Say it with Symbols - Unit Test Review Shet

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1 Name: Class: Date: ID: A Say it with Symbols - Unit Test Review Shet Short Answer 1. What does it mean to say that two algebraic expressions are equivalent? Evaluate the expression for the given value of x. 2. x 2 (x + 7) when x = x when x = x 2 when x = 8 5. (x + 5)(x 1) when x = 0 6. Find y when x = 10: y = 8 5(x + 2) + 2x. 7. Below is a graph of a parabola. a. What are the coordinates of the maximum or minimum point? b. What are the coordinates of the x-intercept(s)? c. What are the coordinates of the y-intercept(s)? d. Could y = (x 4) be the equation of the parabola? Explain why or why not. e. Could y = x 2 be the equation of the parabola? Explain why or why not. f. Does the line y = 6 intersect the parabola? Explain why or why not. 1

2 Name: ID: A 8. Explain how you can tell, without using a calculator, that these expressions are not equivalent. 5 4x 2 4x 2 5 4x(x 5) 9. Solve the following equations. Show your work. a. (x + 4)(x 6) = 0 b. 3(x + 10) + 5(x + 2) = 0 c. x 2 x 20 = 0 d. 2(7x + 15) = x 10. Write each of the following expressions in two different but equivalent forms. Be prepared to explain why the new forms are equivalent to those that are given. a. 7x(3 9x) b. 15x + 8x 2 c. (5x 2 9x + 7) + 4x(3 + 5x) d. (450 8a + 7b) 3(5a 2b) e. (2x + 3)(5x 7) 11. Solve the following equations by rewriting them in equivalent forms from which the roots are easy to find. Give the properties of numbers and operations that justify each step of your solution process. a. 9.5x = 50.5 b. 3x x = 0 c. (x + 4)(3x 6) = 0 d. 2(9x + 15) = 8 + 2x 12. a. Complete the table below. Value of the Expression When Expression x = 1 x = 2 x = 5 x = 6.5 x = 27 3x + 6 3(x + 2) 3(x + 1) + 3 b. What patterns do you notice? c. Are these expressions related? d. How might you verify your answer to part (c)? 2

3 Name: ID: A Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which expression is equivalent to the factored form of x 2 100? A. (x + 100)(x 1) C. (x 90)(x 10) B. (x + 25)(x 4) D. (x 10)(x + 10) 2. If 30(x 10) = 120, then x = A. 14 B. 14 C. 80 D Which of the following equations represents a linear function? A. y = (3x + 10)x C. y = (3 10x)x B. y = (3x 10)(3 + 10) D. y = 3x(x 3) 4. Which of the following equations has a graph with exactly one x-intercept? A. y = x 2 25 C. y = (x + 4)(x 4) B. y = x 2 + 4x + 4 D. y = x 2 + 1x Which of the following expressions is equivalent to 3(x + 4) 6 + 5x? A. 3x + 12 x C. 8x 2 B. 8x + 6 D. 2x Which of the following equations has 1 as a solution? A. 0 = x 2 + 2x + 1 B. 0 = x 2 x Factor the expression. 7. k 2 + kf 2f 2 A. (k 2f)(k + f) C. (k + 2f)(k + f) B. (k + 2f)(k f) D. (k 2f)(k f) Complete. 8. z 2 + 9z 90 = (z 6)(z + ) A. 9 C. 90 B. 15 D. 15 3

4 Name: ID: A 9. Graph the function f(x) = 4 x. A. C. B. D. 10. The base of a triangle is (6h + 16) centimeters. The height of the triangle is (3h 8) centimeters. Find the area of the triangle. A. (18h 2 96h 64) cm 2 C. (18h ) cm 2 B. (9h 2 16h 64) cm 2 D. (9h 2 64) cm 2 4

5 Say it with Symbols - Unit Test Review Shet Answer Section SHORT ANSWER 1. ANS: Equivalent expressions give the same value for any given values of the variables involved. REF: Say It With Symbols Question Bank TOP: Problem 1.2 Determining Equivalence KEY: equivalent expressions 2. ANS: 0 3. ANS: ANS: ANS: 5 6. ANS: 32; Add inside the parentheses first, then multiply, and then subtract and add: y = 8 5(10 + 2) + 2(10) = 8 5(12) + 2(10) = = = 32. 1

6 7. ANS: a. The minimum point is ( 2, 4). b. ( 6, 0) and (2, 0) c. (0, 3) d. No; the parabola opens upward, not downward. e. No; this is a linear equation. f. No; the line y = 6 is below the minimum point. REF: Say It With Symbols Additional Practice Investigation 3 OBJ: Investigation 3: Solving Equations TOP: Problem 3.3 Factoring Quadratic Expressions KEY: x-intercepts y-intercepts coordinate parabola quadratic equation 8. ANS: y = 5 4x 2 y = 4x 2 5 y = 4x(x 5) The first two expressions are not equivalent; the 5 is positive in the first and negative in the second. In fact, all the signs of the terms in the second are opposite from those in the first. If the third expression is expanded, using the Distributive Property, it would be 4 20x, which is not equivalent to the other two expressions. REF: Say It With Symbols Question Bank TOP: Problem 1.2 Determining Equivalence KEY: equivalent expressions 2

