Chapter 1 Test Form K

1 Name Class Date Prentice Hall Foundations Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 67 Chapter 1 Test form KDo you know HOW?Identify a pattern and fi nd the next three numbers in the pattern. 1. 25, 21, 3, 7, c 2. 64, 32, 16, 8, c 3. What properties of real numbers are illustrated by each equation below?

2 A. 2813531(28) b. 41(24)50 c. 2(81t)52?812?t d. 78?8751 Evaluate the expression for the given value of the variable. 4. a222(a11); a53 5. 5(2s21)23(s12); s54 6. Th e expression 1515x models the daily cost in dollars of renting scuba gear from the water sports store. In the expression, x represents the number of hours the scuba gear is used. What is the cost of renting scuba gear for a day when the gear is used for 3 hours? Solve each equation. 7. 2r1253r25 8. 8(t11)564 Solve each equation for x. State any restrictions on the variables. 9. xt218135a 10. 6x2155yEach term is 4 more than the previous term; 11, 15, 1917177$30 Commutative Property of AdditionInverse Property of AdditionDistributive PropertyInverse Property of MultiplicationEach term is half of the previous term; 4, 2, 1x58a223t ; tu0 x55y116 Name Class Date Prentice Hall Foundations Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc.

3 , or its affiliates. All Rights Reserved. 68 Write an equation and solve the problem. 11. Two buses leave Columbus, Ohio at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 48 mi/h. When will they be 618 mi apart? Solve each inequality. Graph the solution. 12. 2n11$7 13. 2a15,6a11 Solve each compound inequality. Graph the solutions. 14. 3x#26 or 2x11$3 15. 22t12,4 and 2t,6 Solve each equation. Check for extraneous solutions. 16. u3x13u518 17. ub12u52b 18. Th e weatherman announced that the temperature T over the next few weeks will be at least 648F and at most 788F. Write an absolute value inequality for the temperature over the next few weeks. Do you UNDERSTAND? 19. What is another name for the multiplicative inverse?

4 20. Reasoning Explain in words why 2uxu,24 has no solution. 21. Open-Ended What is the diff erence between simplifying an expression and evaluating an expression? Chapter 1 Test (continued) form K6 h21034562103456nL3aS121 RtR3x55 or x527 or xL1b52 3 2 10123 3 2 10123reciprocalAnswers may vary. Sample: Dividing both sides by 2 gives |x|R22. The absolute value of any number must be nonnegative, so the inequality has no may vary. Sample: Simplifying an expression is rewriting it using the properties of real numbers and combining like terms, resulting in a simpler expression.

5 Evaluating an expression is substituting values for the variables, resulting in a numerical Hall Foundations Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 87 Name Class Date Do you know HOW?Determine whether each relation is a function. 1. 5(0, 2), (4, 3), (5, 5), (4, 7)6 2. 5(21, 0), (25, 2), (0, 4), (2, 28)6 Evaluate each function for the given value of x, and write the input x and output f(x) as an ordered pair. 3. f(x)57x15 for x522 4. f(x)514 x26 for x58 For each function, determine whether y varies directly with x.

6 If so, fi nd the constant of variation, and write the function rule. 5. 6. Graph each equation. 7. 4x23y522 8. 31x1y50 Write in point-slope form an equation of the line through each pair of points. 9. (5, 8) and (0, 22) 10. (1, 3) and (6, 22) Chapter 2 Test form Kxy358122032xy6915111420no(22, 29)yes; k 5 4; y 5 4xno(8, 24)yesxy 2 222 Oxy 42y2852(x25) or y1252(x20)y2352(x21) or y1252(x26)Prentice Hall Foundations Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 88 Name Class Date Write the function rule g(x) for the given transformations applied to the graph of f(x) 5 x2.

7 11. 4 units down, 12. 7 units up, 1 unit left 3 units right Graph each equation. Th en describe the transformation from the parent function f(x) 5 |x|. 13. y5|x22| 14. y52|x|Graph each absolute-value inequality. 15. y,u3xu11 16. y23$ux15uDo you UNDERSTAND? 17. If y varies directly with x and y518 when x56, what is the constant of variation? Find the value of y when x510. 18. Open-Ended Graph a line that has a slope that is undefi ned. 19. Suppose you manufacture and sell tarps. Th e table at the right displays your current sizes and prices. a. Draw a scatter plot showing the relationship between the area of a tarp and its price. Use area as the independent variable. b. Draw a trend line and write the equation.

8 C. Reasoning Is this an accurate model? Explain. d. Using your model, predict the price of a 250 ft2 2 Test (continued) form KPriceSize (ft2)354880120192200320$ $ $ $ $ $ $ 200300g(x)5(x11)224translation 2 units rightrefl ection in the x-axisg(x)5(x23)217b. Equations should be close to Yes; all the points are very close to the line, so the linear model is about $ 24O 2 4yx2 2 44 Oxy 2224 Oxy 2 4 6246k53; y530 Answers may vary. Sample: a graph of any vertical lineName Class Date Prentice Hall Foundations Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc.

9 , or its affiliates. All Rights Reserved. 67 Chapter 3 Test form KDo you know HOW?Solve each system by substitution or elimination. 1. e2x2y576x23y514 2. e5x12y51226x22y5214 3. e5x12y5284x13y52 Graph the solution of each system. 4. ey$22x13y,x 5. ey21#3xy11#x 6. #2x11 7. You have 13 bills in your wallet in $1, $5, and $10 bills. Th ere are twice as many $1 bills as $5 bills. Th e number of $10 bills is one more than the number of $5 bills. How many of each bill do you have? How much money do you have? Graph the system of constraints.

10 Identify all vertices. Find the values of x and y that maximize or minimize the objective function. Th en fi nd the maximum or minimum value. 8. y#2x174y#x18x$0, y$0 Maximize for P 5 5x 1 2yyx 2 22 4 44yx 22 4 442yx 224642yx4646A(0, 0)B(0, 2)D(7, 0)C(4, 3)2no solution(2, 1)(24, 6)six $1 bills, three $5 bills, four $10 bills; $61max P at (7, 0) 5 35 Name Class Date Prentice Hall Foundations Algebra 2 Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 68 Chapter 3 Test (continued) form K 9.