DISTRIBUTED LEARNING

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1 DISTRIBUTED LEARNING RAVEN S WNCP GRADE MATHEMATICS BC Pre Calculus Math Alberta Mathematics 0 Saskatchewan Pre Calculus Math 0 Manitoba Pre Calculus Math 0S STUDENT GUIDE AND RESOURCE BOOK The Key to Student Success Alan R. Taylor, Ed. D. Bill Kokoskin, M.A. Raven Research Associates April 0

2 Table of Contents MODULE Page Page Section -AbsoluteValue &Introduction to Radicals.D Factoring a[f(x)] + b(f(x)) + c, a 0.E Factoring a [f(x)] b [g(y)] ; a,b 0 9.A Absolute Value & the Number Line.B Equations and Inequalities Involving 0.F Combination of Factoring.G Factor Theorem Absolute Value Send In Assignment #.C Powers and Roots of Numbers 7 Section - Relations and Quadratic Functions.D Ordering Radicals and Using a.a Review of Relations and Functions 9 Calculator to Approximate Values.B Graphs of Quadratic Functions 0.E Simplifying Radicals by Factoring.C Transformations of Quadratic 7 Functions.F Adding and Subtracting Radicals 8.D Reciprocal Functions 79.G Multiplication and Division of.e Graphing the Absolute Value 8 Square Root Radicals Function Send In Assignment #.F Solving Absolute-Value Equations 9 Section - Properties & Applications of Radicals Algebraically and Graphically.A Writing Radicals in Simplest Form.B Product of a Binomial and Binomial 9 Send In Assignment # MODULE.C Conjugates of Binomials and 7 Section - Applications with Quadratic Functions Rationalizing Denominators.A Completing the Square 98.D Relationships between Roots, 0.B Maximum and Minimum Problems 0 Absolute Values and Signs.C Solving Quadratics by Graphing 08.E Solving Equations Involving.D Solving Quadratics by Factoring Radicals.E Solving Quadratics Completing the 7.F Problems With Radical Expressions Square Send In Assignment #.F The Quadratic Formula 9 Section - Rational Expressions and Equations.G The Discriminant.A Rational Numbers (Review) Send In Assignment # 7.B Addition and Subtraction of 7 Section - Sequences and Series Fractions (Review).A Arithmetic Sequences 8.C Multiplication and Division of 7.B Arithmetic Series Fractions (Review).D Rational Expressions 7.C Geometric Sequences.D Geometric Series 9.E Adding and Subtracting Rational 79.E Sums of Infinite Geometric Series 7 Expressions.F Multiplying and Dividing Rational Expressions 8 Send In Assignment # 8 Section - Inequalities.G Multiple Operations with Rational 8.A Graphing Inequalities in One Expressions Variable in Two Dimensions.H Rational Equations 8.B Graphing Inequalities in Two 8.I Solving Problems Involving Rational 89 Variables Equations.C Graphing Systems of Linear and Quadratic Inequalities.D Graphing Quadratic Inequalities in 9 One Variable.E Problems for Quadratic Inequalities Send In Assignment # MODULE Section - Trigonometry.A Definition of Trig Functions and 9 7 Angles in Standard Position Send In Assignment # 9.B Special Angles.C Law of Sines 0 Section - Linear and Quadratic Systems.A Linear-Quadratic Systems 78.D Law of Cosines.E Solving General Triangles 7.B Quadratic-Quadratic Systems.C Problems for Systems 8 8 (Ambiguous Case) Send In Assignment # Send In Assignment # 0 Answers to Exercises 87 Section - Factoring Polynomials Send In Assignments 0.A Review of Factoring in General 8.B Factoring ax + bx + c, a 0.C Factoring a x b y, a 0, b 0 7

3 SAMPLE EXERCISE.A Writing Radicals in Simplest Form A radical expression representing a square root is in its simplest form (or simple radical form) when the following properties are in place.. The radicand contains no integer (other than ) that is a perfect square. No fraction is under the radical sign. No radical is in the denominator. In Chapter we simplified radicals by making sure that the radicand contained no perfect squares other than remained under the radical sign. e.g. Simplify (i) (ii) (iii) 99 (iv) 8a a a a. Also, in the Chapter we simplified radicals containing fractions using properties of division. e.g. Simplify b b b b (i) (ii) b b b b However, we did not concern ourselves in Chapter with expressions containing a radical in a denominator. e.g.. So, according 8 to property #, this is not in simple radical form.

4 . No radical should be left in the denominator In a fraction involving radicals, we prefer to have a whole number denominator. When we have a fraction where the denominator includes a radical, we change the denominator to a rational number (this is called rationalizing the denominator. How do we do this with a single (monomial) term in the denominator? First, recall that when you multiply any number or expression by that its value remains the same. Second, recall that is a rational number that can be written in different ways. e.g., etc., Note: any number written as a fraction with the same (non-zero) numerator and denominator is equal to. So, to rationalize a denominator in a fraction, multiply the numerator and denominator by an expression equal to that clears the radical sign in the denominator and cancel like factors. e.g. Rationalize the following denominators. (i) or (ii) b b b b b b b b b b b Simplifying Radicals with Other than Square Roots In addition to radicals with square roots, radicals with other roots can be simplified in a similar way. e.g. Simply each of the following. (i) (ii) a ( ) ( a a a a) a a a (iii) or

5 Examples with Solutions Simplify Solution. 8y 8y y y y y. 7b 7b b b. x or. x or b b b b b b b b Exercises.A Simplify and write each of the following in simple radical form.....

6 a. 9b. xy y 0. y. a b. 8x