Download Semester 2 Final Review

Name____________________________
Second Semester Final Review
Do your work on a separate piece of paper!
Prerequisite Skills:
Solve each equation.
1) 3(x-5) = 2(x+5)
2) 8 – (3 + a) = a – 9
3)
x
- 3 = -4
4
4) What are the solutions of -10 ≤ -3m +2 < 11? Graph your solutions.
5) Graph the following inequalities on a coordinate plane.
a. x < 3
b. 3x - y ³ 6
Need more practice?
 Look back to sections 2-1 through 2-4 and 3-6 in your book or try problems on p.153-154 #629 and p. 204 #17-22.
Chapter 5 (Linear Functions) Skills:
6) A line passes through (-3, 2) and has slope -2. Write an equation for the line in point-slope form.
7) What are the x- and y-intercepts of the graph of 3x + 4y = 24?
3
7
8) Write the equation y = - x + 5 in standard form using integers.
9) Write an equation in slope-intercept form for the line that passes through (2, 4) and is
perpendicular to the graph of y =
1
x – 1.
3
10) Write an equation in slope-intercept form for the line that passes through (1, 3) and is parallel
to the graph of y = 3x + 2.
11) Make a table for the function f(x) = x - 5 from x = 2 to x = 8.
12) A theater group is having a carwash fundraiser. The group can only spend $34 on soap, which
is enough to wash 40 cars. Each car is charged $5. Write an equation that shows the
relationship between c, the total number of cars washed, and p, profit. What is a reasonable
domain and range for this function?
Chapter 6 (Systems of Equations and Inequalities) Skills:
Solve each system by graphing.
More Practice? Look at
Section 6-1 (p.360) in your
book.
13)
4 x + 3y = 2
3x - 2y = 10
14)
y - 3 = 2(x - 4)
y = -3x + 5
Solve each system by using substitution. Check your solution.
15)
y = 2x -10
2y = x - 8
16)
2y = x -1
-2x - y = 8
More Practice? Look at
Section 6-2 (p.368) in your
book.
Solve each system using elimination. Check your solution.
17)
2x - y = 4
3x - y = 2
18)
x - 2y = 3
3x - y = 4
More Practice? Look at
Section 6-3 (p.374) in your
book.
Solve each system by using the most efficient method. Check your solution.
19)
2y = x + 1
-2x - y = 7
20)
3x - 2y = 8
2x - 2y = 5
Tell whether the system has one solution, infinitely many solutions, or no solution without
graphing.
y = 3x -1
21)
y = 3x + 4
2x + 3y = 6
22)
3
y =- x+4
2
More Practice? Look at
p.362 for help and p.364
#22-30 for practice.
Write a system to represent each situation. You do NOT need to solve the problems.
23) Mark is a student, and he can work for at most 20 hours a week. He needs to earn at least
$75 to cover his weekly expenses. His dog-walking job pays $5 per hour and his job as a car
wash attendant pays $4 per hour. Write a system for the situation and graph make a graph
of the situation.
24) Britney wants to bake at most 10 loaves of break for a bake sale. She wants to make banana
bread that sells for $1.25 each and nut bread that sells for $1.50 each and make at least $24 in
sales. Write a system for the given situation and make a graph of the situation.
Statistics Skills:
25) The test scores in an Algebra 1 class were 75, 91, 76, 89, 78, 53,
64, 100, and 78. Find the mean, median, mode, range, lower
quartile, upper quartile, and interquartile range.
26) Draw a box and whisker plot to represent the data in #25.
More Practice? Look at
Section 12-3 (p.726) in your
book.
More Practice? Look at
Section 12-4 (p.734) in your
book.
27) Draw a scatterplot to represent the following table of data.
Time Spent
Studying (in hours)
2
4.5
8
10
5
3.5
8.5
6
3
Test Score (%)
60
79
99
100
80
77
83
82
75
28) Describe the data in the scatterplot as strong, weak, positive, negative.
29) Draw a line of best fit through the scatterplot. Write an equation for this line.
30) Use the equation you wrote in #27 to determine what test score a student might get if they
studied for 7 hours.
Chapter 7 (Exponents) Skills:
Simplify the expressions. Always write answers with positive powers.
32) 4aw-2
31) 2⁰
34) x⁸ • y² • x-4
35)
1
x -3
36)
33) 3-4
More Practice? Look at
Section 7-1, 7-3, 7-4, and
7-5 (starts on p.414) in your
book.
y3
y6
37) (y-2)⁵
38) (x³y)²
39) (3a)³
15x 9 y 5
40)
3x 2 y 3
æ x7 ö
41) ç 3 ÷
èy ø
æ a 3b 5 ö6
42) ç 8 2 ÷
èa b ø
2
43) Write 0.0034 in scientific notation
More Practice? Look at
Section 7-2 (p.420) in your
book.
44) Write 1256.9 in scientific notation
45) Write 1.789 X 105 in standard notation
46) Write 3.7895 X 10-2 standard notation
47) Order the numbers from least to greatest: 9 x 10², 9 x 10⁷, 9 x 10¹, 9 x 10⁴
48) Simplify (3 x 10⁴) (2 x 10²). Leave your answer in scientific notation.
