ACP Semester 2 Review

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1 lass: Date: P Semester 2 Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. n airplane flight has 228 seats. The probability that a person who buys a ticket actually goes on that flight is about 95%. If the airline wants to fill all the seats on the flight, how many tickets should it sell? 217 tickets 345 tickets 2400 tickets D 240 tickets 2. Yuan tossed a paper cup 40 times and recorded how the cup landed each time. He organized the results in the table shown. ased on Yuan s results, find the probability that the cup will land upside down. Outcome Right-side up Upside down On its side Frequency % 82.5% 21.2% D 571.4% 3. spinner is divided into 3 equal sections labeled,, and. Erik spins the spinner and rolls a fair number cube. The tree diagram shows the sample space for the possible outcomes. Which of the following statements is correct? 1 The probability of the spinner landing on or rolling a 4 is 18. The probability of the spinner not landing on and rolling a 3 is The probability of the spinner landing on or rolling a number greater than 2 is 2 9. D The probability of the spinner not landing on and rolling a prime number is

2 4. Find the area of the figure. 450 mm mm 2 67,500 mm 2 D 150 mm 2 5. Solve 8n 4 = 52. n = 48 n = 7 n = D n = 6 6. It takes 78 days to create a custom motorcycle. Write an algebraic expression to describe the number of days it takes to create n custom motorcycles. How many days will it take to create 6 custom motorcycles? 78 + n; 84 days 78n; 468 days n; 546 days D 78 ; 13 days n 7. Which is a solution to the equation 12a 75 = 69? a = 9 a = 11 a = 10 D a = Tell whether the rectangles are similar. If so, write the similarity ratio and a similarity statement. The measures of the corresponding angles are equal, and the opposite sides are equal. similarity ratio: 3 5 rectangle MNOP ~ rectangle RSTU The rectangles are not similar. similarity ratio: 2 5 rectangle MNOP ~ rectangle RSTU D similarity ratio: 2 3 rectangle MNOP ~ rectangle RSTU 2

3 9. Juan sees a maple tree and a pine tree in the forest. He knows that the pine tree is feet tall. On a sunny day, the shadow of the pine is 4.9 feet long while the maple s shadow is feet long. Estimate the height of the maple tree. about 100 feet about 63 feet about 80 feet D about 97 feet 10. Dilate the figure by a scale factor of 1.5 with the origin as the center of dilation. What are the vertices of the image? J (1.5, 6), K (9, 6), L (9, 1.5), M (1.5, 1.5) J ( 1.5, 6), K ( 9, 6), L ( 9, 1.5), M ( 1.5, 1.5) J (6, 1.5), K (6, 9), L (1.5, 9), M (1.5, 1.5) D J (1.5, 6), K (9, 6), L (6, 1), M (1, 1) 11. y what scale factor does the length of in the figure shown change under the dilation Ê (x, y) 2 3 x, 2 ˆ 3 y ËÁ? D 2 3

4 12. figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at Ê ËÁ 3,4 ˆ? Ê 1,1 1 ˆ ËÁ 2 Ê ËÁ 9,4 ˆ Ê Ë 3,12 D Ê ËÁ 9,12 ˆ 13. Dilate the figure by a scale factor of 0.5. What are the vertices of the image? F (2.5, 3), G (0.5, 5), H (0.5, 1) F ( 3, 2.5), G ( 5, 0.5), H ( 1, 0.5) F (3, 2.5), G (5, 0.5), H (1, 0.5) D F (3, 2.5), G (5, 0.5), H (2, 1) 14. The graph shows the relationship between the number of members in a club and the number of years after the club began. ased on the trend shown in this data, predict the year in which the club will have no members. D 1 year 3 years 6 years 8 years 4

5 15. Write an equation for the trend line on the scatter plot. What is a reasonable interpretation for the slope in this context? D y = x + 80; The number of students decreases by 1 student per year. y = 10x + 80; The number of students decreases by 1 student per year. y = 10x + 80; The number of students decreases by 10 students per year. y = x + 80; The number of students decreases by 10 students per year. 5

6 16. Maya sketches a graph of a linear function. Which graph might she have sketched? D 17. Which is a linear equation? y = 2 5x y = 2 5x 2 y = 5x 2 D y = 5 x 6

7 18. George is selling sandwiches at a deli. The table shows the average number s of sandwiches he sells over time t, in minutes. What linear function is represented by the table? Time (minutes) Sandwiches sold s = 2t + 13 s = 13t + 2 s = 2t D s = 2t Identify the transformation from the original to the image, and tell whether the two figures are similar or congruent. The original figure has solid sides; the image has dashed sides. The transformation is a dilation. The triangles are congruent. The transformation is a translation. The triangles are similar but not congruent. D The transformation is a dilation. The triangles are similar but not congruent. The transformation is a reflection. The triangles are similar but not congruent. 7

