1. Which graph represents the solution to the given system?
y = –2x + 1
y = (Image: one-half)x + 6 (1 point)
(Image: Two lines pass through a coordinate plane and intersect at left-parenthesis negative 2 comma 5 right-parenthesis.)
(Image: Two lines pass through a coordinate plane and intersect at left-parenthesis 2 comma 5 right-parenthesis.)
(Image: Two lines pass through a coordinate plane and intersect at left-parenthesis 2 comma 2 right-parenthesis.)
(Image: Two lines pass through a coordinate plane and intersect at left-parenthesis negative 2 comma 2 right-parenthesis.)
2. How many solutions does the system of equations have?
3x + 15y = 35 and y = –(Image: one-fifth)x + (Image: seven-thirds) (1 point)
one
two
infinitely many
none
3. Which inequality represents the graph below?
(Image: A coordinate graph shows a shaded area covering all positive and negative values of x and positive and negative values of y up to 5.) (1 point)
y ≥ 5
x ≥ 5
y ≤ 5
x ≤ 5
4. Jack has $55, and Emily has $28. Jack is saving $4 per day, and Emily is saving $13 per day. After how many days will Jack and Emily have the same amount of money?
1 day
3 days
4 days
8 days
5. Which system is represented by the graph?
(Image: Two lines are graphed on a coordinate plane. One line passes through points left parenthesis 0 comma negative 1 right parenthesis and left parenthesis 1 comma 2 right parenthesis. The other line passes through points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 1 right parenthesis.) (1 point)
(Image: y equals 3 x minus 2 line break y equals 3 x minus 1)
(Image: y equals negative 3 x minus 2 line break y equals negative 3 x minus 1)
(Image: y equals one-third x minus 2 line break y equals one-third x minus 1)
(Image: y equals 3 x plus 2 line break y equals 3 x plus 1)
6. What is the solution of the system?
(Image: y equals 9 x minus 2 line break y equals 7 x plus 3) (1 point)
(Image: left parenthesis negative 5 over 2 comma negative 29 over 2 right parenthesis)
(Image: left parenthesis 5 over 2 comma 41 over 2 right parenthesis)
(Image: left parenthesis 2 over 5 comma 29 over 5 right parenthesis)
(Image: left parenthesis 1 over 2 comma 13 over 2 right parenthesis)
7. Which graph represents the given inequality?
y > 5x – 2 (1 point)
(Image: a graph)
(Image: a graph)
(Image: a graph)
(Image: a graph)
8. What system of inequalities is represented by the graph?
(Image: A coordinate graph is shown of overlapping areas formed by two lines.) (1 point)
(Image: y greater than or equal to negative 5 x minus 1) and (Image: y less than or equal to 3 x plus 4)
(Image: y less than or equal to 5 x minus 1) and (Image: y greater than or equal to negative 3 x plus 4)
(Image: y greater than or equal to 5 x minus 1) and (Image: y less than or equal to negative 3 x plus 4)
(Image: y less than or equal to negative x plus 5) and (Image: y greater than or equal to 4 x minus 3)
9. A company sells a container of mixed nuts that is 12% peanuts and another container that is 60% peanuts. How many cups of each mixture would be needed to make 12 cups that is 40% peanuts?
4 cups of the 12% peanuts and 8 cups of the 60% peanuts
8 cups of the 12% peanuts and 4 cups of the 60% peanuts
5 cups of the 12% peanuts and 7 cups of the 60% peanuts
3 cups of the 12% peanuts and 9 cups of the 60% peanuts
10. Represent the system of equations in augmented matrix form.
y = (Image: three-fourths)x – 6
y =–8x + 2 (1 point)
(Image)
(Image)
(Image)
(Image)
11. Suppose that the amount of algae in a pond doubles every 6 hours. If the pond initially contains 50 pounds of algae, how much algae will be in the pond after 18 hours?
400
10,800
300
600
12. The diameters of four different types of hairs are given below.
Hair A: 1.7 × 10–4 cm
Hair B: 1.4 × 10–3 cm
Hair C: 1.2 × 10–5 cm
Hair D: 1.9 × 10–4 cm
What is the order of the hairs from least to greatest diameters? (1 point)
C; B; A; D
D; A; B; C
C; A; D; B
B; D; A; C
13. What is the order of the numbers from least to greatest?
A = 1.5 × 103; B = 1.4 × 10–1; C = 2 × 103; D = 1.4 × 10–2 (1 point)
D < B < A < C
C < A < B < D
D < B < C < A
B < D < A < C
14. Ken has decided to raise rabbits but has been warned that the number of rabbits he will have will double every month. Ken started out with 30 rabbits and the function y = 30 • 2x models the number of rabbits he will have after x months. Which graph represents this function?
