Topic 1 Practice Test- Mrs. Daniel Algerba 1

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1 Name: Class: Date: ID: A Topic 1 Practice Test- Mrs. Daniel Algerba 1 1. Solve the equation q 3 = 31. Write a reason for each step. 2. Solve 39 = 9 2z. Write a reason for each step. 3. Solve 3(a + 3) 6 = 21. Write a reason for each step. 4. You want to know the number of minutes that you can use on a $20.00 phone card. The card company charges $0.50 for the card and $0.10 for each minute used. The equation $ $0.10m = $20.00, where m is the number of minutes on the card, represents this situation. Solve the equation and write a reason for each step. If necessary, round your answer to the nearest hundredth. 5. Solve 3(a + 3) 6 = 21. Write a reason for each step. 6. Find the total weight of the boxes of cheddar cheese in a shipment of 3 lb boxes of cheddar cheese and 2 lb boxes of Swiss cheese. (1) There were 20 fewer 2 lb boxes of Swiss cheese than 3 lb boxes of cheddar cheese. (2) The total weight of the shipment was 510 lb. As part of your solution, fill in the table below. Define any variables you use to solve the problem. Weight per box (lb) Number of boxes = T otal weight (lb) Cheddar??? Swiss??? 7. The size of Cooper s garden is 14 square feet more than the size of Elena s garden. Write an algebraic expression for the size of Cooper s garden. Be sure to indicate what the variable in your expression represents. 8. Dave s favorite baseball team has won 10 fewer games than Kimiko s favorite baseball team. Write an algebraic expression for the number of games Dave s favorite team has won. Be sure to indicate what the variable in your expression represents. 9. Ms. Sanders invested in a stock. During the first year, the value of the stock tripled. The next year, the value of the stock decreased by $600. Write an expression that can be used to represent the value of her stock at the end of the second year. Be sure to indicate what the variable in your expression represents. 10. Write an algebraic expression that represents 2 less than 18 times a number? A 18(x 2) C 18x 2 B 2 18x D 2x 18 1

2 Name: ID: A 11. How many terms are in the algebraic expression 2x 9xy + 17y? A 1 C 3 B 17 D At the zoo, a child pays c dollars for a ticket and an adult pays g dollars. Explain in words the meaning of g = 2c. A An adult ticket costs twice as much as a child ticket. B An adult ticket costs half as much as a child ticket. C Twice as many child tickets as adult tickets are sold. D Half as many adults as children go to the zoo. 13. Hana makes beaded bracelets for sale. The materials for each bracelet cost $2.00 and she sells the bracelets for $7.25 each. To find her profits, she writes the equation p = 7.25x 2.00x. Explain what the variable x represents. A profit from the sales C number of bracelets sold B cost of materials D total amount of sales 14. Salvador s class has collected 88 cans in a food drive. They plan to sort the cans into x bags, with an equal number of cans in each bag. Write an expression to show how many cans there will be in each bag. A 88 x C 88 + x B 88x D 88 x 15. Juan scored 26 points in the first half of the basketball game, and he scored n points in the second half of the game. Write an expression to determine the number of points he scored in all. Then, find the number of points he scored in all if he scored 18 points in the second half of the game. A 26 + n; 44 points C 26n; 44 points 26 B ; 8 points D 26 n; 8 points n 16. A theme park costs $25.00 to enter. One of the food stands within the park sells hot dogs for $2.50 each and hamburgers for $3.50 each. If Paul enters the park, walks to the food stand, and purchases d hot dogs and b hamburgers, the amount of money m he spends can be modeled by the equation m = 2.5d + 3.5b Which of the following are correct interpretations for parts of this equation? A B C D E F G H 2.5d represents the cost of entering the park. 2.5d represents the cost of purchasing d hot dogs. 2.5d represents the cost of purchasing d hamburgers. 3.5b represents the cost of entering the park. 3.5b represents the cost of purchasing b hot dogs. 3.5b represents the cost of purchasing b hamburgers. 25 represents the cost of entering the park. 25 represents the cost of purchasing d hot dogs and b hamburgers. 2

