ALGEBRA 1
NAME_______________________________DATE______________________BLOCK______
2016 SPRING FINAL EXAM REVIEW
1. Use systems to solve: Goofy and Pluto together have
$19. Pluto has $9 more than Goofy. How much
money does Pluto have?
$5
2. Simplify: (5x + 3)(7x – 2)
$10
$14
$28
Which pair of equations corresponds to the two lines
in the graph?
3.
4. Match the inequality with its graph. (Two inequalities will
not have a matching graph.)
_____ 𝑦 > 𝑥 + 3
𝑎. 𝑦 = 𝑥 + 2
_____ 𝑦 ≥ −𝑥 − 3
1
𝑦=− 𝑥−5
2
_____ 𝑦 < 𝑥 + 3
𝑏. 𝑦 = 2𝑥 − 6
A
_____ 𝑦 ≤ −𝑥 − 2
1
𝑦=− 𝑥+2
3
_____ 𝑦 > −𝑥 − 2
𝑐. 𝑦 = −2𝑥 − 5
𝑦=
1
𝑥+2
3
𝑑. 𝑦 = −2𝑥 − 1
𝑦=
5
𝑥+1
6
What is the solution to the
system of equations in the
graph? ________________
5. At a student bake sale cakes sold for $4 each and
pies sold for $5 each. The students sold a total of 75
cakes and pies and made $340. Which pair of linear
equations would determine the number of each ticket
sold?
A.𝑥 − 𝑦 = 75
4𝑥 − 5𝑦 = 340
6.
Simplify:
A. −
B. −
20𝑥 3 𝑦 4 𝑧 2
8𝑥 3 𝑧
3𝑦
7𝑦
5𝑧
B. 5𝑥 = 4𝑦 + 340
𝑥 + 𝑦 = 75
C. −
C. 75(𝑥 + 𝑦) = 340
4𝑥 + 5𝑦 = 9
D. −
D. 4𝑥 + 5𝑦 = 340
𝑥 + 𝑦 = 75
7. A rectangle has an area of x2 + 5x – 14. What 2
binomial represent the area?
−28𝑥 3 𝑦 5 𝑧
14𝑥 2 𝑦
4𝑧 3
7𝑥 6 𝑦 9 𝑧 3
10
8. Multiply: 3𝑥²(4𝑥 2 − 𝑥𝑦 − 𝑦²)
2
10. A square room has an area of 4x2 + 16x + 16. What is the
length of each side?
9. Factor: 64y2 - 25
11. Simplify: (25b7)1/2
12. Find the missing factor:
72𝑥 8 𝑦 5 = (6𝑥 2 𝑦)(3𝑥𝑦)(__? __)
9𝑥𝑦
4𝑥 5 𝑦 3
8𝑥 4 𝑦 3
4𝑥 4 𝑦 2
13. Find the volume of the figure below.
14. What is the area of the rectangle modeled below?
6𝑥 + 7
2𝑥
2𝑥 − 3
4𝑥
12𝑥 2 − 14𝑥 − 21
12𝑥 2 − 4𝑥 − 21
12𝑥 2 − 18𝑥 − 21
12𝑥 2 + 22𝑥 − 21
16. The length of a side of a square is 4𝑥 + 3. What is the
area, A, of this square in terms of x? (Hint: Draw a
square.)
7𝑥
15. Simplify: (3𝑎3 )(4𝑎3 ) + (2𝑎5 )(𝑎)
𝐴 = 16𝑥 2 + 24𝑥 + 9
𝐴 = 16𝑥 2 − 24𝑥 + 6
𝐴 = 16𝑥 + 9
𝐴 = 8𝑥 2 + 6
17. Simplify: (2𝑎𝑏 4 )3 (−3𝑎2 𝑏 2 )2
18. Factor Completely: 𝑥 2 − 13𝑥 + 36
19. A rectangle has a length of 5𝑎2 𝑏 3 𝑐 4 and a width of
4𝑎3 𝑏𝑐 4 . What is the area of the rectangle?
20. Graph and label the vertex for each:
i. y = -(x + 4)2 - 5
ii. y = 4x2 + 16x + 16
21. Find the area of a square with a length of
𝑥3𝑦5
7𝑧 9
inches.