49) Graph the exponential function y = 2•3x.
50) Evaluate
More Practice? Look at
Section 7-6 (p.447) in your
book.
1 x
× 4 for x = 3
2
51) An investment of $5000 doubles in value every decade. Write a function to represent this
situation. How much is the investment worth after 30 years?
52) Suppose you have 70 tribbles (a small furry animal) and the number of tribbles increase 45%
every week.
a. What is the initial amount?
b. What is the growth factor?
c. write an equation to represent the situation
d. How many tribbles will there be in 8 weeks?
Chapters 8,9 (Quadratics) Skills:
Simplify. Write in standard form.
53) (2w3 – w + 8) + (-w3 + w - 3)
54) (4h3 + 3h + 1) - (-5h3 + 6h - 2)
Factor each expression completely.
55) 6x2 +2x
56) 4x5 - 24x3 + 8x
Find each product.
57) 6x2(4x2 + 3)
58) (x + 2)(x – 9)
59) (4b – 1)(b – 8)
60) (k – 3)(k + 3)
61) (2x + 5) 2
62) (z - 1)(z2 -4z + 9)
Factor each expression completely.
63) x2 – 11x + 24
64) x2 + 5x – 36
65) x2 - 3x – 10
66) 2x2 + 13x + 6
67) 4x2 - 8x + 3
68) 4x2 - 4x – 35
69) Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of
the function
y = -3x2 + 12x + 1.
Solve each equation.
70) z2 = 49
71) h2 – 25 = 75
Factor and solve:
72) x2 + 8x + 15 = 0
73) 4x2 – 21x = 18
Solve for x by completing the square. Round to the nearest hundredth.
74) r2 – 4r = 30
75) t2 + t – 28 = 0.
76) Use the quadratic formula to solve 2x2 + 5x + 3 = 0.
77) A ball is thrown in the air. The height, h, in feet, of the ball can be modeled by the equation
h = -16t2 + 20t + 6, where t is the time, in seconds, that the ball is in the air. At what time(s)
will the ball be 3 feet in the air?
78) The figures below are squares. Find an expression for the area of the shaded region. Write your
answer in standard form.
Answers:
1) x = 25
2) a = 7
3) x = -4
4) -3 < m ≤ 4
5) a.
6) y – 2 = -2(x + 3)
7) (8, 0) and (0, 6)
b.
8) 3x + 7y = 35
9) y = -3x + 10
10) y = 3x
11) posted in class
13) (2, -2)
12) p = 5c - 34
0 ≤ c ≤ 40
-34 ≤ p ≤ 168
14) (2,-1)
15) (4, -2)
16) (-3,-2)
21) No solution
17) (-2, -8)
18) (1, -1)
19) (-3, -1)
20) (3, 0.5)
22) One solution
23) D = # of hrs. dog walking
C = # of hrs. car washing
D + C ≤ 20
5D + 4C ≥ 75
D ≥ 0 and C ≥ 0
24) B = # of loaves of banana bread
N= # of loaves of nut bread
B + N < 10
1.25B + 1.5N ≥ 24
B ≥ 0 and N ≥ 0
25) mean = 78.2; median = 78; mode = 78; range = 47; lower quartile = 69.5; upper quartile = 90; IQR = 20.5
26) Answer posted in class
27) See bottom of page
28) Moderate, positive
29) See graph for trendline. y = 4x + 60 (bottom of page)
30) Answers may vary.
31) 1
32)
6 2
38) x y
4a
w2
39) 27a
33)
3
1
34
7 2
40) 5x y
34) x⁴y² 35) x³
x14
b18
41) 6 42) 30
y
a
43) 3.4 x 10-3
44) 1.2569 X 10³
47) 9 X 10¹, 9 x 10², 9 x 10⁴, 9 x 10⁷
49)
see bottom of page
36)
45) 178,900
48) 6 x 10 ⁶
46) 0.037895
50) 32
1
1
37) 10
3
y
y
35) a⁸b⁴
51) y = 5000⋅ 2x
$40,000
52) a. 70
b. 1.45
c. t = 70 • 1.45x
d. t = 1368 tribbles after 8 weeks
53) w3 + 5
54) 9h3 – 3h + 3
57) 24x4 + 18w2
55) 2x(3x + 1)
58) x2 – 7x – 18
59) 4b2 – 33b + 8
61) 4x2 + 20x + 25
62) z3 – 5z2 + 13z – 9
64) (x + 9)(x – 4)
65) (x – 5)(x + 2)
66) (2x + 1)(x + 6)
68) (2x + 5)(2x – 7)
69) x = 2; (2, 13)
70) z = 7 or -7
72) x = -3 or -5
73) x = -3/4 or 6
76) x = -1 or -3/2
77) t = 1.5 seconds
Test Score (%)
100
80
60
40
20
0
2
4
6
8
Time Spent Studying (hrs)
10
60) k2 – 9
63) (x – 8)(x – 3)
67) (2x – 3)(2x – 1)
71) h = 10 or -10
74) r = 7.83 or -3.83 75) t = 4.82 or -5.82
120
0
56) 4x(x 4 - 6x2 + 2)
12
78) A = 12x + 36