3 Name: ID: A 17. Maria buys lunch every work day. She always eats at the same restaurant and spends no more than $5.25 for lunch. She has created a budget in which she has allowed herself $1700 for the year to buy lunches during her five-day work week. Assume Maria spends the maximum she allows for each lunch. Write an equation to determine how much of her budget, in dollars, remains unspent at the end of a particular week of the year? Include definitions of the variables you used. A B = 26.25n 1700, where B is her budget balance and n is the number of complete weeks of work B B = 5.25n 1700, where B is her budget balance and n is the number of complete weeks of work C B = n, where B is her budget balance and n is the number of complete weeks of work D B = n, where B is her budget balance and n is the number of complete weeks of work 18. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions. A 100 n 240 B 100 n 240 C n 240 D 100 < n < John is considering accepting one of two sales positions. ABC Company offers a yearly salary of $45,000. XYZ Company offers a yearly salary of $38,000 plus a 2% annual commission on sales. For what amount of sales s is the salary at XYZ Company greater than the salary at ABC Company? A s > 7000 C s > 70,000 B s > 35,000 D s > 350, The maximum capacity of a theater is 471 people. So far, 254 people are seated in the theater. Which inequality can be solved to show the number of people p that can still enter the theater? A p < 471 C p > 471 B p 471 D p 471 3

4 Name: ID: A 21. Jennifer, Luis, Robert, Anna, and Tonya are figuring out how to split the check for lunch. The total bill, with tax and tip, is $ Anna puts in $15, and Tonya puts in $8. The rest of the group splits the rest of the bill equally. Which equation and solution represent the amount a that each of the remaining people pay? A 3a + 23 = 65.45; a = $14.15 B 5a = ; a = $17.69 C 3a = 88.45; a = $29.49 D 5a + 23 = 65.45; a = $ An essay must be at least 500 words long to be accepted. Define a variable and write an inequality for the acceptable number of words in an essay. Graph the solutions. 23. While rock climbing, Farrell starts at 10 feet above sea level and climbs upward at a rate of 3 feet per minute. Theresa starts at 250 feet above sea level and climbs down at a rate of 2.5 feet per minute. Tell whether each equation can be used to find the time t in minutes it takes for the two climbers to reach the same height. a t = t Yes No b t = t Yes No c. 3t + 2.5t = 240 Yes No d. 3t = 2.5t Yes No 24. Which problem could be solved using the inequality 2c < 70? A The product of 2 and a number is equal to 70. B Two students split a restaurant bill that came to $70. C Two equal-priced shirts came to at least $70. D Marty earned under $70 for 2 hours of work. 25. Solve 3 4 x = 2. A 3 8 C 3 2 B 2 3 D Solve 54 = a A 32 B Solve 8m = 48. A 6 B 6 C 40 D 56 4

5 Name: ID: A 28. Solve 13m = 156. A 13 C 12 B 12 D Which is the graph of 6x < 12 OR 3x 9? A B C D 30. Solve 2 ( a + 8) > 18. A a > 1 C a > 13 B a > 5 D a > Solve 2 10 b = 99. A b = 20 C b = 10 B b = 495 D b = Solve 50q 43 = 52q 81. A q = 38 C q = 38 B q = 19 D q = Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week. Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how many more songs Carlotta can download. A s 3 B s > 3 C s 3 D s < 3 5

6 Name: ID: A 34. Which graph shows the solutions of 4x 6 > 2x 9? A C B D 35. A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an equation to find the salaries for the second month if the first month s salaries are $10,205. A 10,205 + x = 21,894 The salaries for the second month are $32,099. B 10,205 + x = 21,894 The salaries for the second month are $11,689. C 10,205 + x = 21,894 The salaries for the second month are $21,894. D 10,205 + x = 21,894 The salaries for the second month are $10, Solve the inequality. 30 4a (2 3 a) 37. Solve the equation. 1 = d Solve the equation. 3 ( x + 1) 1 = 3x Ernesto and his family have just finished dinner at a restaurant in a region where meal tax is 5% of the price of the meal. Ernesto leaves a 17% tip. With tax and tip, the total cost is $ The equation = 0.05p p + p, where p is the price of the meal without tax or tip, can be used to model this situation. Determine which of the following could be steps in calculating the price of the meal p. a. 23p = Yes No b. p p = Yes No c. p = Yes No 1.22 d. p ( ) = Yes No e. p Yes No 1.22 =

