Int Math 1 Midterm Review Handout (Modules 1-5) 1 Short Answer: (Put answer in box below.) A small hotel with 4 rooms was destroyed in a fire. After the hotel was rebuilt, the owner took out a loan to buy new beds. The recursive rule a 1 = $7,200,a n = a n 1 $720 gives the amount left on the loan at the beginning of month n. Write an explicit rule for the sequence. 2 Which graph below would match the situation described? A car travelling at 22 mi/h accelerates to 46 mi/h in 5 seconds. It maintains that speed for the next 5 seconds, and then slows to a stop during the next 5 seconds. A C B D 3 Evaluate the algebraic expression 9(x + y) 2 when x = 5 and y = 3. A 5184 C 576 B 99 D 288 1
4 Short Answer: (Put answer in box below.) Write 3x 4y = 6 as a function of x. 5 Aaron graphed the ordered pairs generated by f( 8), f( 3), f( 2), f(1), f(2), f(5), f(6), and f(8) on a coordinate plane. He then connected the points as shown. What is f(x)? A f(x) = 2x + 1 C f(x) = x 1 B f(x) = 2x 1 D f(x) = x 2 2
6 You rode your bicycle for 35 minutes and burned 210 calories. How many calories did you burn per minute? A 245.053 calories per minute C 7 calories per minute B 245 calories per minute D 6 calories per minute 7 Short Answer: (Put answer in box below.) Complete the table. Then graph the function. y = 2 3 x 3 x 3 2 0 2 3 y 8 If a coordinate pair (x, y) makes the equation 5x + 3y = 6 true, which of the following statements is true? A B The point (x, y) is not on the graph of 5x + 3y = 6. The point (x, y) is on the graph of 5x + 3y = 6. C D These values of x and y are the only ones that satisfy 5x + 3y = 6. The coordinate pair (2x, 2y) also makes the equation true. 9 The cost of a school banquet is $80 plus $12 for each person attending. Write an equation that gives total cost as a function of the number of people attending. What is the cost for 83 people? A y = 80x 12; $6628 C y = 12x 80; $916 B y = 80x + 12; $6652 D y = 12x + 80; $1076 3
10 Mr. Jackson and Mrs. Gutierrez have monthly payments to pay off their car loans. The table and graph show their loan information. Compare the loans by finding and interpreting slopes and y-intercepts. Mrs. Gutierrez Loan Mr. Jackson s Loan Months 0 2 4 6 Loan Balance ($) 9000 8400 7800 7200 A For Mrs. Gutierrez loan, the slope is $350 and the y-intercept is $9,500. For Mr. Jackson s loan, the slope is $300 and the y-intercept is $9,000. The slope is the beginning loan balance. The y-intercept is the rate of change, or the monthly payment. Mrs. Gutierrez had the greater initial balance than Mr. Jackson. Mrs. Gutierrez is also paying more per month than Mr. Jackson. C For Mrs. Gutierrez loan, the slope is $700 and the y-intercept is $9,500. For Mr. Jackson s loan, the slope is $600 and the y-intercept is $9,000. The slope is the rate of change, or the monthly payment. The y-intercept is the beginning loan balance. Mrs. Gutierrez had the greater initial balance than Mr. Jackson. Mrs. Gutierrez is also paying more per month than Mr. Jackson. B For Mr. Jackson s loan, the slope is $350 and the y-intercept is $9,500. For Mrs. Gutierrez loan, the slope is $300 and the y-intercept is $9,000. The slope is the rate of change, or the monthly payment. The y-intercept is the beginning loan balance. Mr. Jackson had the greater initial balance than Mrs. Gutierrez. Mr. Jackson is also paying more per month than Mrs. Gutierrez. D For Mrs. Gutierrez loan, the slope is $350 and the y-intercept is $9,500. For Mr. Jackson s loan, the slope is $300 and the y-intercept is $9,000. The slope is the rate of change, or the monthly payment. The y-intercept is the beginning loan balance. Mrs. Gutierrez had the greater initial balance than Mr. Jackson. Mrs. Gutierrez is also paying more per month than Mr. Jackson. 4
11 Short Answer: (Put answer in box below.) Suppose your business has a special checking account used just for paying the phone bill. The balance is $740.00 this month. Next month the balance will be $707.60, after that it will be $675.20, and on the third month the balance will be $642.80. a.) Write a recursive formula and an explicit formula to represent the balance in the account as an arithmetic sequence. b.) How many months can you pay your phone bill withut depositing any more money in the account? 12 Determine whether the graph represents a function. A The relation is not a function. B The relation is a function. 5
13 A movie theater charges $11.50 for an adult ticket to an evening showing of a popular movie. To help the local animal shelter, the theater management has agreed to reduce the price of each adult ticket by $0.75 for every can of pet food a customer contributes to a collection barrel in the theater lobby. Which of the following shows both an equation in which y represents the cost of an adult ticket in dollars for a customer who contributes x cans of pet food, and the graph of the cost if a customer brings in 2, 5, 8, or 10 cans of pet food? A y = 12x 0.75 C y = 12x 0.75 B y = 11.5 + 0.75x D y = 11.5 0.75x 14 Solve p = 13 n for n. 12 A n = 12 13 p C n = 12 13 p B n = 13 12 p D n = 13 12 p 6
