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Algebra 1
Midterm Exam
Name ________________________
Chapters 1/2
Properties
2
2
0
1)
5
5
___
2)
If 12  8  4 , then 8  4  12 ___
3)
2  3  4  2  3  4
___
4)
5 7
 1
7 5
___
5)
63  3 6
___
6)
81  8
___
7) Which property justifies the statement?
8) Simplify:
A:
B:
C:
D:
E:
F:
G:
H:
I:
J:
K:
Additive Identity
Multiplicative Identity
Multiplicative Inverse
Multiplicative Property of Zero
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Substitution Property of Equality
Commutative Property
Associative Property
Distributive Propert
 412  2x  3   48  8x  3 ?
4x  3  5x  2  17 x  5  x
PEMDAS
9)
6  22  3  9
16
10)
82  64
4
25
11)
Evaluate
2
 y
12)    4 y when y  6
2
14)
13) x 3  4 x  1 when x  3
1
1
x  y when x  18 and y  12
2
3
1
6
2

 2  42 3
Sets of Numbers
Real, Rational, Irrational, Natural, Whole and Integer
Identify which sets each number belongs to:
15) 93
16) - 0.0625
17)
8
7
18)
 144
3
35
2
2
Absolute Value
19)
16  25   18
 12  1  4
20)
Ordering Real Numbers
Write each set of numbers in order from least to greatest.
21) 0.03
2
8
0.17
22) -
84
30
 8

7
8
23) - 8.5 
Translations
24)
18 less than a number
25)
Twice a number increased by 10
26)
Antonia’s age a is three times as much as her son Nicky’s age n
Matrices
 8 5 
M   0 1 
12  7
27) What are the dimensions of this matrix? ____________________________
28) Where is 12 located in this matrix? ______________________________
29) What number is located in M 21 ? ______________________________
2
19
20
 9 7
A

  5 3
 8 4 0
B

 1  6 2
 5 3  9 
C

 1 0  2
30) What are the dimensions of matrix A? ________________________
31) What are the dimensions of matrix B? ________________________
32)
A+B
33)
34)
-9B
Chapter 3
Solving Equations
35)
5  2x  3  4 x  8
37)
1
3 1 3
x   x
2
4 5 2
36)
3x  1  5  3x  2
39)
a
mr
x
Literal Equations
Solve for x.
38)
ax  by  c
3
C–B
Word Problems
40) Find three consecutive integers whose sum is 171.
41) Find three consecutive integers such that the sum of twice the smallest and 3 times
the largest is 126.
42) The perimeter of the rectangle shown below is 42. Which equation best represents
this situation?
(Perimeter of a Rectangle is P  2l  2w ).
3x + 1
2x
Proportions
43)
x  5 2x  1

