SUMMER PACKET Answer Key

Transcription

1 BELLEVUE SCHOOL DISTRICT SUMMER PACKET Answer Key FOR STUDENTS GOlNG lnto: GEOMETRY

2 Section A1.1.A 1. s = 27 s = 2r a) A. f(n) = b) The number of dollars Julie will get on day 12 is $2048. If you interpreted it as the number of dollars after 12 doublings the answer is $ B. t = 4n a) Let c represent the number of cups in the stack. Then when, H = c or H = (c 1) b) D. 37 cups 5. Let E represent the earnings on day d. a) Plan 1: E = 100 (since the earnings are the same amount each day) Plan 2: (since the earnings double each day, but adjusting for the fact that the earnings don t reach $2 until day 2). b) The values of d are limited to the integers such that for both models. c) Plan 1 provides a total of 31 days x 100 dollars/day = $3100 in earnings. Plan 2 provides a daily earnings of $4096 on August 13, with larger amounts on subsequent days. Therefore, Plan 2 will maximize her earnings. Section A1.1.B / A1.1.C The two websites have equal costs with 4 games and $ Clyde s plumbing company is less expensive when fewer than six hours of plumbing work are completed. (Note that this is because the visit fee includes the first hour of work, so five additional hours causes the two plumbing companies to cost the same amount.) 4. Let Mixture A be the mixture with 85% milk and Mixture B be the mixture with 60% milk. Then, a mixture of one cup of 70% milk should contain 2/5 th of a cup of Mixture A and 3/5 th of a cup of Mixture B.

3 5. a) b) c) Answers may vary. Sample answers include: 6 (or more) DVD players 10 (or more) CD players 3 (or more) DVD players and 5 (or more) CD players Section A1.1.E. 1. a) Exact x-values may vary. x (time, in minutes) y (number of cells) b) Using x and y as defined above: If I is defined as the number of 30-minute intervals, the equation can be written as. c) (or ) d) 1024 bacteria e) After the 10 th 30-minute interval. 2. Only graph B correctly accounts for the negative on the x = 10. This solution can be gathered using tables, graphs, or manual multiplication.

4 4. When x = 0, f(x) = 1. On the graph, this can be seen on the y-intercept. On the table, look for the value where x = 0. Section A1.2.A. 1. None of the answers are correct. In order from least to greatest, the values are: 2. D. Note that this question can be answers by looking at the exponents in ascending order. Section A1.2.B. 1. C is the best answer choice. More specifically, a has to be a fraction that in reduced form has a 1 in the numerator. 2. When. 3. D. when a is negative and n is odd. 4. Square roots are defined when the radicand (the number inside of the radical) is nonnegative. Therefore, the correct answer is when. (none of the answer choices match) Section A1.2.C. 1. or 2. or 3. A is the best answer. 4. D is the best answer. 5. Section A1.3.A. 1. A. D: {-5, 0, 2, 5} R: {-20, 0, 7, 8} B. D: {1, 2, 3, 4, 5} R: {2, 4, 6, 8, 10} C. D: R: D. D: {1, 2, 3, 5, 6} R: {2, 9, 25, 36, 81} 2. A. The expression is a function. B. The expression is a function.

5 3. A. The graph is not a function. The x-value of 3 has more than one y-value. B. The graph is a function. Each x-value has no more than one y-value. 4. The independent variable is n (the number of hours). The dependent variable is f(n) (the number of miles). The domain should be limited to (and perhaps capped at some number indicating that the train can t continue indefinitely) and the range should be limited to (and if the domain is capped, the range should be capped at 85n). 5. The correct answer is D. 6. The correct answer is C. 7. All of listed expressions are functions except for and. Section A1.3.B. 1. Group y = 1/x 1/-5 1/-2-1 Undefined 1 ½ 1/5 y = 5/x -1 5/-2-5 Undefined 5 5/2 1 y = -5/x 1 5/2 5 Undefined -5-5/2-1 The first graph is closest to the axes in quadrants one and three. The second graph is further from the axes in quadrants one and three. The third graph is in quadrants two and four. As the number in the numerator grows more positive, the function stretches further from the axes. If the number in the numerator is negative, it reflects the graph across the x-axis.

6 Group y = (1/x ) /5 5/2 2 Undefined 4 7/2 16/5 y = (1/x ) 3-16/5-7/2-4 Undefined -2-5/2-14/5 The +3 takes the graph of y = 1/x and moves it up 3 units. The -3 moves it down by three units. 2. Pair y = x y = 2x The 2 increases the steepness of the graph. The first equation is closer to the x-axis.