22. Factor Completely: 15𝑣 2 + 4𝑣 − 4
(3𝑣 − 4)(5𝑣 + 1)
3
23. The graph of the function f (𝑥) = 𝑥 2 is shown. If the
parabola is changed by the criteria below, then write the
new function.
(3𝑣 − 2)(𝑣 + 2)
(3𝑣 + 2)(5𝑣 − 2)
(3𝑣 + 4)(5𝑣 − 1)
A. shifts down 2 units ____________
B. shifts up 2 units _______________
C. twice as narrow _______________
D. twice as wide _________________
E. opens downward ______________
24. Factor Completely: 12𝑛3 − 30𝑛2 + 18𝑛
i. 6𝑛(2𝑛 − 3)(𝑛 − 1)
ii. 6𝑛(2𝑛 − 1)(𝑛 − 3)
iii. 6𝑛(2𝑛 + 3)(𝑛 − 1)
D. 6𝑛(2𝑛 + 1)(𝑛 − 3)
25. Solve for 𝒙: (𝑥 − 5)(𝑥 + 7) = 0
26. The area of a rectangle is 36𝑥 2 − 121. Which of the
following represents the dimensions?
27. Solve: 3𝑎2 − 𝑎 − 2 = 0
i. (3𝑥 − 11)(12𝑥 − 11)
ii. (9𝑥 + 11)(4𝑥 − 11)
iii. (6𝑥 + 11)(6𝑥 − 11)
i. (2𝑥 + 11)(18𝑥 + 11)
28. Match the following functions to their graphs.
A.
2
i.
𝑎 = − ,1
ii.
𝑎 = ,2
iii.
𝑎 = ,1
iv.
𝑎 = − , −2
1
3
3
2
3
1
3
29. The area of a triangle is given by the equation
𝒉𝟐 − 𝟑𝒉 = 𝟏𝟎 where 𝒉 is the height of the triangle.
What is the value of 𝒉?
_____ 𝑦 = 𝑥
_____ 𝑦 = 𝑥 2
B.
30. What are the zeros to the quadratic function graphed
below?
2
_____ 𝑦 = 𝑥
2, −1
C.
0, 3
0, 1
1, 3
31. For the function 𝑓(𝑥) = 8𝑥² − 4𝑥 − 3 what is the value
of 𝑓(𝑥) when 𝑥 = 2?
i.
–23
ii.
1
iii. 41
iv. 21
32. You deposit $500 into a savings account that pays 2.4%
interest yearly. Write an exponential function (y = abx) that
models the situation after x years.
33. Which statement describes the change in the graph
of 𝑦 = 2.5𝑥 2 when the equation is changed to
𝑦 = 2.5𝑥 2 + 4?
4
34. You bought a new iphone for $625. The value of the phone
decreases each year by 5%. Write an exponential function
that represents the value after x years.
a.The graph of the parabola moves left 4 units.
b.The graph of the parabola moves right 4 units.
c.The graph of the parabola moves up 4 units.
d.The graph of the parabola moves down 4 units.
35. What are the x-intercepts of
𝑓(𝑥) = 5𝑥² − 22𝑥 + 8?
i.
ii.
iii.
iv.
36. The function h(x) = 7(3)x represents the number of mice in
a lab experiment after x years. What does the y-intercept
of the graph represent?
(0.4,0) 𝑎𝑛𝑑 (4,0)
(−5,0) 𝑎𝑛𝑑 (−2,0)
(−4,0) 𝑎𝑛𝑑 (−0.4,0)
(2,0) 𝑎𝑛𝑑 (4,0)
𝑥 2 −𝑦 2
37. Houses depreciate in value over time. Erin bought a
house for $235,000, but it loses 15% of its value over
time. What does the asymptote y = 0 represent in this
situation?
38. Evaluate
39. Write an equation of a line that is parallel to
𝟒
i. 𝒚 = − 𝒙 + 𝟕.
41. The lengths of the sides of a quadrilateral are given as
shown. Express the perimeter in terms of 𝒙.
𝟑
40. What has to be true for two lines to be parallel?
2𝑧
for
𝑥 = 3, 𝑦 = −1, 𝑧 = −2.
