Questions

zMath 180 - Unit 36: Second Semester Final

1) A tree that is 22 meters tall, casts a shadow of 28 meters. A building located nearby casts a shadow of 56 meters. What is the height of the building?

A) 40m

B) 39m

C) 44m

D) 42m

Refer to the figure below to answer the next four questions.

2) Select the names of the two triangles that are similar. (Hint: Use a thin paper to trace the angles of the triangles. In similar triangles, all angles are congruent.)

A) Triangles JKL and QRS are similar

B) Triangles RSQ and NPM are similar

C) Triangles JKL and MNP are similar

D) Triangles NMP and QSR are similar

3) What is the scale factor between the similar triangles? State the answer as a simplified ratio comparing the larger triangle to the smaller one.

A) 3:2

B) 3:1

C) 3:0

D) 3:3

4) What is the value of “x” in triangle MNP?

a.) x = 6

b.) x = 8

c.) x = 10

d.) There is not enough information given to determine the value of “x”.

5) What is the value of “y” in triangle QRS?

a.) x = 6

b.) x = 8

c.) x = 10

d.) There is not enough information given to determine the value of “y”.

6) Find the missing ordered pair of a rectangle with three vertices as follows: (2, 9), (2, 1), (6, 9), (x, y).

A) (6,1)

B) (2.9)

C) (6,9)

D) (X,Y)

7) What type of transformation is shown in the figure below?

a.) translation

b.) rotation

c.) reflection

d.) dilation

8) Refer to triangle ABC on the coordinate plane below located at A(–5, 1), B(–5, 5), C(–2, 1). Translate the triangle 8 units to the right and 7 units down. What are the new coordinates of the translated triangle?

A) A'(-3, -6), B'(3, –2), C'(6, –6)

B) A'(3, 6), B'(3, 2), C'(6, 6)

C) A'(-3, 6), B'(3, 2), C'(6, 6)

D) A'(3, –6), B'(3, –2), C'(6, –6)

9) Consider the given relation. Describe in words the relationship between the x-coordinate and the y-coordinate, and then write an equation to represent the relation.

A) The x-coordinate equals the product of 4 and the y-coordinate plus 2

B) The y-coordinate equals the product of 3 and the x-coordinate plus 1. The equation to represent this relationship is y = 3x + 1

C) The equation to represent this relationship is X=3y-2

10) What kind of variation is represented by the following equation: xy = 16?

a.) direct variation

b.) inverse variation

11) Which graph represents indirect variation?

a.) Graph A

b.) Graph B

c.) Graph C

d.) Graph D

12) Which graph that is displayed in the previous problem represents direct variation?

a.) Graph A

b.) Graph B

c.) Graph C

d.) Graph D

13) Use Is the function represented in the table linear or nonlinear?

a.) The function is linear.

b.) The function is nonlinear.

Consider points C (1, –4) and point D (6, 8) on segment CD, and then answer the next three questions.

14) What is the slope of segment CD?

A) m=5/12

B) m=-14/15

C) m = 12/5

15) What is the length of segment CD? (Hint: Use the distance formula.)

A) CD = 14

B) CD = 15

C) CD = 13 (Note: The square root of 169 is 13.)

16) Graph both equations and write a statement comparing the slopes of the lines.

A) The first equation (y = 5x) has a flat slope while the second equation (y = (1/5)x) has a steep slope.

B) The first equation (y = 5x) has a steep slope while the second equation (y = (1/5)x) has a flatter slope.

C) The first equation (y = 5x) has a steep slope while the second equation (y = (1/5)x) has no slope.

Refer to the two tables and the following scenario to answer the next four questions: Jennifer works at the local diner as a waitress. She earns an average of $15.00 an hour in tips on Saturdays and an average of $9 an hour in tips on Sundays. She wants to determine how much money she would make based on the numbers of hours she works. Fill in the tips portion of the two tables for each day and then answer the next six questions.

17) After completing the charts, (a) state the amounts of money that could be made in tips for working 6, 7, 8, and 9 hours on Saturday and (b) state the amounts of money that could be made in tips for 6, 7, 8, and 9 hours on Sunday.

A) (a) Saturday: $90, $105, $120, $135,
B) (b) Sunday: $54, $63, $72, $81
C) (a) Saturday: $80, $106, $121, $136
D) (b) Sunday: $95, $110, $125, $140

18) Write an algebraic expression to describe the amount of money in tips Jennifer can earn on Saturday. Let "A" represent the amount in tips and "h" represent the 15 hours she worked.

A) A =15a

B) A = 15h

C) 15 = Ah

19) Write an algebraic expression to describe the amount of money in tips Jennifer can earn on Sunday. Let "U" represent the amount in tips and "h" represent the number of hours worked.