8 20. Which set of vertices forms a figure that is similar but NOT congruent to the figure shown? ( 3, 3), (2, 1), (2, 1), ( 3, 3) ( 6, 6), ( 2, 4), (2, 4), (6, 6) ( 2, 6), (0, 1), (2, 1), (4, 6) D ( 3, 3), ( 1, 2), (1, 2), (3, 3) 21. Triangle EFG has vertices E( 3, 1), F(1, 1), and G(4, 5). Find the coordinates of the image of point F after a reflection across the x-axis. (1, 1) ( 1, 1) (1, 1) D ( 1, 1) 22. Describe the difference between the two given transformations. Transformation 1: (x,y) (x + 4,y + 4) Transformation 2: (x,y) (4x,4y) The image in Transformation 1 has an area that is 4 times greater than the image in Transformation 2. The image in Transformation 2 moves the original triangle 4 units in each direction. ll but one of the vertices in the image of Transformation 1 is different from the original. D The image in Transformation 2 has a perimeter that is 4 times greater than the perimeter of the image in Transformation Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of one star are (0, 8). The point representing the star is then translated left 3 units. What are its new coordinates? (3, 8) (0, 5) (0, 11) D ( 3, 8) 8

9 24. If triangle is reflected across the x-axis, what are the new coordinates of point? Ê Ë Á 3, 1 ˆ Ê ËÁ 1, 3 ˆ 25. Find how the perimeter and the area of the figure change when its dimensions change. D When the dimensions of the triangle are doubled, the perimeter is doubled, and the area is four times greater. When the dimensions of the triangle are doubled, the perimeter is doubled, and the area is doubled. When the dimensions of the triangle are doubled, the perimeter is four times greater, and the area is four times greater. When the dimensions of the triangle are doubled, the perimeter is four times greater, and the area is doubled. 9

10 26. Figure is the image of figure after a dilation centered at the origin. What is the scale factor of the dilation? D Which of the statements is true about the data displayed in the scatter plot? It shows a positive correlation. It shows no correlation. It shows a negative correlation. D s study time increases, grade decreases. 10

11 28. Tell whether x and y have a positive association, a negative association, or no association. Explain your reasoning. positive; the slope is positive no correlation; the slope is close to zero negative; the slope is negative D cannot determine 29. Tell whether x and y have a positive association, a negative association, or no association. Explain your reasoning. negative; the slope is negative positive; the slope is positive no correlation; the slope is close to zero D cannot determine 30. Find the mean absolute deviation for this data set. 2, 3, 1, 5, 4 2,1 2 1 D

12 31. Terri has a balance of $795 on his credit card. He is currently making monthly credit card payments of $20 a month. What will happen if he increases the amount he is paying by $18 a month? It will take him longer to repay the His interest rate will increase. loan. It will take him less time to repay the loan. D His interest rate will decrease. 32. Nelson took out a $12,750 loan in 2009 to open a food trailer. He has paid $1,700 of the principal. The interest rate on his loan is 6.5%. He wants to pay off the rest of the loan in 5 years. How should he fill in the blanks on the online calculator modeled below to figure out the amount he should pay each month? Enter your loan balance Enter the loan s interest rate Enter desired months until debt free 12,750; 6.5%; 60 11,050; 6.5%; 5 12,750;0.065%; 5 D 11,050; 6.5%; new house costs $260, Sara wants to buy the house and needs $35, for a down payment. Sara currently has $28, in a savings account that earns 9% simple interest. How long must she keep the money in the savings account in order to have enough for the down payment on the house? 92.1 years 3 years 14 years D 3 months 34. Jenny has $1,200 in her savings account. If the bank pays 3% interest per year on savings, how much interest does she earn in one year? $36 $ What is the surface area of the right rectangular prism shown in the figure? 143 m m m 2 D 486 m 2 12

13 36. Juliana is wrapping a present for her friend s birthday gift. The gift will fit in a box that she will have to fold and tape together, like the one shown below. Juliana decides to wrap that box in one in which each side is 4 times as long as the gift box. How much more wrapping paper will she need to wrap the larger box than she would need for the original gift box? S = 7 D Juliana needs an additional 4,410 square inches of wrapping paper to wrap the larger box. Juliana needs an additional 16 square inches of wrapping paper to wrap the larger box. Juliana needs 294 square inches of wrapping paper to wrap the larger box. Juliana needs 4,704 square inches of wrapping paper to wrap the larger box. 37. Solve 1 + 8a = 10 3a. a = 7 a = 1 a = 1 D a = hockey season ticket holder pays $72.48 for her tickets plus $6.00 for a program each game. second person pays $18.08 for a ticket to every game, but doesn t buy programs. In how many games will they have paid the same amount? D Solve 2 + x 2 + 3x 8 = 16. x = 5 x = 16 x = D x = Solve a 2 = a. a = 4 15 a =

14 Numeric Response 1. ased on a sample survey, a principal claims that 77% of the students like math. Out of 1,300 students, how many would you predict do NOT like math? 2. The figure is a square placed on top of a trapezoid. The perimeter of the square is 76 cm. Find the area of the figure in square centimeters. 3. The data set shows the number of participants at a fundraiser and the amount of funds raised. Use a graphing calculator to find the least-squares line for the data with number of participants as the independent variable. Then calculate the mean absolute deviation. Round your answer to the nearest hundredth.. Family House Fundraiser Number of participants Funds raised ($) Short nswer 1. ) Write a real-world problem to match the equation x = x. ) Solve the equation, and interpret the answer. 14

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