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Day 12 Test Review.notebook

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PreCalculus 110Unit 5: Rational Expressions and Equations

May 7, 2019: Day #10

1. Test Friday


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Jan 299:29 AM

Curriculum Outcomes

AN4: Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

AN5: Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

AN6: Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials).


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ACHIEVEMENT INDICATORS

§ Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.

§ Explain why a given value is nonpermissible for a given rational expression.

§ Determine the nonpermissible values for a rational expression.

§ Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the nonpermissible values of the equivalent rational expression.

§ Simplify a rational expression.

§ Explain why the nonpermissible values of a given rational expression and its simplified form are the same.

AN4: Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or

trinomials).


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May 07, 2019

May 81:24 PM

AN5: Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or

trinomials). ACHIEVEMENT INDICATORS

§ Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.

§ Determine the nonpermissible values when performing operations on rational expressions.

§ Determine, in simplified form, the sum or difference of rational expressions with the same denominator.

§ Determine, in simplified form, the sum or difference of rational expressions in which the denominators are not the same and which may or may not contain common factors.

§ Determine, in simplified form, the product or quotient of rational expressions.

§ Simplify an expression that involves two or more operations on rational expressions.


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May 07, 2019

May 81:25 PM

AN6: Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or

trinomials). ACHIEVEMENT INDICATORS

§ Determine the nonpermissible values for the variable in a rational equation.

§ Determine the solution to a rational equation algebraically, and explain the process used to solve the equation.

§ Explain why a value obtained in solving a rational equation may not be a solution of the equation.

§ Solve problems by modeling a situation using a rational equation.


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Format:

5 Multiple Choice5 Open Response1 Bonus

Total = 25 Marks


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Topics: 1. Identifying nonpermissible roots2. Simplifying rational expressions3. Multiplying and dividing rational expressions4. Adding and subtracting rational expressions5. Solving rational equations6. Identify the error and correct7. Word Problem


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Textbook:

Minimum Preparation:

p. 352354

# 3, 5, 6b, 9, 10, 11, 13, 14, 15, 20, 22, 23


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Attachments

Standard Form Demor.GSP

Warm ups.notebook

SMART Notebook

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Apr 13-1:09 PM McGraw-Hill Ryerson Pre-Calculus 11 Chapter 6 Rational Expressions and Equations

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Apr 13-1:35 PM McGraw-Hill Ryerson Pre-Calculus 11 Teacher Notes 1. This lesson is designed to help students conceptualize the main ideas of Chapter 6. 2. The lesson was written using SMART Notebook 10.0. Other versions of the software do not offer the same functionality. 3. Minimum screen resolution is 1024 × 768. 4. For best results, set the view to Page Width. 5. When you exit this lesson, do not save changes.

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Apr 13-1:23 PM Answer Non-Permissible Values For each rational expression, determine all non-permissible values. State the domain for each expression. Use the pen tool to write your answers. Drag the Answer tab under each question to reveal the answer. Chapter 6 The non-permissible value is x = –2. The domain is { x ∈ R, x ≠ –2} The non-permissible value is p = 5. The domain is { p ∈ R, p ≠ 5} The non-permissible value is x = 0. The domain is { x ∈ R, x ≠ 0} The non-permissible values are x = 0 and y = 0. The domain is { x,y ∈ R, x ≠ 0 , y ≠ 0 } The non-permissible values are x = 2 and x = –2. The domain is { x ∈ R, x ≠± 2} The non-permissible values are x = y . The domain is { x,y ∈ R, x ≠ y } 1. 2. 3. 4. 5. 6. Hint A non-permissible value is any value for a variable that makes an expression undefined. In a rational expression, it is a value that results in a denominator of zero.

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Apr 13-1:23 PM Simplifying Rational Expressions Identify each of the following as true or false. Click on the box to reveal the solution. Chapter 6

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Apr 13-1:23 PM Apply Rational Expressions Chapter 6 The area of a rectangular garden can be represented by the polynomial x 2 + 3 x + 2 and its width by x + 1. Use the pen tool to answer the following: a) Write a rational expression that represents the length. b) Write the expression in simplest form. c) If x represents 1 unit of length, what is the ratio length : width for this garden? Solution , x > –1 , x > –1 a) b)

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Apr 13-1:23 PM Multiply Rational Expressions Chapter 6 Click here for the solution. ( ( ) ) Answer x = –7, 0, ± 3 Simplify. Use the pen tool to show your work. Hint 1. Factor expressions in the numerator and denominator. 2. State any restrictions on the variables. 3. Reduce to lowest terms by dividing out any common factors.

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Apr 13-1:23 PM Divide Rational Expressions Simplify. Use the pen tool to show your work. Chapter 6 Hint Click here for the solution. Hint 1. Factor expressions in the numerator and denominator. 2. Multiply by the reciprocal. 3. State any restrictions on the variables. 4. Reduce to lowest terms by dividing out any common factors. Answer

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Apr 13-1:23 PM Multiply and Divide Rational Expressions Simplify using the pen tool. State any restrictions on the variables. Chapter 6 Click here for the solution.

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Apr 13-1:23 PM x – 1 x + 6 Apply Rational Expressions Chapter 6 Determine the area of the triangular region if the area of A 1 is 2 x 2 + 10 x – 12 and has a width of x + 6. The area of A 2 is 2 x 2 – 3 x + 1 and has a width of x – 1. Use the pen tool to show your work. Hint Click on the rectangles to see the steps. Click on the triangle to see the solution for the area.

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Apr 13-1:23 PM Check Check Check Check Check Determine the LCD Check Check Check Check Check Use the pen tool to check the box that represents the lowest common denominator for the group of rational expressions listed. Click on Check to check your work. Chapter 6

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Apr 13-1:23 PM Equivalent Expressions Drag all expressions that are not equivalent to the expression , in the red box, to the trash can. If the expression is equivalent it cannot be thrown away. Chapter 6

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Apr 13-1:23 PM Add or Subtract Rational Expressions Click here for the solution. Use the pen tool to write the sum or difference below each expression. Chapter 6 Answer

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Apr 13-1:23 PM Rational Equations Click here for the solution. Chapter 6 Erin and Andrea set off at the same time on a 30-km walk for charity. Erin, who has trained all year for this event, walks 1 km/h faster than Andrea. Erin finishes the walk 1 h ahead of Andrea. How fast was each sister walking, and how long did it take for each sister to finish the walk? Use the pen tool to complete your answer. Let x represent Andrea's walking speed. Distance (km) Speed (km/h) Time (h) Erin Andrea

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Apr 13-1:23 PM Add and Subtract Rational Expressions Chapter 6 Drag the expressions from the right to arrange them in the correct order to simplify the given expression. Answer

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Apr 13-2:18 PM The following pages contain solutions for the previous questions.

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Apr 13-1:23 PM Solution 1 1 1 1 1 1 Go back to the question ( ( ) ) ) ) ( ( ( ( ) ) = = x = –7, 0, ± 3

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Apr 13-1:23 PM Hint Go back to the question 1 1 1 1 Solution

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Apr 13-2:20 PM Solution ab 2 xy 2 3 Go back to the question

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Apr 13-2:20 PM Solution Go back to the question

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Apr 13-1:23 PM Solution The difference in the times of the two sisters is 1 hour. Andrea's walking speed is 5 km/h, taking her 6 hours to finish. Erin's walking speed is 6 km/h taking her 5 hours to finish. –6 is an extraneous root which does not make sense in the context of walking speeds. Go back to the question Distance (km) Speed (km/h) Time (h) Erin 30 x + 1 Andrea 30 x

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