CT Algebra 1 S2 Final Exam Review Packet (2016)
Name: ___________________________________
Solve:
1. 3x 
4
15  10 x   16
5
Graph:
4. 4y – x = 8
2.
5.
y = ____________________
7.
x=5
2x  3 x  7

5
2
3.
-9x + 3y = -18
6.
y = ____________________
8.
y = -2
3
x  2  16
4
5x – 4y = 8
y = ____________________
9.
y=x
Write the following in all three forms of a line (Point-slope, slope-intercept, and standard)
10. A line with a slope of 7 and goes through (-2, 5) 11. A line through points (1, -3) and (3, 3)
Point Slope:
Point Slope:
Slope-intercept:
Slope-intercept:
Standard Form:
Standard Form:
Write an equation or inequality for the following graphs.
12.
13.
14.
Solve:
15. x – 5 ≤ 3x + 7
16.
5 – 8x ≥ 11
17.
18.
-6 < -3x – 15 < 12
-2 < x + 1 < 2
Solve using substitution or elimination. Write your answer as an ordered pair.
19. 3x – 2y = 23
20. 2x + 5y = 7
21. 3x + 2y = -5
y = 3x – 19
-4x – 10y = 2
4x – 3y = 16
22. Julie sold 500 tickets for the spring musical. Student tickets cost $2 and adult tickets cost $5. Julie’s
sales totaled $1789. How many student and how many adult tickets did Julie sell?
23. Joe has 120 coins, all nickels and dimes. He has 20 more dimes then nickels.
a) Write a system of equations representing the scenario.
b) How many nickels and how many dimes does Joe have?
Solve
24. | 2x + 5 | = 7
25.
3| x – 6 | = 9
Solve the following systems of equations by graphing. Write your solution as an ordered pair.
27. y = 2x + 5
2
26. y =  x 1
x + 3y = -6
3
2
y = x3
3
Solve the following systems of inequalities.
28. x + y < 6
1
y≥- x+4
3
29. y < 2x – 4
y > -½x + 1
30. Write a system of inequalities to describe the shaded area of the graph.
Answer:
_______________________________
_______________________________
Simplify
31. a. 32
b.
56
32.
a. 2 3  2
b. 3 6  5 3
Simplify using Exponent Rules:
35. 4x 6
38.
18b3c 0 3ab 2

4bc3 5a 2c3
33.
36.
39.
 3x y    2 x y 
5
 2x5 
 3 
 y 
2
3
a.
5
2
b.
3
3
20x15
34. a.
96x 25
b.
37.
3x5 y 4
40.
 2 x3 y 2 
 4 
 3x y 
3
2
Classify by degree and number of terms.
41. 2 y3  y 2  3 y  4
42. 7 x  2
43.
 x2  5x  12
Degree: _____________________
Number of terms:______________
Degree: _____________________ Degree: _____________________
Number of terms:_____________ Number of terms:_____________
Simplify:
44. (3z3 + 2z2 + 7) – (z3 – 3z – 6)
45. (5t4 – 6) – (5t + 2) + (7t4 + 4t)
46. (x – 5)(x + 9)
47. (3x – 2)(x + 4)
48. (4x + 7)2
49. (2x – 5)(3x2 + 4x – 8)
Factor:
50.
x2 – 49
51.
16 x 2  25
52.
9 y3  18 y 2  5 y  10
53.
x 3  3x 2  x  3
54.
2x3 – 16x2 + 30x
55.
3x3 – 12x2 – 15x
56.
4x2 – 20x + 25
57.
36w5 z8  9w2 z 3  18w3 z 6
58.
.
x2 – 11x + 30
Solve by factoring, square root method, completing the square, or by using the quadratic formula:
−𝑏±√𝑏 2 −4𝑎𝑐
𝑥=
. Make sure that you practice each method at least one time.
2𝑎
59. x2 – 6x = -1
x 3
x
61. x2  17 x  30  0
60.

8
x3
62.
3x2 = 75
63.
5x2 – 3x = 2
64.
12a2 – 3a = 0
65.
𝑥 2 + 4𝑥 = 8
66.
2 x2  6 x  3  0
67.
1
2
 x  4   24
2
68.
4 x2  4 x 1  0
69.
5
x

x 3 x  4
70.
x2  14 x  45
Solve: Check for extraneous solutions.
71.
72.
a  4  10
18  2 x  3  4
73.
State the domain and range of each graph:
74.
75.
Domain
Domain
Range
Range
3x  4  5x  12
What number must be added to complete the square?
76.
x 2  10 x  ______
77.
x 2  18x  ______
Find the vertex and the equation of the axis of symmetry line.
78. y = 2x2 – 16x + 6
79. y = x2 + 4x + 5
Vertex: ___________________________
Vertex: ___________________________
AoS: ________________________________
AoS: ________________________________
80.
y = -(x – 3)² + 7 (SKIP)
81.
y = 2(x + 8)² – 5 (SKIP)
Vertex: ___________________________
Vertex: ___________________________
AoS: ________________________________
AoS: ________________________________
82. What are the roots of the graph
below?
83. What are the solutions of the
quadratic function graphed below?
84. What are the zeroes of the
quadratic function graphed below?
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
-2
-10 -8 -6 -4 -2
2
-4
-4
-6
-6
-8
-8
-10
-10
What do you know about the discriminant
based on the # of roots?
What do you know about the discriminant
based on the # of solutions?
Find the discriminant.
85. x2  2 x  3  0
86.
5x2  6 x  1  0
4
6
8 10
-2
What do you know about the discriminant
based on the # of zeros?
87.
4 x2  4 x  1  0
88. The equation h = -4.9t2 + 44.1t + 40 models the path of firework shot off the roof of a building, where height h in
meters and time t in seconds. Round to the nearest hundredth.
Starting height _____________
Height after 6 seconds _____________
Time it takes to reach the highest point _____________
Highest point reached (max height) _____________
Time it takes to hit the ground______________
89. The equation h = -16t2 + 104t + 6 models the path of an apple launched upwards into the air, where height h in feet
and time t in seconds. Round to the nearest hundredth.
Starting height _____________
Height after 5 seconds _____________
Time it takes to reach the highest point (max height) _____________
Highest point reached _____________
Time it takes to hit the ground______________
Graph using 5 points. Hint: Find the vertex first.
Then make a t-chart.
90.
y  x2  4 x  5
Graph using 5 points. Hint: Find the vertex first.
Then make a t-chart.
91. y  x 2  8x  12
Identify the following relationship as causation or correlation.
92. The age of a child and his/her 93. The amount of rainfall and the 94. Reading in dim lighting and
weight.
level of water in the rain gauge.
the need for glasses.
Identify the following sample as biased or unbiased.
95. 800 children under the age of 96. Every 4th person at the zoo
16 were asked if the town should
was asked what is their favorite
have more ice cream trucks.
type of music was.
97. Kyle is at the Colt’s game and
is taking a survey on people’s
favorite NFL team.
A sample of men was taken to study the relationship between age and baldness. The data is
summarized in the table.
Bald
Yes
No
Total
Age is < 45
18
41
59
Age is ≥ 45
34
7
41
98. What is the percentage of men < 45 that are bald?
99. What is the percentage of men who are bald and age ≥ 45?
100. What is the percentage of men who are not bald?
Total
52
48
100