(Image: graph)
(Image: graph)
(Image: graph)
(Image: graph)
15. Multiply. Give your answer in standard form.
(3n2 + 2n + 4)(2n – 1) (1 point)
6n3 + n2 + 6n – 4
6n3 + 7n2 + 6n – 4
6n3 – n2 + 10n – 4
6n3 + n2 + 10n – 4
16. What is a simpler form of the following expression?
(t + 5)(t – 5) (1 point)
t2 – 10t – 25
t2 – 10t + 25
t2 + 10t + 25
t2 – 25
17. Multiply.
(3x + 5)(3x – 5) (1 point)
9x2 – 30x – 25
9x2 + 30x + 25
9x2 – 25
9x2 + 25
18. The area of a rectangular painting is given by the trinomial x2 + 4x – 21. What are the possible dimensions of the painting? Use factoring.
(x + 7) and (x + 3)
(x – 7) and (x + 3)
(x – 7) and (x – 3)
(x + 7) and (x – 3)
19. The area of a rectangular picture frame is given by the trinomial (Image: 3 x squared minus 13 x minus 30). What are the possible dimensions of the frame? Use factoring.
(Image: left parenthesis 3 x plus 5 right parenthesis) and (Image: left parenthesis x minus 6 right parenthesis)
(Image: left parenthesis 3 x plus 5 right parenthesis) and (Image: left parenthesis negative x minus 6 right parenthesis)
(Image: left parenthesis 3 x minus 5 right parenthesis) and (Image: left parenthesis x minus 6 right parenthesis)
(Image: left parenthesis 3 x minus 5 right parenthesis) and (Image: left parenthesis x plus 6 right parenthesis)
20. Graph the function and identify the domain and range.
y = –1.5x2 (1 point)
(Image: graph)domain: (Image: mc010-2.jpg)
range: (Image: mc010-3.jpg)
(Image: graph)domain: (Image: mc010-5.jpg)
range: (Image: mc010-6.jpg)
(Image: graph)domain: (Image: mc010-8.jpg)
range: (Image: mc010-9.jpg)
(Image: graph)domain: (Image: mc010-11.jpg)
range: (Image: mc010-12.jpg)
21. A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = –16t2 + 148t + 30. What is the boulder’s maximum height? How long does it take the boulder to reach its maximum height? Round to the nearest hundredth, if necessary.
Reaches a maximum height of 30 feet in 9.25 seconds.
Reaches a maximum height of 640.5 feet in 4.63 seconds.
Reaches a maximum height of 1,056.75 feet in 4.63 seconds.
Reaches a maximum height of 372.25 feet in 4.63 seconds.
22. Solve the equation using the Zero Product Property.
–2x (5x – 2) = 0 (1 point)
0, (Image: The fraction is 2 over 5.)
0, 2
0, –(Image: The fraction is 2 over 5.)
0, –2
23. Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x2 + 3 = –4x
1, 3
–1, –3
–1, 3
1, –3
24. A model rocket is launched from a root into a large field. The path of the rocket can be modeled by the equation y = –0.02x2 + 2.3x + 6, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land?
57.5 meters
115 meters
117.55 meters
235.1 meters
25. How many real-number solutions does the equation have?
(Image: 0 equals negative 5 x squared plus 8x minus 7) (1 point)
one solution
two solutions
no solutions
infinitely many solutions
1. (Image: Two lines pass through a coordinate plane and intersect at left-parenthesis 2 comma 5 right-parenthesis.)
2. one
3. y ≤ 5
4. 8 days
5. (Image: y equals negative 3 x minus 2 line break y equals negative 3 x minus 1)
6. (Image: left parenthesis 5 over 2 comma 41 over 2 right parenthesis)
7. (Image: a graph)
8. (Image: y greater than or equal to negative 5 x minus 1) and (Image: y less than or equal to 3 x plus 4)
9. 3 cups of the 12% peanuts and 9 cups of the 60% peanuts
10. (Image)
11. 6,400
12. C; B; A; D
13. D < B < A < C
14. (Image: graph)
15. 6n3 - n2 + 10n - 4
16. t2 - 25
17. 9x2 - 25
18. (x + 7) and (x - 3)
19. (Image: left parenthesis 3 x + 5 right parenthesis) and (Image: left parenthesis x - 6 right parenthesis)
20. (Image: graph) domain: all real numbers range: y ≤ 0
21. Reaches a maximum height of 372.25 feet in 4.63 seconds.
22. 0, (Image: The fraction is 2 over 5.)
23. –1, 3
24. 115 meters
25. two solutions