7 Name: ID: A 40. Solve A = bh for b. A b = Ah C b = ha B b = A h D b = h A 41. Solve z = 9 c for c. 13 A c = 9 13 z C c = 9 13 z B c = 13 9 z D c = 13 9 z 42. Solve y = 5 b + 10 for b. 8 A b = 8 5 y + 16 C b = 5 8 y 10 B b = 8 5 y 16 D b = 5 8 y The coefficient of friction, µ, is a ratio that compares the friction acting on a dragged object to its weight, w. The relationships between the mass m and the acceleration a of an object that is being dragged across a flat surface, such as a table top, by a force F, is given by the equation ma = F µw. What formula can you use to find the coefficient of friction? A µ = ma F C µ = F ma w w B µ = ma F + w D µ = F ma w 44. The formula for the resistance of a conductor with voltage V and current I is r = V. Solve for V. I A I = Vr C V = I r B V = r I D V = Ir 7

8 Name: ID: A 45. Solve A = 1 bh for h. 2 A B C D h = A 2b h = b 2A h = 2A b h = A 1 2 B 46. Solve 300 = xq + n for x. 47. Solve 10q + 15n = 49 for q. 8

9 ID: A Topic 1 Practice Test- Mrs. Daniel Algerba 1 Answer Section 1. ANS: q = 31 Given 3 ( 3)( q 3 ) = ( 31) ( 3 ) Multiplication Property of Equality q = 93 PTS: 1 DIF: DOK 1 NAT: A-REI.A.1 A-REI.B.3 STA: MACC.912.A-REI.1.1 TOP: Apply Properties of Equality KEY: proof justification justify linear equation 2. ANS: 39 = 9 2z Given 9 9 Subtraction Property of Equality 30 = 2z 30 2 = 2z 2 Division Property of Equality 15 = z PTS: 1 DIF: DOK 1 NAT: A-REI.A.1 A-REI.B.3 STA: MACC.912.A-REI.1.1 TOP: Apply Properties of Equality KEY: proof justification justify linear equation 3. ANS: 3(a + 3) 6 = 21 Given 3a = 21 Distributive Property 3a + 3 = 21 3a + 3 = 21 Subtraction Property of Equality 3 3 3a = 18 3a 3 = 18 Division Property of Equality 3 a = 6 PTS: 1 DIF: DOK 1 NAT: A-REI.A.1 A-REI.B.3 STA: MACC.912.A-REI.1.1 TOP: Apply Properties of Equality KEY: proof justification justify linear equation 1

10 ID: A 4. ANS: m = Given m = m = m = 195 Subtraction property of equality Division property of equality The phone card can be used for 195 minutes. PTS: 1 DIF: DOK 2 NAT: A-REI.A.1 A-REI.B.3 STA: MACC.912.A-REI.1.1 TOP: Apply Properties of Equality KEY: equation word property algebra algebraic two-step proof justification justify linear equation 5. ANS: 3(a + 3) 6 = 21 Given 3a = 21 Distributive Property 3a + 3 = 21 3a + 3 = 21 Subtraction Property of Equality 3 3 3a = 18 3a 3 = 18 Division Property of Equality 3 a = 6 PTS: 1 DIF: DOK 1 NAT: A-REI.A.1 A-REI.B.3 STA: MACC.912.A-REI.1.1 TOP: Apply Properties of Equality KEY: proof justification justify linear equation 2

