Semester Exam Review ANSWERS. b. The total amount of money earned by selling sodas in a day was at least $1, F 200 F

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1 Unit 1, Topic 1 P W L or P2 L or P L or P L A. 5F 160 C 9 3. B. The equation is always true, because both sides are identical.. A. There is one solution, and it is x C. The equation is never true, because solving gives the statement a. H 00 b. The total amount of money earned by selling sodas in a day was at least $1,000. c. H S F d. S C e. HP FP 2000 H F f. 200 orders of fries were sold F 3F F 200 F 7. 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 Page 1

2 9. a. His score was S b. She got 20 questions wrong. W W W 5 20 W c. He got 1 questions correct C 80 2C 2 C 1 Unit 1, Topic B b 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) a8b 8 True Adding the same number to both sides of an inequality does not change the direction of the inequality. a7b 7 True Subtracting the same number to both sides of an inequality does not change the direction of the inequality. 7a 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 True Dividing both sides of an inequality by a negative number means that the direction of the inequality must be changed. MCPS Page 2

3 12. a. $320 b h 600 c. h 5.5 d 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. x a $69.25 b w w 63 w 16.8 Kendall can buy Young Teen magazine for 16 weeks. MCPS Page 3

4 Unit 1, Topic A. 25 x 16. C x x7 17. a. Month Number of Comic Books that Jared has Number of Comic Books that Sally has b. 12 months after Jared started collecting, or months after Sally started collecting c. 3 m d. 9 m8 e. 16 months (solution below) m m8 3 9 m 3 3 m m8 2m16 m2m16 m 16 MCPS Page

5 18. a. b 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 because the first Bevus bacteria was put in its dish hours after the first Cranicus bacteria was put in. e , 32 2 f. 10 hours (solution below) h h h h 3h5h20 2h 20 h a. x x 27 x 5 b. x1 x x x 5 2x 2 x3 x c. x2 x x x 2x 3x x d. x 1 x3 8 2x 3x x3x9 9 5x 9 x 5 MCPS Page 5

6 Unit 2, Topic a. The price of a pizza is a function of the number of toppings. 21. a. b. P c. 0,1, 2,3, d. No, there is not a constant increase in the price for each additional topping. e ,11.75,12.50,13.00,13.25 w Tw b. Independent Variable: number of games won (w) Dependent Variable: number of prize tokens ( Tw ) c. The number of prize tokens is a function of the number of games won. 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 7. f. { 0, 1, 2, 3,, 5, 6, 7} g. w C. 3, A. The point 5,12 is on the graph of the function f. 2. B. 13 MCPS Page 6

7 25. y Points can be connected by straight or curved lines. O 1 1 x 26. a. 0t 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. 3t 6 or 3,6 f. Five hours after midnight, the temperature of the freezer is 2 o F. 27. 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 1 x ) 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 ( and 8). f. The relation is a function. For every element of the domain, there is exactly one range element. MCPS Page 7

8 28. a. = b. < c. > 29. a. Column A b. Column A c. Column B d. equal e. Column A Unit 2, Topic a. t Option A Option B A t t B t 0 $60,000 0 $60,000 1 $63,000 1 $61,800 2 $66,000 2 $63,65 3 $69,000 3 $65, b. Option A Option B A 0 60, 000 At At 1 3, 000 B 0 60, Bt1 B t c. Option A Option B At 60,000 3,000t Bt 60, t d. Option A Option B A t B t t t 31. D. Sequences 1, 2, and a. 100 coupons after 1 week, 170 coupons after 2 weeks b. 60 coupons after 1 week, 120 coupons after 2 weeks MCPS Page 8

9 33. a. 3, 6, 12, 2, 8 b. I would use the explicit formula. Using the recursive formula, I would start with f 1, then find f 2, f 3, f, and so on until I got to f 30. Using the explicit formula, I just need to substitute into the rule. 3. a. A An An or An An b. $,608 c. B Bn B n d. $6,1 e. n An B n 0 8,192 8, ,1 7,168 2,608 6,1 3 3,56 5,120 2,592, ,9 3, ,58 2,08 7 1, , After the 7 th year, the value of the computer using Option A will be greater. MCPS Page 9

10 35. a. An explicit rule for an arithmetic sequence would be a linear function. 36. a. 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. c. The sequence 10, 12, 1, 16, 18, 20 has a constant difference of 2. d. The sequence 10, 20, 0, 80, 160 has a constant ratio of 2. n R n b. Day 12: n 1 n 12 c. R Rn R n 1 80 d. R n n1 or R n 80n a. or b. t N t MCPS Page 10

11 c Number of Squares Figure Number d. N 1 1 2Nt1 N t e. 1 N t 2 t f. It is a geometric sequence; there is a constant ratio of 2. MCPS Page 11

12 38. a. Joe will charge a total of 25 50x dollars b. Kathy will charge a total of 70 0x dollars c x 70 0x 10x 5 x.5 If a brake job takes.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 p dollars. The total charge for Make Em Envious Emporium will be p dollars p p 5p 200 p 0 If they invite 0 people, then it doesn t matter which location they choose; the cost will be the same. If they invite fewer than 0 people, then Over the Top Party Palace will be cheaper. If they invite more than 0 people, then Make Em Envious Emporium will be cheaper. 0. A. All of the statements below are true. 1. B. exactly 1 solution (the lines have different slope, so they intersect in one point.) 2. B. y 3 MCPS Page 12

13 3. a. 12cg c2g 20 b. Multiply the first equation by 2, then subtract. 2c2g c2g 20 26c 208 c 8 g 10 Old MacDonald has 8 cows and 10 goats.. D. 5. D. MCPS Page 13

14 6. a. wk 1 25w10k 200 b. 20 Hours Worked at the Bike Shop Hours Worked at Piggly Wiggly c. Example: Lance works 8 hours at Piggly Wiggly and hours at the Bike Shop MCPS Page 1

15 7. a. b. 0x30y1200 2x3y90 y 50 Number of Middle School Students Number of High School Students x 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: d. The lines intersect at the point 15,20. MCPS Page 15