ALGEBRA 1
NAME_______________________________DATE______________________BLOCK______
SPRING 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?
4. Solve: 7 +
𝑥
4
≤ 10
A. $5
B. $10
C. $14
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
D. $28
2. Which pair of equations corresponds to the two lines
in the graph?
5. 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 = −2𝑥 − 5
A.
_____ 𝑦 < 𝑥 + 3
B. 𝑦 = 2𝑥 − 6
𝑦=
1
−3𝑥
_____ 𝑦 ≤ −𝑥 − 2
+2
_____ 𝑦 > −𝑥 − 2
C. 𝑦 = −2𝑥 − 5
1
3
𝑦 = 𝑥+2
D. 𝑦 = −2𝑥 − 1
What is the solution to the
system of equations in the
graph? ________________
5
6
𝑦 = 𝑥+1
3. 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
B. 5𝑥 = 4𝑦 + 340
𝑥 + 𝑦 = 75
C. 75(𝑥 + 𝑦) = 340
4𝑥 + 5𝑦 = 9
D. 4𝑥 + 5𝑦 = 340
𝑥 + 𝑦 = 75
6. Which graph below best represents the solution to the
inequality? 10g + 4 ≤ 5g − 11
2
7. Solve: 12 (−𝑥
1
− 4) −
15 ≤ −4(𝑥 − 2) + 6
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
13. Multiply: 3𝑥²(4𝑥 2 − 𝑥𝑦 − 𝑦²)
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
8. You receive $20 in allowance each week. Each time
you forget to make your bed, your parents deduct
$1.50 from your allowance. You want to purchase a
song on I-tunes. Which inequality can be used to
calculate how many times that you can forget to
make your bed, 𝑏, and have at least $12 left to afford
the song you want?
A. 20 − 1.5𝑏 ≥ 12
B. (20 + 1.5)𝑏 ≤ 12
C. 12 − 20 > 1.5𝑏
D. 20 + 1.5𝑏 ≥ 12
9. Simplify: (2𝑓 2 − 3𝑓 − 5) − (−2𝑓 2 − 3𝑓 + 10)
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
10. Find the volume of the figure below.
14. Simplify:
A. −
B. −
−28𝑥 3 𝑦5 𝑧
20𝑥 3 𝑦 4 𝑧 2
8𝑥3 𝑧
3𝑦
7𝑦
5𝑧
C. −
14𝑥2 𝑦
4𝑧3
D. −
7𝑥6 𝑦9 𝑧3
10
15. Find the missing factor:
72𝑥 8 𝑦 5 = (6𝑥 2 𝑦)(3𝑥𝑦)(__? __)
A. 9𝑥𝑦
B. 4𝑥 5 𝑦 3
C. 8𝑥 4 𝑦 3
D. 4𝑥 4 𝑦 2
16. What is the area of the rectangle modeled below?
6𝑥 + 7
2𝑥
2𝑥 − 3
4𝑥
7𝑥
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
11. Simplify: (3𝑎3 )(4𝑎3 ) + (2𝑎5 )(𝑎)
A.
B.
C.
D.
12𝑥 2 − 14𝑥 − 21
12𝑥 2 − 4𝑥 − 21
12𝑥 2 − 18𝑥 − 21
12𝑥 2 + 22𝑥 − 21
17. 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.)
𝐴 = 16𝑥 2 + 24𝑥 + 9
𝐴 = 16𝑥 2 − 24𝑥 + 6
𝐴 = 16𝑥 + 9
𝐴 = 8𝑥 2 + 6
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
A.
B.
C.
D.
12. Simplify: (2𝑎𝑏 4 )3 (−3𝑎2 𝑏 2 )2
18. Factor Completely: 𝑥 2 − 13𝑥 + 36
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
3
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?
24. Jasmine is taking Algebra 1 this year. Her goal for the six
weeks is to average at least an 85 for her 4 unit tests.
During her first three tests, she scores 92, 67, and 80.
Which inequality best represents the situation if S
represents the score for her fourth test?
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
20. Graph the inequality and determine which of the
points are solutions.
𝑦 ≤ −𝑥 + 2
A. A only
A.
92+67+80
3
B. S >
C.
92+67+80
3
92+67+80+𝑆
4
B. A and B only
C. C and D only
D.
92+67+80+𝑆
4
D. A, B, C, and D
21. Factor Completely: 15𝑣 2 + 4𝑣 − 4
+ 𝑠 ≥ 85
≤ 85
≥ 85
25. 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.
A. shifts down 2 units ____________
A. (3𝑣 − 4)(5𝑣 + 1)
B. shifts up 2 units _______________
B. (3𝑣 − 2)(𝑣 + 2)
C. twice as narrow _______________
C. (3𝑣 + 2)(5𝑣 − 2)
D. twice as wide _________________
D. (3𝑣 + 4)(5𝑣 − 1)
E. opens downward ______________
22. Factor Completely: 12𝑛3 − 30𝑛2 + 18𝑛
26. Solve for 𝒙: (𝑥 − 5)(𝑥 + 7) = 0
A. 6𝑛(2𝑛 − 3)(𝑛 − 1)
B. 6𝑛(2𝑛 − 1)(𝑛 − 3)
C. 6𝑛(2𝑛 + 3)(𝑛 − 1)
D. 6𝑛(2𝑛 + 1)(𝑛 − 3)
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
23. The area of a rectangle is 36𝑥 2 − 121. Which of the
following represents the dimensions?