A) U = 9h

B) H =9U

C) U = H9

20) True or False. If Jennifer works 9 hours on Sunday, she will make less money in tips than the amount of money she would earn in tips for working 6 hours on Saturday.

True

False

21) Aaron decides to visit his brother in California. He travels 4 hours at 65 MPH. He then enters a construction area and must slow down to 40 MPH for 4 hours. How many miles did he travel in the 8 hours?

A) Aaron traveled 400 miles. (65(4) + 40 ($4)

B) Aaron traveled 450 miles. (65(4) + 40 ($4)

C) Aaron traveled 420 miles. [65(4) + 40(4)]

22) What is the midpoint (M) of segment AB with endpoints A(–5, 2) and B(4, –4)?

A) M = (–1/2, 1)

B) M = (–1/2, –1)

C) M = (1/2, –1)

23) On a coordinate grid, a lighthouse is located at (10, 70) and a sailboat is located at (80, 20). If the units on the grid represent yards, what is the direct distance between the lighthouse and the sailboat to the nearest yard?

A) d = 86 yd

B) distance = 80 yd

C) d = 70yd

24) Is the graph linear or nonlinear?

a.) linear

b.) nonlinear

25) Graph the quadratic equation. What are the roots of the quadratic equation?

A) x = –3, x = –3

B) x = 3, x = 3

C) x = –3, x = 3

26) Graph the quadratic equation. What are the roots of the quadratic equation? (Hint: Use x-values that range between –8 and 8 to find ordered pairs to graph the parabola.)

A) x = 1, x = 6

B) x = –1, x = 6

C) x = –1, x = –6

27) Graph the quadratic equation, and then compare the change in the location of the graph to the location of the graph in the previous problem.

A) This graph slides up vertically parallel to the y-axis.

B) This graph slides down horizontally to the X-axis

C) This graph slides up vertically parallel to the x-axis.

28) What algebraic expression represents the following phrase: “Five more than twice a number x”?

A) D

B) C

C) A

D) B

29) Write an algebraic expression for the following phrase: “Ten less than the product of 6 and a number.”

A) 6x - 10

B) 6x -12

C) 3x -10

30) Simplify.

A) 5x -9

B) 2x +5

C) 6x -3

31) Simplify by using the distributive property.

A) C

B) D

C) A

D) B

32) Solve for “x”.

A) x = 10

B) x = 9

C) x = 7

33) Solve for “m”.

A) m = 8

B) m = 6

C) m = 42

34) Solving the system of equations by using substitution. State the solution for “x” and for “y”.

A) x = 5, y = 2

B) x = 25, y = 5

C) x = 3, y = 8

35) What is the solution of the system of equations shown below? Assume that each space in the grid represents one unit.

a.) (0, 0) or x = 0, y = 0

b.) (2, 3) or x = 2, y = 3

c.) (–3, 2) or x = –3, y = 2

d.) (2, –3) or x = 2, y = –3

36) The sum of two numbers is 14. One of the numbers is 6 greater than the other. What are the two numbers? (Hint: You may write a system of equations to solve the problem.) The two numbers are 4 and 10. (The system of equations is x + y = 14 and y = x + 6.)

True

False

37) What type of correlation does the scatter plot display?

a.) There is a positive correlation.

b.) There is a negative correlation.

c.) There is no correlation.

38) Complete the sentence. Since the line of “best fit” for the scatter plot below passes through EVERY point, the given data is said to be _________?

a.) linear

b.) nonlinear

c.) scattered

d.) curved

39) Describe in words how and where to conduct a convenience sample to survey sports fans.

A) Watch Sports TV

B) Survey people arriving at a local football game.

C) Watch the news and the sports section of the show

40) Consider the given data set. What is the mean rounded to the nearest tenth?

A) mean = 17.4

B) mean = 18

C) mean = 16

41) In the data set of the previous problem, replace the 16 with a 6. What is the new mean?

A) mean - 18

B) mean = 17

C) mean = 16

42) Explain how the change in the data points in the previous problem affected the mean. T/F: The mean is smaller and less representative of the average of most of the data points in the group.

True

False

43) Steve's garage door has a security keypad and only he knows the five-digit code that opens the door. He remembers that the digits are 3, 4, 5, 8, and 9; but, he cannot remember the correct sequence of the numbers. How many different ways could he enter the security code?

A) A and C

B) A and D

C) B and C

D) A and B

44) Three people are chosen at random to receive free movie tickets from a group of fifteen people. (a) How many ways could the three people be chosen? (b) Is this problem a permutation or a combination?