7 Pair y = x y = x The +2 moves the graph of the absolute value function to the left 2 units. The -2 moves the graph of the absolute value function to the right 2 units. Pair y = x y = x

8 The +5 moves the graph of the absolute value function up 5 units. The -5 moves the graph of the absolute value function down 5 units. 3. D. 4. C. 5. a) x Y 1 ½ ¼ 1/8 1/32 1/1024 1/2048 b) c) ( ) 6. a) k = 12

9 b) c) x y Undefined Section A1.3.C. 1. A. 2. x = f(x) = 6 4. Let C represent the cost and p represent the number of people. C(p) = 18p C. $ B. 22 people. Section A.1.4.A. 1. a. One solution b. No solutions c. No solutions d. One solution

10 e. One solution 2. x = -7 and x = 17 x = 17 and x = a. all real numbers b. c. all real numbers d. 4.. The solution is B. (If you selected D here, remember that when multiplying or dividing by a negative number, you have to change the direction of the inequality sign.) 5. D. 4 < x < 9 6. A. x < 0 or x > 3 7. or. The solution is D. Section A.1.4.B. 1. B. 2. A. 3. D. 4. C. 5. A. 6. C. 7. A. 8. D. 9. D. steep increasing line that passes through the point (0, -3) 10. C. gradual increasing line that passes through the point (2, 7) Section A.1.4.C. 1. B. Laura and Catarina are the same distance away at school.

11 2. D. Catarina is traveling at a faster rate than Laura. 3. D. f(g) = 25g C. 36 hours 5. C. 6. A. AB has a slope of and BC has a slope of, which are negative reciprocal slopes. Section A.1.4.D. 1. D. (-1, 0) 2. C. (4, -2) 3. B. 4. B. (2, 6) 5. x = 2 6. Solution: (-4, 7)

12 7. Vertically shaded region represents valid solutions to the first inequality. Horizontally shaded region represents valid solutions to the second inequality. Cross-shaded region represents valid solutions to both inequalities. a) (0, 0) is a solution to the system. b) (-4, 5) is not a solution to the system (it doesn t work for the second inequality). 8. The region that meets both criteria is the unshaded region in answer choice B. Section A.1.4.E. 1. Graph D. 2. Graph A. 3. D. C = $ $75h 4. The coefficient of h is changed from $75 to $ The graph is steeper when the filming costs increase. 6. y-intercept: (0, $5,000) x-intercept: (50, $0)

13 7. C. 35 hours. Section A.1.6.A. 1. a. The median (of $94) is fairly typical of Cathy s average purchases. b. The mean (of $60.50) is the smallest of these three measures, and should be the one Cathy uses to demonstrate the smallest amount of spending. c. The mode (of $99) is the largest of these three measures, and should be the one Cathy uses to demonstrate that she needs an increase in her allowance. 2. a. Tim has the fastest time. b. Tim has the slowest time. c. Jamal is the fastest runner, because all of his one-mile times are faster than at least one of Tim s one-mile times. 3. a. B. 20 b. A. about 8 Section A1.6.B. c. B. The East department gave the least number of citations in one day. 1. a. The graph is misleading for a number of reasons, including: The sum of the percentages in the graph is 80, not 100. The math/computers portion of the circle at 25% represents significantly more than its share of the circle. The arts portion of the circle at 15% represents significantly less than its share of the circle. b. Someone might believe that arts gets very little money, or that math/computers gets nearly half the money. c. Anybody who is interested in a school budget (principals, superintendents, etc.) 2. The conclusion is justified. The completion of homework directly contributes to a student s capacity to do well on tests. 3. The conclusion is not justified. The increased number of police officers is more likely a response to increased crime, rather than a cause of it. 4. The conclusion is not justified. The common variable that connects these two ideas is that people will both rent boats and eat ice cream during the summertime.

14 Section A1.6.C. 1. Mean Median Range Mode Standard Deviation Increase by 10% Increased by 10% No Change Increased by 10% No Change 2. None of the choices! When every employee s salary is doubled, that multiplies the salary by 2. That would double the standard deviation, mean, median, and range. 3. C. Only the mean decreases by $0.25. Section A1.6.D. 1. (Best Fit Line - calculator regression) 2. The y-intercept would represent the number of miles per gallon when the speed is zero (the car is not moving). 3. The slope indicates that for every mile per hour increase in speed, there is a.49 mile per gallon increase in gas mileage. 4. At 100 miles per hour, the car would get miles per gallon using the equation. This seems unlikely. As speed increases, there gets to be a point where gas mileage decreases. 5. A linear function models the data fairly well, but not the situation since the mileage decreases as the speed increases.

15 Section A.1.6.E. 1. A. strong positive 2. D. weak negative 3. E. no correlation Section A1.7.A. 1. A) is best represented by graph b. B) is best represented by graph d. 2. Table B is correct. 3. C. 4. B. $250. Section A1.7.B 1. B B C. Section A1.7.C. 1. D An arithmetic formula should be used, such as 3. D. 4. A geometric formula should be used, such as (4) 5. C A geometric formula should be used, such as. 7. D. about 4216 lemmings Section A1.7.D. 1. B. 2. B. 3. D.