27. Solve: 3𝑎2 − 𝑎 − 2 = 0
2
A. (3𝑥 − 11)(12𝑥 − 11)
A. 𝑎 = − 3 , 1
1
B. (9𝑥 + 11)(4𝑥 − 11)
B. 𝑎 = 3 , 2
C. (6𝑥 + 11)(6𝑥 − 11)
C. 𝑎 = , 1
D. (2𝑥 + 11)(18𝑥 + 11)
D. 𝑎 = − 3 , −2
2
3
1
4
28. Match the following functions to their graphs.
A.
32. 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?
B.
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
_____ 𝑦 = 𝑥
_____ 𝑦 = 𝑥 2
_____ 𝑦 =
33. What are the zeros to the quadratic function graphed
below?
2
𝑥
A. 2, −1
C.
B. 0, 3
C. 0, 1
D. 1, 3
29. For the function 𝑓(𝑥) = 8𝑥² − 4𝑥 − 3 what is the
value of 𝑓(𝑥) when 𝑥 = 2?
34. If 𝑦 varies directly as 𝑥, what happens to 𝑦 if 𝑥 increases?
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
A. –23
B. 1
C. 41
D. 21
30. Which statement describes the change in the graph
of 𝑦 = 2.5𝑥 2 when the equation is changed to 𝑦 =
2.5𝑥 2 + 4?
If 𝑦 varies inversely as 𝑥, what happens to 𝑦 if 𝑥
increases?
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
35. Write an equation in slope-intercept form of the line that
passes through the point (2, -2) and has a slope of -3.
A. 𝒚 = −𝟑𝒙 − 𝟒
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.
B. 𝒚 = −𝟑𝒙 − 𝟏
C. 𝒚 = −𝟑𝒙 + 𝟒
D. 𝒚 = −𝟑𝒙 + 𝟏
D. The graph of the parabola moves down 4 units.
31. What are the x-intercepts of
𝑓(𝑥) = 5𝑥² − 22𝑥 + 8?
36. Graph each of the following equations.
A. 𝒚 = −𝟐𝒙 + 𝟑
A. (0.4,0) 𝑎𝑛𝑑 (4,0)
B. (−5,0) 𝑎𝑛𝑑 (−2,0)
C. (−4,0) 𝑎𝑛𝑑 (−0.4,0)
D. (2,0) 𝑎𝑛𝑑 (4,0)
𝟏
𝟐
B. 𝒚 = 𝒙 − 𝟑
5
37. At Algebra High School the ratio of freshmen to
sophomores is 5 to 4. If there are 320 sophomores,
then how many freshmen are there?
42. Evaluate
𝑥 2 −𝑦 2
2𝑧
for 𝑥 = 3, 𝑦 = −1, 𝑧 = −2.
𝑨𝒏𝒔𝒘𝒆𝒓: ______________________
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
38. Write an equation of a line that is parallel to 𝒚 =
𝟒
− 𝟑 𝒙 + 𝟕.
43. The lengths of the sides of a quadrilateral are given as
shown. Express the perimeter in terms of 𝒙.
A. 𝟔𝒙𝟒 + 𝟔
𝑨𝒏𝒔𝒘𝒆𝒓: ______________________
B. 𝟒𝒙𝟐 + 𝟏
What has to be true for two lines to be parallel?
C. 𝟖𝒙𝟐 + 𝟕
________________________________________
39. Graph each of the following equations. (Hint: Each
graphs a line.)
A. 𝒙 = 𝟑
B. 𝒚 = 𝟑
D. 𝟗𝒙 − 𝟏
44. Which of the following is the quadratic formula for all real
values of a,b, and c where a ≠ 0?
A. 𝑥 =
B. 𝑥 =
C. 𝑥 =
Which graphed line is an example of an equation with a
slope of zero? ___________________ What is the slope
of the other graphed line?____________________
D. 𝑥 =
𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
Now solve 4𝑥 2 − 𝑥 − 5 = 0.
𝑏±√𝑏 2 +4𝑎𝑐
2𝑐
−𝑏±√𝑏 2 −4𝑎
2𝑎𝑐
−𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
𝐴𝑛𝑠𝑤𝑒𝑟: ______________________
40. Solve: 17𝑥 − 7 = 4(3𝑥 − 2)
A. 𝑥 = −0.2
49
45. Simplify completely: √100
A.
7
50
B.
√7
√10
C.
7
10
D.
√49
√100
B. 𝑥 = 0.5
C. 𝑥 = 2
D. 𝑥 = 0.2
41. Two lines have the equations:
𝒙 + 𝟐𝒚 = −𝟒
𝟒𝒚 = 𝟑𝒙 + 𝟏𝟐
At what point do the lines intersect?
A. (3, -2)
B. (2, -3)
C. (4, -4)
D. (-4, 0)
46. Choose the type of function represented below.
A. Linear
B. Quadratic
C. Exponential
D. None of the above
47. Choose the type of function represented below.
A. Linear
B. Quadratic
C. Exponential
D. None of the above
48. Match the type of function represented below.
A. Linear
B. Quadratic
C. Exponential
x
−1
0
1
2
3
y
4
1
0
1
4
x
−2
−1
0
1
2
y
1
3
5
7
9
x
0
1
2
3
4
y
1
5
25
125
625
49. Suppose 𝑥 and 𝑦 vary inversely, and 𝑥 = 3 when 𝑦 =
1.2. Find the function that models the inverse
variation, and find 𝑦 when 𝑥 = 9.
2
A. 𝑦 = 5
B. 𝑦 = 4
1
C. 𝑦 = 4
1
D. 𝑦 = 6
50. State the vertex and x -intercepts(s) of the given
graph.
A. vertex: (-1, -2)
x-intercept(s): 4, 1
B. vertex: (-2, -8)
x-intercept)s): 0
C. vertex: (-2, -7)
x-intercept(s): -4, 0
D. vertex: (-4, 1)
x-intercept(s): -4, 0