angle given two similar triangles and numeric values for side lengths or angle measure Determine the length of a side or the measure of an angle given two similar triangles and algebraic expressions for side lengths or angle measures Determine a length in a triangle using a midsegment and given numeric values for lengths Determine a length in a triangle using a midsegment and given algebraic expressions for lengths Determine a length in a triangle using parallel lines and proportional parts AM™ CC Math 2 Library • • • • • • • • • • • • • • • Determine a length given the perimeters of similar triangles or the lengths of corresponding interior line segments Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangle WP: Determine a length in a triangle using similarity Complete a proof using congruence and similarity theorems Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle Solve a multi-step problem using the properties of a 45-45-90 degree triangle and/or a 30-60-90 degree triangle Determine a sine, cosine, or tangent ratio in a right triangle Determine a length using a sine, cosine, or tangent ratio in a right triangle Determine the measure of an angle using a sine, cosine, or tangent ratio in a right triangle Solve a problem using the Pythagorean theorem and a sine, cosine, or tangent ratio in a right triangle WP: Solve a problem involving a complex figure using the Pythagorean theorem WP: Determine a length in a right triangle using a sine, cosine, or tangent ratio WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio Determine the value of a trigonometric expression for an acute angle using the Pythagorean identity Topic 6 - Circles With and Without Coordinates • Determine the length of a line segment, the measure of an angle, or the measure of an arc given a tangent to a circle P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 3 of 5 R57259.140114 Scope and Sequence • • • • • • • • • Determine a length using the relationship between chords and radii Determine the measure of an arc or an angle using properties of an inscribed triangle or quadrilateral Determine the measure of an angle using the relationship between inscribed angles, circumscribed angles, and/or central angles Determine the length of an arc Determine the area of a sector of a circle Determine an equation of a circle Determine the radius or center of a circle given an equation Complete the square to determine the center or radius of a circle given the equation Derive the equation of a vertically oriented parabola given a focus and a directrix AM™ CC Math 2 Library • • • • • • • Derive the equation of a horizontally oriented parabola given a focus and a directrix Determine the volume of a right pyramid or a right cone Determine a measurement given the volume of a right pyramid or a right cone WP: Determine a measurement given the volume of a right pyramid or a right cone Determine a measurement given the volume of a sphere WP: Determine a measurement given the volume of a sphere WP: Solve a problem involving the volume of a complex solid figure P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 4 of 5 R57259.140114 Scope and Sequence Accelerated Math Libraries include an almost unlimited supply of dynamic algorithm-generated problems for both assisted-response (multiplechoice) and free-response assignments. Twenty libraries are available: Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Algebra 1 Algebra 2 Geometry Math 1 Math 2 Math 3 Probability & Statistics Pre-Calculus Calculus Financial Literacy Math 1 Financial Literacy Math 2 AM™ CC Math 2 Library Please call us toll-free at 1-800-338-4204 to order this Accelerated Math library or to request the Scope and Sequence for other libraries. Accelerated Math Library AM CC Math 2 Library P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com © 2014 Renaissance Learning, Inc. All rights reserved. Page 5 of 5 R57259.140114