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ALGEBRA 1 A Semester Exam Review ANSWERS Algebra 1 A Semester Exam Review Answers 2015-2016 MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS Unit 1, Topic 1 P 2L 1 P 1 or P 2 L or L or P L 2 2 2 2 1. W 2. A. C 3. B. The equation is always true, because both sides are identical. 4. A. There is one solution, and it is x 30 . 5. C. The equation is never true, because solving gives the statement 27 15 . 6. a. H 400 b. The total amount of money earned by selling sodas in a day was at least $1,000. c. H SF d. S C e. H PH F PF 2000 5 F 160 9 1500 F 3F 700 f. 7. 200 orders of fries were sold. 800 4 F 200 F Distributive Property Addition Property of Equality Multiplication Property of Equality 8. Subtraction Property of Equality (Addition Property is ok) Multiplication Property of Equality Distributive Property MCPS © 2015–2016 ALGEBRA 1 A 9. a. Semester Exam Review ANSWERS His score was 69. S 2 36 b. 12 69. 4 She got 20 questions wrong. 53 2 29 53 58 W 4 W 4 W 4 20 W 5 c. He got 41 questions correct. 8 4 80 2C 2 80 2C C 41 Unit 1, Topic 2 10. B. 20.00 3.75b 41.25 11. Statement True or False? Justification (Note: It is ok to pick two numbers for a and b and show that the statements are true or false based on those numbers) a 8 b8 True Adding the same number to both sides of an inequality does not change the direction of the inequality. a7 b7 True Subtracting the same number to both sides of an inequality does not change the direction of the inequality. 7 a 7b False Multiplying the same side of the inequality by a negative number means that the direction of the inequality must be changed. a b 10 10 True Dividing both sides of an inequality by a negative number means that the direction of the inequality must be changed. MCPS © 2015–2016 ALGEBRA 1 A 12. Semester Exam Review ANSWERS a. $320 b. 50 100h 600 c. h 5.5 d. 0 1 2 3 4 5 6 7 e. In order for Mr. Flood to pay at most $600, the plumber can spend at most 5.5 hours fixing the leak. 13. B. 4 x 9 17 14. a. 88 5 3.75 $69.25 b. 88 3.75w 25 3.75w 63 w 16.8 Kendall can buy Young Teen magazine for 16 weeks. MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS Unit 1, Topic 3 15. A. 25x 16. C. 164 x 16 x 7 17. a. Month 0 1 2 3 4 5 6 7 8 9 10 Number of Comic Books that Jared has 1 3 9 27 81 243 729 2187 6561 19683 59049 Number of Comic Books that Sally has 1 9 81 b. 12 months after Jared started collecting, or 4 months after Sally started collecting c. 3m d. 9m8 e. 16 months (solution below) 3m 9m8 2 m8 3m 3 3m 32 m16 m 2m 16 m 16 MCPS © 2015–2016 ALGEBRA 1 A 18. a. 84 4096 b. 322 1024 c. The number of Cranicus bacteria h hours after on cell of Cranicus bacteria was put in the dish. d. The number of Bevus bacteria h hours after one cell of Cranicus bacteria was put in its dish. The exponent is h 4 because the first Bevus bacteria was put in its dish 4 hours after the first Cranicus bacteria was put in. e. 8 2 3, 32 2 5 f. 10 hours (solution below) 8h 32h4 5 h4 23h 2 3h 5h 20 2h 20 h 10 19. a. 3x 2 37 x27 x5 19. Semester Exam Review ANSWERS b. 25 x 1 5 x 3 2 x 1 5 5 x 3 2x 2 x 3 x 5 MCPS © 2015–2016 ALGEBRA 1 A 19. Semester Exam Review ANSWERS c. 9 x 2 27 x 2 x2 3 33 x 2 x 4 3x x4 19. d. 1x 8 x 3 4 3 x 3 22 x 2 2 x 3 x 9 9 5x 9 x 5 Unit 2, Topic 1 20. 21. a. The price of a pizza is a function of the number of toppings. b. P 2 12.50 c. 0,1, 2,3, 4 d. No, there is not a constant increase in the price for each additional topping. e. 10.75,11.75,12.50,13.00,13.25 a. b. w T w 0 2 4 50 66 82 Independent Variable: number of games won (w) Dependent Variable: number of prize tokens ( T w ) c. The number of prize tokens is a function of the number of games won. MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS d. The variables are discrete. The number of games won and the number of prize tokens can be whole numbers only. e. The number of prize tokens after winning 3 games is 74. f. { 0, 1, 2, 3, 4, 5, 6, 7} g. w5 22. C. 3, 2 23. A. The point 5,12 is on the graph of the function f. 24. B. 13 y 25. Points can be connected by straight or curved lines. 1 O 26. 1 x a. 0 t 7 or 0, 7 b. 3 F 3 or 3,3 c. The temperature when t 0 or the temperature at midnight. d. t 6 e. 3 t 6 or 3, 6 f. Five hours after midnight, the temperature of the freezer is –2o F. MCPS © 2015–2016 ALGEBRA 1 A 27. 28. 