15 Graph the linear equation 6x + 2y = 12 by finding the x- and y-intercepts. A C B D 16 Short Answer: (Put answer in box below.) At 89 km/h, how far can you travel in 7.5 h? Use unit analysis to check your answer. 7
17 The function y = 35x describes how far from home Jose is as he drives from San Francisco to Dawson. Graph the function. Use the graph to estimate how far from home Jose is in 12 hours. A C B Jose is about 12 miles from home in 12 hours. D Jose is about 35 miles from home in 12 hours. Jose is about 47 miles from home in 12 hours. 18 Write a recursive rule for the sequence. a n = 5 + 8n Jose is about 420 miles from home in 12 hours. A a 1 = 13,a n = a n 1 + 5 C a 1 = 5,a n = a n 1 + 8 B a 1 = 5,a n = a n 1 + 5 D a 1 = 13,a n = a n 1 + 8 8
19 Graph 2x + 3y = 6 for the domain D: { 6, 3, 0, 3, 6}. A C B D 20 Short Answer: (Put answer in box below.) Lucy pays $265 in advance on her account at the athletic club. Each time she uses the club, $9 is deducted from the account. Write a linear function that gives the value remaining in her account after x visits to the club. Find the value remaining in the account after 14 visits. 9
21 Leah scored a total of 29 points in the basketball game, and she scored p points in the second half of the game. Write an expression to determine the number of points she scored in the first half of the game. Then, find the number of points she scored in the first half of the game if she scored 5 points in the second half of the game. A 29 + p; 34 points C 29 p; 24 points B 29 p ; 24 points D 29p; 34 points 22 Give the domain and range of the relation. Tell whether the relation is a function. A D: 3 x 1; R: 5 y 4 The relation is a function. B D: 5 x 4; R: 3 y 1 The relation is not a function. 23 Short Answer: (Put answer in box below.) Write a recursive rule for the sequence. 3, 7, 11, 15,... C D: 3 x 1; R: 5 y 4 The relation is not a function. D D: 5 x 4; R: 3 y 1 The relation is a function. 10
24 Short Answer: (Put answer in box below.) Model the function rule y = 1 x + 3 with a table of values and a graph. If any of the y values come out as 6 decimals, change them to fractions. x 2 1 0 1 2 y 25 A pipe is leaking at the rate of 16 fluid ounces per minute. Use dimensional analysis to find out how many gallons the pipe is leaking per hour. A 7,680 gal/h C 7.5 gal/h B 0.03 gal/h D 34.13 gal/h 26 What is the coefficient of x in the algebraic expression (5a)x 19x 2 + 6a? A 19 C 5a B 6 D 5 11
27 Graph the equation on a coordinate grid. 4x 8 = 0 A C B D 28 Short Answer: (Put answer in box below.) Solve 4(a + 5) 4 = 20. Write a reason for each step. 12
29 For f(x) = 5x + 12, what is the value of x for which f(x) = 27? A x = 0 C x = 4 B x = 3 D x = 3 30 Short Answer: (Put answer in box below.) A monthly phone bill, b, in dollars, consists of a $23 service fee plus $0.13 per minute, m, of long distance calls. The amount of the bill is a function of the minutes used, b = 23 + 0.13m. Part A: Draw a graph for up to and including 120 minutes of long distance calls made in a month. Part B: Estimate the bill if 91 minutes of long distance calls are made. 31 For f(x) = 4x + 5, find f(x) when x = 3. A 32 C 7 B 11 D 17 13
32 Find a coordinate pair for a point on the graph of 3x + 2y = 8. A (0, 4) C (0, 4) B ( 4, 0) D (4, 0) 33 Use rates of change to determine whether the function is linear or nonlinear. x 3 5 8 9 y 6 12 21 24 A linear B nonlinear 34 Short Answer: (Put answer in box below.) Sketch the line given by 3x 4y = 12. Label the x- and y-intercepts. 35 Write an algebraic expression that represents 19 less than 9 times a number? A 9x 19 C 19x 9 B 9(x 19) D 19 9x 36 A professional cyclist is training for the Tour de France. What was his average speed in kilometers per hour if he rode the 194 kilometers from Laval to Blois in 4.1 hours? Use the formula d = rt, and round your answer to the nearest tenth. A 795.4 kph C 189.9 kph B 47.3 kph D 118.6 kph 14
37 Short Answer: (Put answer in box below.) Graph the function with the given domain. Classify the function as discrete or continuous. Then identify the range of the function. y = 1 x + 3; domain: x = 4, 2, 0, 2, 4 2 38 Give the domain and range of the relation. x y 5 11 6 13 0 0 8 15 39 Use the graph of the function f(x) = x 1 to find the value of y when x = 1. A D: {0}; R: {5, 6, 8, 11, 13, 15} B D: { 15, 11, 13}; R: { 8, 5, 6} C D: { 15, 0, 11, 13}; R: { 8, 0, 5, 6} D D: { 8, 0, 5, 6}; R: { 15, 0, 11, 13} A 2 B 1 C 4 D 0 15
In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure they form? 40 Short Answer: (Put answer in boxes below.) Use the figure above to answer the following questions. a.) Fill in the table and then graph the above relationship. b.) Write the recursive and the explicit formula for the relationship. c.) Represent the relationship between the number of triangles and the perimeter of the figure they form as an equation. How does this equation relate to the method you would use to find the perimeter of n + 1 triangles from the perimeter of n triangles? 16