11 ID: A 6. ANS: The total weight of the boxes of cheddar cheese was 330 pounds. Sample explanation: Let c be the number of boxes of cheddar cheese. Weight per box (lb) Number of boxes = T otal weight (lb) Cheddar 3 c 3c Swiss 2 c 20 2(c 20) Since the total weight of the shipment was 510 lb: 510 = 3c + 2(c 20) 510 = 3c + 2c = 5c = 5c 110 = c There were 110 boxes of cheddar cheese in the shipment. Since each box of cheddar cheese weighs 3 lb, the total weight of the boxes of cheddar cheese was 110 boxes 3 lb/box = 330 lb. PTS: 1 DIF: DOK 2 NAT: N-Q.A.1 N-Q.A.2 STA: MACC.912.N-Q.1.1 LOC: NCTM.PSSM.00.MTH.9-12.ALG.2.c NCTM.PSSM.00.MTH.9-12.ALG.3.b NCTM.PSSM.00.MTH.9-12.PRS.3 NCTM.PSSM.00.MTH.9-12.REP.2 KEY: problem solving chart mixture 7. ANS: Let E represent the size of Elena s garden. Then E + 14 represents the size of Cooper s garden. PTS: 1 DIF: DOK 2 NAT: N-Q.A.2 STA: MACC.912.N-Q.1.2 TOP: Expressions and Variables KEY: variable word expression write relationship 8. ANS: Let K represent the number of games won by Kimiko s favorite team. Then K 10 represents the number of games won by Dave s favorite team. PTS: 1 DIF: DOK 2 NAT: N-Q.A.2 STA: MACC.912.N-Q.1.2 TOP: Write Expressions KEY: word expression relationship variable write 9. ANS: Let d represent the amount of the original investment in dollars. Then 3d 600 represents the value of the stock at the end of the second year. PTS: 1 DIF: DOK 2 NAT: N-Q.A.2 STA: MACC.912.N-Q.1.2 TOP: Variables and Expressions KEY: variable word expression real-life 3

12 ID: A 10. ANS: C PTS: 1 DIF: DOK 1 NAT: A-SSE.A.1a STA: MACC.912.A-SSE.1.1a KEY: variable expressions 11. ANS: C PTS: 1 DIF: DOK 1 NAT: A-SSE.A.1a STA: MACC.912.A-SSE.1.1a KEY: variable expressions 12. ANS: A PTS: 1 DIF: DOK 2 NAT: A-SSE.A.1a STA: MACC.912.A-SSE.1.1a KEY: variable expressions 13. ANS: C PTS: 1 DIF: DOK 2 NAT: A-SSE.A.1a STA: MACC.912.A-SSE.1.1a KEY: variable expressions 14. ANS: D PTS: 1 DIF: DOK 1 OBJ: Translating from Words to Algebraic Symbols NAT: A-SSE.A.1a A-SSE.A.1b STA: MACC.912.A-SSE.1.1 LOC: MTH.C TOP: Variables and Expressions KEY: expression algebraic expression 15. ANS: A PTS: 1 DIF: DOK 1 OBJ: Application NAT: A-SSE.A.1a A-SSE.A.1b STA: MACC.912.A-SSE.1.1 LOC: MTH.C MTH.C TOP: Variables and Expressions KEY: algebraic expression word problem operation 16. ANS: B, F, G The problem statement says that the stand sells hot dogs for $2.50 each, so 2.5d represents the cost of purchasing d hot dogs. The problem statement says that the stand sells hamburgers for $3.50 each, so 3.5b represents the cost of purchasing b hamburgers. The problem statement says that the theme park costs $25.00 to enter, so 25 represents the cost of entering the park. Correct Incorrect Feedback That s correct! Review the scenario to determine what each number in the equation represents. PTS: 2 DIF: DOK 1 NAT: A-SSE.A.1a* STA: MACC.912.A-SSE.1.1a KEY: terms of expressions coefficients 17. ANS: D PTS: 1 DIF: DOK 2 NAT: N-Q.A.2 STA: MACC.912.N-Q.1.2 TOP: Writing Two-Step Equations KEY: two-step solve equation real-life 18. ANS: B PTS: 1 DIF: DOK 2 OBJ: Application NAT: A-CED.A.1 STA: MACC.912.A-CED.1.1 LOC: MTH.C MTH.C TOP: Solving Compound Inequalities KEY: inequalities compound 19. ANS: D PTS: 1 DIF: DOK 2 NAT: A-CED.A.1 A-REI.B.3 STA: MACC.912.A-CED ANS: B PTS: 1 DIF: DOK 2 NAT: A-CED.A.1 STA: MACC.912.A-CED.1.1 4