29. Semester Exam Review ANSWERS a. The relation is a function. For every element of the domain, there is exactly one range element. b. The relation is NOT a function. Several elements of the domain (for example x 1 ) has multiple range elements paired with it. c. The relation is NOT a function. The domain element 2 is paired with two different range elements (7 and 12). d. The relation is a function. For every element of the domain, there is exactly one range element. e. The relation is NOT a function. The domain element 5 is paired with two range elements (4 and 8). f. The relation is a function. For every element of the domain, there is exactly one range element. a. = b. < c. > a. Column A b. Column A c. Column B d. equal e. Column A MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS Unit 2, Topic 2 30. a. Option A Option B t A t t B t 0 1 2 3 $60,000 $63,000 $66,000 $69,000 0 1 2 3 $60,000 $61,800 $63,654 $65,563.62 b. Option A Option B A 0 60, 000 B 0 60, 000 A t A t 1 3, 000 B t 1.03 B t 1 c. Option A Option B A t 60, 000 3, 000t d. B t 60, 000 1.03t Option A Option B t 31. D. Sequences 1, 2, and 3 32. a. 100 coupons after 1 week, 170 coupons after 2 weeks b. 60 coupons after 1 week, 120 coupons after 2 weeks MCPS © 2015–2016 t ALGEBRA 1 A 33. Semester Exam Review ANSWERS a. 3, 6, 12, 24, 48 b. I would use the explicit formula. Using the recursive formula, I would start with f 1 , then find f 2 , f 3 , f 4 , and so on until I got to f 30 . Using the explicit formula, I just need to substitute into the rule. 34. A 0 8192 a. 3 A n A n 1 or A n 0.75 A n 1 4 b. $4,608 c. d. B 0 8192 B n B n 1 1024 $6,144 e. n A n B n 0 1 2 3 4 5 6 7 8 8,192 6,144 4,608 3,456 2,592 1,944 1,458 1,093.50 820.13 8,192 7,168 6,144 5,120 4,096 3,072 2,048 1,024 0 After the 7th year, the value of the computer using Option A will be greater. MCPS © 2015–2016 ALGEBRA 1 A 35. Semester Exam Review ANSWERS a. An explicit rule for an arithmetic sequence would be a linear function. b. The recursive formula f 0 20, f n 30 f n 1 represents a geometric sequence; its explicit rule would be an exponential function. 36. c. The sequence 10, 12, 14, 16, 18, 20 has a constant difference of 2. d. The sequence 10, 20, 40, 80, 160 has a constant ratio of 2. a. b. n R n 1 2 3 4 5 6 700 780 860 940 1020 1100 Day 12: 1580 700 80 n 1 n 12 c. R 1 700 R n R n 1 80 d. R n 700 80 n 1 or R n 80n 620 MCPS © 2015–2016 ALGEBRA 1 A 37. Semester Exam Review ANSWERS a. or b. c. t N t 1 2 3 4 5 6 7 1 2 4 8 16 32 64 130 120 110 100 Number of Squares 90 80 70 60 50 40 30 20 10 0 0 d. 1 2 3 Figure Number 4 5 6 7 N 1 1 N t 2 N t 1 e. N t 2t 1 f. It is a geometric sequence; there is a constant ratio of 2. MCPS © 2015–2016 ALGEBRA 1 A 38. a. Joe will charge a total of 25 50x dollars b. Kathy will charge a total of 70 40 x dollars Semester Exam Review ANSWERS c. 25 50 x 70 40 x 10 x 45 x 4.5 If a brake job takes 4.5 hours, the total charge will be the same. 39. Let p represent the number of people they will invite. The total charge for Over the Top Party Palace will be 100 15 p dollars. The total charge for Make ‘Em Envious Emporium will be 300 10 p dollars. 100 15 p 300 10 p 5 p 200 p 40 If they invite 40 people, then it doesn’t matter which location they choose; the cost will be the same. If they invite fewer than 40 people, then Over the Top Party Palace will be cheaper. If they invite more than 40 people, then Make ‘Em Envious Emporium will be cheaper. 40. A. All of the statements below are true. 41. B. exactly 1 solution (the lines have different slope, so they intersect in one point.) 42. B. y 3 MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS 43. a. b. 12c g 106 50c 2 g 420 Multiply the first equation by 2, then subtract. 24c 2 g 212 50c 2 g 420 26c 208 c 8 g 10 Old MacDonald has 8 cows and 10 goats. 44. D. 45. D. MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS 46. a. s k 14 25s 10k 200 b. 20 18 Hours Worked at the Bike Shop 16 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 Hours Worked at the Supermarket c. Example: Lance works 8 hours at the Supermarket and 4 hours at the Bike Shop. 8 4 12 14 25 8 4 10 300 200 MCPS © 2015–2016 ALGEBRA 1 A Semester Exam Review ANSWERS 47. a. 40 x 30 y 1200 2 x 3 y 90 b. y Number of Middle School Students 50 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 35 40 45 50 x Number of High School Students c. Choose any point in the viable region and show that its coordinates make each inequality true. For example: 25 high school students and 10 middle school students: 40 25 30 10 1300 1200 2 25 3 10 80 90 d. The lines intersect at the point 15, 20 . MCPS © 2015–2016