1. Simplify. 2. Simplify. 3. Simplify. 4. Solve the following equation for x.
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1 Assignment 2 Unit 4 Rational Expressions Name: Multiple Choice Identify the choice that best completes the statement or answers the question. BE SURE TO SHOW ALL WORKINGS FOR MULTIPLE CHOICE. NO MARKS WILL BE GIVEN IF WORKINGS ARE NOT PROVIDE 1. Simplify. 2. Simplify. 3. Simplify. 4. Solve the following equation for x. x = 2 x = 3 x = 4 x = 5 5. Determine the lowest common denominator for the pair and. 3c 3 + c 2 c 2 1 3c 2 3 c + 1
2 6. Which rational expression represents the speed of a car that has travelled 70 km? Speed = km, d > 0 Speed = km/h, t 0 Speed = km/h, t > 0 Speed = km, d 0 7. Determine all the non-permissible values of the variable. g 1, 3, 3, 9 g 1, 9 g 3, 9 g 3 3, 9 8. Simplify. 9. Simplify. 10. Identify the root(s) of the following equation. x = 2 x = 3 x = 4 A and B
3 11. Simplify. A) B) C) D) E) F) 12. Solve the following equation for x. State the non-permissible values of the variable. A) B)
4 C) D) 13. When working together, Marcia and Jon can do their housework in 90 minutes. Working independently, it takes Marcia 10 minutes longer than Jon to do all of the housework. How long does it take Jon to do all of the housework on his own? 14. It takes Susan 3 hours to paint a room and Jacqueline 2 hours to paint a room that is the same size. How long would it take them to point their room if they worked together? 15. Rima bought a case of concert T-shirts for $450. She kept two shirts for herself and sold the rest for $560, making a profit of $10 on each shirt. If x represents the original number of shirts in the case, and her profit is modelled by the equations 10, algebraically determine how x 2 x many shirts were in the case.
5 Unit 4 Rational Expressions Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson ANS: A PTS: 1 DIF: Grade 12 REF: Lesson ANS: C PTS: 1 DIF: Grade 12 REF: Lesson ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.5 OBJ: 3.1 Determine the non-permissible values for the variable in a rational equation. 3.2 Determine, algebraically, the solution to a rational equation, and explain the strategy used to solve the equation. 3.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation. 3.4 Solve a contextual problem that involves a rational equation. TOP: Solving Rational Equations KEY: rational equation 5. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 4.1 OBJ: 1.1 Compare the strategies for writing equivalent forms of rational expressions to writing equivalent forms of rational numbers. 1.2 Explain why a given value is non-permissible for a given rational expression. 1.3 Determine the non-permissible values for a rational expression. 1.4 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 non-permissible values of the equivalent rational expression. TOP: Equivalent Rational Expressions KEY: rational expression 6. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 4.4
6 KEY: rational expression 7. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson ANS: D PTS: 1 DIF: Grade 12 REF: Lesson ANS: A PTS: 1 DIF: Grade 12 REF: Lesson ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.5 OBJ: 3.1 Determine the non-permissible values for the variable in a rational equation. 3.2 Determine, algebraically, the solution to a rational equation, and explain the strategy used to solve the equation. 3.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation. 3.4 Solve a contextual problem that involves a rational equation. TOP: Solving Rational Equations KEY: rational equation SHORT ANSWER 1. ANS:, x 0 PTS: 1 DIF: Grade 12 REF: Lesson 4.4
7 2. ANS: x = 0, x = 4; x 2 PTS: 1 DIF: Grade 12 REF: Lesson 4.5 OBJ: 3.1 Determine the non-permissible values for the variable in a rational equation. 3.2 Determine, algebraically, the solution to a rational equation, and explain the strategy used to solve the equation. 3.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation. 3.4 Solve a contextual problem that involves a rational equation. TOP: Solving Rational Equations KEY: rational equation non-permissible value PROBLEM 1. ANS: n PTS: 1 2. ANS: o PTS: 1 3. ANS: 1 PTS: 1
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