13 ID: A 21. ANS: A Anna and Tonya pay a total of $15 + $8 = $23, so this plus 3 times the amount Jennifer, Luis, and Robert each pay totals $65.45: 3a + 23 = a = a = a = = Feedback A That s correct! B The remainder of the bill is divided among 3 people, not 5, and the amount owed by those 3 people is the bill minus Anna s and Tonya s contributions. C The amount owed by the remaining 3 people is the total bill minus Anna s and Tonya s contributions. D The remainder of the bill is divided among 3 people, not 5. PTS: 1 DIF: DOK 2 NAT: A-CED.A.1* MP.4 STA: MACC.912.A-CED.1.1 KEY: linear equations 22. ANS: w = number of words; w 500 PTS: 1 DIF: DOK 1 NAT: A-CED.A.1 STA: MACC.912.A-CED ANS: a. Yes b. No c. Yes d. No PTS: 2 DIF: DOK 2 NAT: A-CED.A.1* MP.4 STA: MACC.912.A-CED.1.1 KEY: linear equations 24. ANS: D PTS: 1 DIF: DOK 2 NAT: A-CED.A.3 STA: MACC.912.A-CED.1.3 TOP: Solve Inequalities Using Multiplication and Division KEY: inequality word translate 25. ANS: D PTS: 1 DIF: DOK 1 NAT: A-REI.B ANS: A PTS: 1 DIF: DOK 1 NAT: A-REI.B ANS: A PTS: 1 DIF: DOK 1 NAT: A-REI.B ANS: C PTS: 1 DIF: DOK 1 NAT: A-REI.B.3 5

14 ID: A 29. ANS: D PTS: 1 DIF: DOK 1 NAT: A-REI.B ANS: A PTS: 1 DIF: DOK 1 NAT: A-REI.B ANS: B PTS: 1 DIF: DOK 2 OBJ: Solving Equations That Contain Fractions NAT: A-REI.B.3 LOC: MTH.C TOP: Solving Equations by Multiplying or Dividing 32. ANS: D PTS: 1 DIF: DOK 2 OBJ: Solving Equations with Variables on Both Sides NAT: A-REI.B.3 LOC: MTH.C MTH.C TOP: Solving Equations with Variables on Both Sides KEY: equation two-step multi-step 33. ANS: A PTS: 1 DIF: DOK 2 OBJ: Problem-Solving Application NAT: A-CED.A.1 A-REI.B.3 STA: MACC.912.A-CED.1.1 LOC: MTH.C MTH.C TOP: Solving Inequalities by Adding or Subtracting KEY: solving inequality word problem 34. ANS: B PTS: 1 DIF: DOK 2 NAT: A-REI.B ANS: B PTS: 1 DIF: DOK 2 OBJ: Application NAT: A-CED.A.1 A-REI.B.3 STA: MACC.912.A-CED.1.1 LOC: MTH.C MTH.C TOP: Solving Equations by Adding or Subtracting KEY: equation solving addition subtraction 36. ANS: a 16 PTS: 1 DIF: DOK 1 NAT: A-REI.B ANS: d = 130 PTS: 1 DIF: DOK 2 NAT: A-REI.B ANS: x =all real numbers PTS: 1 DIF: DOK 2 NAT: A-REI.B ANS: a. No b. No c. Yes d. Yes e. No PTS: 2 DIF: DOK 2 NAT: A-REI.B.3 MP.4 KEY: solving equations modeling 40. ANS: B PTS: 1 DIF: DOK 1 NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 6

15 ID: A 41. ANS: D PTS: 1 DIF: DOK 1 NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b TOP: Rewrite Equations and Formulas KEY: equation solve 42. ANS: B PTS: 1 DIF: DOK 1 NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b TOP: Rewrite Equations and Formulas KEY: equation solve 43. ANS: D PTS: 1 DIF: DOK 1 NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b NCTM.PSSM.00.MTH.9-12.PRS.2 TOP: Rewrite Equations and Formulas KEY: solve equation word real-life formula 44. ANS: D PTS: 1 DIF: DOK 2 OBJ: Solving Formulas for a Variable NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 LOC: MTH.C TOP: Solving for a Variable KEY: literal equation solving variables 45. ANS: C PTS: 1 DIF: DOK 2 NAT: A-CED.A.4 STA: MACC.912.A-CED ANS: x = 300 n q PTS: 1 DIF: DOK 1 NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b TOP: Rewrite Equations and Formulas KEY: equation solve 47. ANS: 49 15n q = 10 PTS: 1 DIF: DOK 1 NAT: A-CED.A.4 STA: MACC.912.A-CED.1.4 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b TOP: Rewrite Equations and Formulas KEY: equation solve 7