𝒂. 𝟔𝒙𝟒 + 𝟔
𝒃 𝟒𝒙𝟐 + 𝟏
C. 𝟖𝒙𝟐 + 𝟕
𝒅. 𝟗𝒙 − 𝟏
______________________________________
42. Graph each of the following equations. (Hint: Each
graphs a line.)
𝒙=𝟑
𝒚=𝟑
a. Which graphed line is an example of an
equation with a slope of zero?
b. What is the slope of the other graphed line?
43. Which of the following is the quadratic formula for all real
values of a,b, and c where a ≠ 0?
𝑥=
𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
𝑥=
𝑏 ± √𝑏 2 + 4𝑎𝑐
2𝑐
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎
2𝑎𝑐
𝑥=
−𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
Now solve 4𝑥 2 − 𝑥 − 5 = 0.
5
44. Solve: 17𝑥 − 7 = 4(3𝑥 − 2)
45. Simplify completely: √
49
100
i.
ii.
iii.
iv.
𝑥
𝑥
𝑥
𝑥
= −0.2
= 0.5
=2
= 0.2
7
i.
50
√7
ii.
iii.
iv.
√10
7
10
√49
√100
46. Two lines have the equations:
x + 2y = −4
4y = 3x + 12
i. At what point do the lines
intersect?
A. (3, -2)
B. (2, -3)
C. (4, -4)
D. (-4, 0)
47. Choose the type of function represented below.
48. Choose the type of function represented below.
49. What is a reasonable domain for the graph below?
i.
Linear
ii.
Quadratic
Linear
Quadratic
Exponential
None of the above
iii. Exponential
iv. None of the above
50. Match the type of function represented below.
Linear
x
−1
0
1
2
3
Quadratic
y
4
1
0
1
4
Exponential
x
−2
−1
0
1
2
y
1
3
5
7
9
x
0
1
2
3
4
y
1
5
25
125
625
52. A quadratic function is shown. If it is translated 5 units
to the right and 2 units up, what would be the new
equation?
51. Solve the following systems of equations:
a. 3x – 2y = 14
6x + y = 18
b.
-4
10
1
0
5
-8
8
-14
12
-22
y2
1
6
10
13
17
53. A quadratic has zeros of 5 and -7. Which of the following
statements about the function is false?
a. The solutions are -7 and 5.
b. The standard form is y = x2 + 2x – 35.
c. The factored form is (x + 5)(x – 7).
d. The factored form is (x – 5)(x + 7).
a. y = ½ (x + 3) + 6
b. y = 2(x – 3) – 6
c. y = -2(x + 3) 2 – 6
1
d. y = - (x – 3)2 + 6
2
x
y1
a. =
1
2
(
x
–
54. State the vertex and x -intercepts(s) of the given
graph.
6
55. Identify the transformations to graph the following functions
from the parent function y = x2:
f(x) = -2(x + 4)2 – 6
y = (x – 5)2 + 1
y = ½ (x + 9)2 – 4
A.
B.
C.
D.
vertex: (-1, -2)
vertex: (-2, -8)
vertex: (-2, -7)
vertex: (-4, 1)
x-intercept(s): 4, 1
x-intercept)s): 0
x-intercept(s): -4, 0
x-intercept(s): -4, 0
56. Given the table, identify the axis of symmetry, vertex,
y-intercept, and x-intercepts:
x
y
0
12
3
-3
6
0
9
21
12
60
57. Based on the graph, between which 2 values of x is a zero
located?
58. An art student is drawing an arc that has a vertex at
(5, 7). If one x-intercept is at (0, 0), where will the
other x-intercept hit the x-axis?
59. Which function has a vertex of (3, -1) and goes through the
point (1, 3)?
a. y = (x–3)2 - 1
b. y = (x+3)2 – 1
2
c. y = 2(x+3) - 1
d. y = x2 + 3
60. Find the roots of the following quadratic functions:
61. What is the range of the function f(x) = 2x2 + 6?
4n2 + 7n + 3 = 0
y2 – 81 = 0
2a2 – 4a = 6
a. All real numbers.
b. All real numbers greater than or equal to 0.
c. All real numbers greater than or equal to 6.
d. All real numbers less than or equal to 6.