7 9. ANS: a. (x + 4)(x 6) = 0 x + 4 = 0 and x 6 = 0 x = 4 and x = 6 b. 3(x + 10) + 5(x + 2) = 0 3x x + 10 = 10 8x + 40 = 0 8x = 40 x = 5 c. x 2 x 20 = 0 (x + 4)(x 5) = 0 x + 4 = 0 and x 5 = 0 x = 4 and x = 5 d. 2(7x + 15) = x 14x 30 = x 16x 30 = 18 16x = 48 x = 3 REF: Say It With Symbols Question Bank OBJ: Investigation 3: Solving Equations TOP: Problem 3.4 Solving Quadratic Equations KEY: solve quadratic equation equation 10. ANS: These are all possible answers. a. 21x 63x 2 or 21x(1 3x) b. x(15 + 8x) or 8x x c. 5x 2 9x x + 20x 2 or 25x 2 + 3x + 7 d a + 7b 15a + 6b or 23a + 13b e. 10x 2 14x + 15x 21 or 10x 2 + x 21 REF: Say It With Symbols Question Bank NAT: CC 8.EE.7 CC 8.EE.7.a CC 8.EE.7.b CC 8.F.2 TOP: Problem 2.3 Using Equations KEY: equivalent expressions simplifying expressions 3

8 11. ANS: Many solution paths are possible for each equation. One sample is shown for each. a. 9.5x = 38 (subtract 12.5 from each side) x = 4 (divide each side by 9.5) b. 3x(x + 4) = 0 (use the Distributive Property to factor the expression) x = 0 and x = 4 (use the Zero Product Property) c. x + 4 = 0 when x = 4, and 3x 6 = 0 when x = 2, so the original equation has roots 4 and 2. d. 18x + 30 = 8 + 2x (use the Distributive Property) 16x = 22 (subtract 2x and 30 from both sides) x = = or x = REF: Say It With Symbols Question Bank OBJ: Investigation 3: Solving Equations TOP: Problem 3.4 Solving Quadratic Equations KEY: linear equation quadratic equation solve 12. ANS: a. Value of the Expression When Expression x = 1 x = 2 x = 5 x = 6.5 x = 27 3x (x + 2) (x + 1) b. The numbers in each column are equal. c. Students may remark that the expressions seem to be equivalent. If they recognize the expressions are linear, they can say that they are equivalent. d. Using the Distributive and Commutative properties each expression is equivalent to 3x + 6. Since all the expressions are linear and two values for x give the same value of y, the expressions are equivalent (any linear expression containing the same two points as another linear expression is equivalent to that expression). REF: Say It With Symbols Additional Practice Investigation 1 TOP: Problem 1.2 Determining Equivalence KEY: table evaluate expressions substitute finding patterns MULTIPLE CHOICE 1. ANS: D REF: Say It With Symbols Multiple-Choice Items OBJ: Investigation 3: Solving Equations TOP: Problem 3.3 Factoring Quadratic Expressions KEY: factor quadratic equation 2. ANS: B REF: Say It With Symbols Multiple-Choice Items OBJ: Investigation 3: Solving Equations TOP: Problem 3.1 Solving Linear Equations KEY: linear equation solve 4

9 3. ANS: B REF: Say It With Symbols Multiple-Choice Items OBJ: Investigation 4: Looking Back at Functions NAT: CC 8.EE.7.b CC 8.F.3 CC 8.F.4 CC 8.F.5 CC 8.G.9 TOP: Problem 4.3 Sorting Functions KEY: linear equation 4. ANS: B REF: Say It With Symbols Multiple-Choice Items OBJ: Investigation 3: Solving Equations TOP: Problem 3.4 Solving Quadratic Equations KEY: x-intercepts linear equation quadratic equation 5. ANS: B REF: Say It With Symbols Multiple-Choice Items TOP: Problem 1.2 Determining Equivalence KEY: equivalent expressions 6. ANS: A REF: Say It With Symbols Multiple-Choice Items OBJ: Investigation 3: Solving Equations TOP: Problem 3.4 Solving Quadratic Equations KEY: solve linear equation quadratic equation 7. ANS: B REF: Say It With Symbols Skills Practice Investigation 3 OBJ: Investigation 3: Solving Equations TOP: Problem 3.3 Factoring Quadratic Expressions KEY: polynomial factoring trinomials 8. ANS: B DIF: L1 REF: Say It With Symbols Skills Practice Investigation 3 OBJ: Investigation 3: Solving Equations TOP: Problem 3.3 Factoring Quadratic Expressions KEY: polynomial factoring trinomials 9. ANS: A DIF: L3 REF: Say It With Symbols Skills Practice Investigation 4 OBJ: Investigation 4: Looking Back at Functions NAT: CC 8.EE.7.b CC 8.F.3 CC 8.F.4 CC 8.F.5 CC 8.G.9 TOP: Problem 4.2 Linear Exponential KEY: graphing a nonlinear function 10. ANS: D REF: Say It With Symbols Skills Practice Investigation 1 TOP: Problem 1.4 Revisiting the Distributive Property KEY: binomial area of a triangle distributive property 5