Math for College Readiness

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1 # % <! $ ± Θ Δ Π Σ SECONDARY MATHEMATICS CURRICULUM GUIDE Math for College Readiness Course #: Textbook: ALGEBRA FOR COLLEGE STUDENTS (6 TH EDITION) HILLSBOROUGH COUNTY SCHOOL DISTRICT Last Revised June 2012 # % <! $ ± Θ Δ Π Σ
2 The purpose of this course is to prepare students for Algebra II and/or the college readiness test called PERT. In order to prepare students for the PERT, sections of this course should be taught without the use of a calculator. There will be some questions on the PERT that do allow students to use a calculator. These sections and units will be labeled NonCalculator on the guide. For these sections, teachers should instruct students how to do these topics without the use of a calculator. Students should also be assessed without the use of a calculator. It would be beneficial for students to have some multiple choice assessments throughout the course. For sections that are not labeled NonCalculator, the calculator usage is at the discretion of the teacher; the section may be taught with a fourfunction calculator or with no calculator at all. Students may use a scientific calculator for the last unit that covers exponential functions and logarithms. Questions on the exam for this unit will not require a scientific calculator. A fourfunction calculator will be allowed for both the first and second semester exams. SEMESTER ONE I. The Real Number System (Sections ) NonCalculator A. Basic Concepts (1.1) Students will be able to use and apply set notation, number lines, additive inverse, absolute value, and inequality symbols. B. Operations on real numbers (1.2) Students will be able to add, subtract, multiply and divide real numbers. C. Exponents, Roots and Order of Operations (1.3) 1. Define exponents and roots. 2. Use order of operations to simplify exponents. D. Properties of Real Numbers (1.4) 1. Identify distributive, inverse, identity, commutative, and associative properties. 2. Apply properties to simplify expressions. II. Linear Equations, Inequalities and Applications (Sections ) NonCalculator A. Linear Equations in One Variable (2.1) The students will be able to solve multistep equations with rational solutions. B. Formulas (2.2) Students will be able to solve literal equations using basic geometry formulas. C. Application of Linear Equations ( ) Students will be able to solve word problems using linear equations. D. Linear Inequalities in One Variable (2.5) The students will be able to solve multistep inequalities with rational solutions. E. Set Operations and Compound Inequalities (2.6) Students will be able to use interval notation to express the answer of an inequality. F. Absolute Value Equations and Inequalities (2.7) 1
3 III. Graphs, Linear Equations and Functions (Sections ) A. Coordinate System (3.1) 1. Identify and graph order pairs. 2. Graph horizontal and vertical lines. 3. Use the midpoint formula to find the midpoint of a line. 4. Identify x and y intercepts of a line. B. Slope of a Line (3.2) 1. Find the slope of a line when given two points on the line, the equation of the line, and the graph of the line. 2. Find the slope of parallel and perpendicular lines. C. Linear Equations in two variables (3.3) 1. Write equations of lines using slopeintercept and pointslope form. 2. Convert linear equations from standard to slopeintercept form. 3. Graph lines using slopeintercept form. D. Linear Inequalities in Two Variables (3.4) 1. Graph the inequality on a coordinate plane. 2. Graph the solution of a system of inequalities on a coordinate plane. E. Introduction to functions (3.5) 1. Define relations, functions, domain, and range. 2. Determine if a relation is a function from a graph, from a set of ordered pairs, and from an equation. 3. State the domain and range of a function. IV. Systems of Linear Equations (Sections 4.1&4.3) A. Linear Equations in Two Variables (4.1) Students will be able to solve linear equations by graphing, substitution, and elimination. B. Applications of Systems of Linear Equations (4.3) Students will be able to solve 1. Geometry problems by using two variables. 2. Money problems by using two variables. 2
4 V. Exponents, Polynomials, and Polynomial Functions ( ) NonCalculator A. Integer Exponents and Scientific Notation (5.1) 1. Use the product, quotient, and power rules of exponents to simplify expressions. 2. Use the rules of exponents to write numbers in scientific notation. B. Adding and Subtracting Polynomials (5.2) 1. Classify polynomials by their number of terms and degree. 2. Identify leading coefficients and constant terms. 3. Add and Subtract Polynomials. C. Polynomial Functions, Graphs, and Composition (5.3) 1. Evaluate polynomial functions. 2. Find the composition of functions. D. Multiplying Polynomials (5.4) E. Dividing polynomial (5.5) Students will be able to use long division to divide polynomials 1. By a monomial. 2. By a linear binomial with a leading coefficient of one only. 3
5 SEMESTER TWO I. Factoring ( ) Be sure to include NonCalculator practice. A. Greatest Common factors and Factor by Grouping (6.1) The student will be able to 1. Factor by using the Greatest Common Factors. 2. Factor by Grouping. B. Factoring Trinomials (6.2) The student will be able to 1. Factor a trinomial of the form ax 2 +bx +c with leading coefficient of one. 2. Factor a trinomial of the form ax 2 +bx +c leading coefficient not equal to one. C. The student will be able to factor special forms which include the difference of squares, perfect square trinomial, & sum/difference of cubes. (6.3) D. A General Approach to Factoring (6.4) Students will be able to determine which method of factoring to use. E. Solving Equations by Factoring (6.5) II. Rational Expressions and Functions ( , ) Be sure to include NonCalculator practice. A. Rational Expressions and Functions; Multiplying and Dividing. (7.1) Student will be able to 1. Simplify rational expressions. 2. Identify the domain and restrictions. 3. Multiply and divide rational expressions. B. Adding and Subtracting Rational Expressions. (7.2) Students will be able to add and subtract rational expressions. C. Equations with Rational Expressions(7.4) Students will be able to Solve rational expressions. D. Applications of Rational Expressions (7.5) 1. Solve Literal Equations using rational expressions. 2. Solve word problems using rational expressions. 4
6 III. Roots, Radicals, and Root Functions ( ) Be sure to include NonCalculator practice. A. Radical Expressions and Graphs (8.1) Students will be able to find the square roots of numbers. B. Rational Exponents (8.2) 1. Use exponential notation for n th roots. 2. Convert between radicals and rational exponents. 3. Apply rules of exponents to simplify expressions involving rational exponents. C. Simplifying Radical Expressions (8.3) 1. Simplify radical expressions including those with variables. 2. Use the product and quotient rule. 3. Use the Pythagorean Theorem and Distance formula. D. Adding and Subtracting Radical Expressions (8.4) E. Multiplying and Dividing Radical Expressions (8.5) Students will be able to rationalize denominators with monomials only. F. Solving Equations With Radicals (8.6) 1. Solve radical equations by using the power rule. 2. Solve radical equations that require additional steps. 3. Solve radical equations with indexes greater than two. G. Introduction to imaginary numbers (i). (8.7) 1. Simplify. 2. Leave answers in simplest radical form. IV. Quadratic Equation and Inequalities ( ) A. Solving by using the Square Root Property. (9.1) Students will be able to solve using both real and imaginary solutions. B. The Quadratic Formula (9.2) Students will be able to 1. Solve by using the quadratic formula. 2. Use the discriminant to identify the types of solutions. 5
7 V. Graphs of Functions and Relations ( ) A. Review of Operations and Composition (10.1) Students will be able to form composite functions by adding, subtracting, and multiplying. B. Graphs of Quadratic Functions (10.2) Students will be able to identify transformations. C. More About Parabolas (10.3) 1. Find the vertex. 2. Find the axis of symmetry. 3. Find the x and y intercepts. 4. Find the direction the parabola opens. 5. Graph the function. VI. Inverse, Exponential, and Logarithmic Functions ( ) A scientific calculator may be used for this unit. A. Inverse Functions (11.1) Students need a Basic Definition, Basic notation, and Finding the inverse of a function. B. Exponential Functions (11.2) 1. Students will be able to be able to graph, find domain and range, and apply transformations. 2. Solve exponential equations with like bases. 3. Evaluate exponential expressions. C. Logarithmic Functions ( ) 1. Define Logarithm as an exponent. 2. Convert between exponential and Logarithmic form. 3. Expand and Condense. D. Common and Natural Logarithms (11.5) 1. Evaluate Natural Logs and Logs. 2. Change of Base. E. Exponential and Logarithmic Applications (11.6) Students will be able to find interest using 1. Compound Interest. 2. Continuous Compound Interest. 6
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