4
3
Percent of Change
44) A company buys a pair of jeans at wholesale price for $25. Then they sell the jeans
at a department store for $125. What is the percent increase in the cost of the jeans?
4
Discount & Tax
45) Jessie is on a dinner date with Lindsay. Jessie wants to tip the waiter 15% because
the service was good. The total bill is $35. How much money does he need to pay the
bill and tip the waiter?
Chapter 6.1-6.3
Solve and graph the Inequalities
46) 3 2d  1  4 2d  3  3
47) –10x – 5 < –2x + 3
Word Problems
48) Justin must have an average of at least 90% on five tests to receive a grade of A. His
grades on the first four tests were 85%, 93%, 88% and 94%. Write an inequality he can
use to find the minimum percent score he must make on the fifth test to receive an A.
49) Alfonso is a sales manager for a company that rents beach condominiums on
Emerald Isle. Alfonso’s weekly goal is for his sales team to average $9000 in sales each
day this week. Their sales for the first four days of this week were $8,200, $9,100,
$9,300, and $7,400. Write an inequality he can use to find the minimum sales his team
must achieve on Friday to average $9,000 each day for the week.
50) Carl has budgeted $60 to buy pork ribs and chicken legs for a faculty barbecue.
Pork ribs cost $3.75 per pound, and chicken legs cost $0.75 per pound. If Carl plans to
but x pounds of chicken, write an inequality in standard form that represents the number
of pounds y of ribs he can buy and not exceed his budget.
5
Chapter 4
Midpoint
Find the midpoint:
51) 1,5 and 3,1
52) 2,7 and  2,2
Find the other endpoint:
54) Endpoint: 5,2
Midpoint: 3,10
53) Endpoint: 2,6
Midpoint:  7,1
Relations, Functions, Domain & Range
State whether each set is a function. Answer yes or no. Find the domain and the range.
55)
{(4, 3), (-2, 10), (5, -6), (10, 7)}
Domain:
Range:
56)
{(8, 6), (-5, 2), (0, 6), (-5, 1)}
Domain:
Range:
Use the vertical line test to determine whether each graph is the graph of a function.
Answer yes or no.
57)
58)
59)
6
60) _______
Independent and Dependent Variables
61)
Time (Hours)
Temperature
1
-2
4
7
7
16
10
25
13
34
Independent Variable:
Dependent Variable:
62)
A baby is 18 inches long at birth and 27 inches long at ten months.
Independent Variable:
Dependent Variable:
Evaluate Functions
63) g(x) = 2x4 – 7x, what is g(3)?
Graphing Linear Equations Using A Table & Calculator:
64) 3x – 5y = 30
x
y
Graphing Linear Equations Using x and y intercepts:
65) Graph 2x + 3y = -18
x-intercept:
y-intercept:
7
Arithmetic Sequences
66)
Find the nth term of the arithmetic sequence described.
a1 = 5, d = 2, n = 25
67)
200 is the ______th term of 24, 35, 46, 57, . . .
68)
Write an equation for the nth term of the arithmetic sequence -13, -15, -17, -19, . .
.
Recursive Sequences
69) Find the 4th term
an  3an 1  2
a0  5
Chapter 5
Slope
Find the slope of the line through the given points.
70) 3,  5 and 6, 4
71) 2,  6 and 2, 9
Direct Variation
73) If x  9 2 when y = 10, find x when y = 15.
74) If y  49 when x = 6, find y when x = 9
75) If y = 16 and x = -2, what is the constant of variation?
8
72)  3, 7 and 8, 7
76) Hooke’s Law states that the distance a vertical spring stretches varies directly with
the weight hanging from it. A spring stretches 14 inches when a 35-pound weight is
hanging from it. How much weight is needed to stretch the spring 44 inches?
Graphing in slope intercept form
Solve for y, graph and write the slope.
77)
5x  2 y  8
78)
Slope:
x  3y  6
80) x  7
79) y  5
Slope:
Slope:
Slope:____
Writing Linear Equations
Write in Point Slope Form then write simplify your answer in slope intercept and
standard form:
81)
5,  2
83)
 2, 4 and 1,  5
m7
82)
 4, 1
m
2
5
84) (5, 2) m = undefined
9
Slope of Parallel and Perpendicular Lines
Solve for y. Find the slope. Find the slope of a line parallel to the original line. Find the
slope of a line perpendicular to the original line.
Slope
Parallel
Perpendicular
85) 10x + 2y = –10
86) x = 3
87) y = 2
Writing Equations for Parallel and Perpendicular Lines
Find the equation of the line through the given point that is
(a) parallel to the given line
(b) perpendicular to the given line
(c) Write the equation in slope-intercept form and standard form.
88) 2x + 6y = 12
(5, –1)
Linear Regression
89) Find the line of best fit.
x
y
40
25
42
29
45
34
46
35
50
43
52
45
55
51
90) Let x = 0 correspond to the year 1980. Find the line of best fit.
x
y
1980
4.5
1985
6.6
1990
11.6
1995
12.6
1996
12.7
1997
13.1
10
1998
12.9
1999
12.4
Use the table to answer questions
All students in a class were surveyed after they took a chapter test. The teacher wanted to
know if studying at home produced a good test grade. After the survey was taken, the
following data were recorded in a table.
Hours Spent
Studying
Average
Chapter Test
Grade
0
0.25
0.5
0.75
1
1.5
2
3
5
7
29
32
35
38
40
47
54
66
79
89
91) Sketch the scatterplot and draw the line of best fit.
92) Find the line of best fit.
__________________________
93) Tell whether the data has a positive correlation, a negative correlation, or no
correlation.
___________________________
94) What is the independent variable? _________________________________
What is the dependent variable? ___________________________________
95) Estimate the grade a student would get who studied 4 hours? __________________
96) Estimate the number of hours needed to earn a grade of 93 on the chapter test.
____________________________
11
Chapter 7
Solving Systems of Equations:
Solve by substitution.
97)
Solve by elimination.
2 x  4 y  18
98)
3x  y  13
Solve by graphing.
99)
x  2 y  4
3x  4 y  12
100) Given
6 x  3 y  42
4 x  2 y  4
. What is x  y ?
12
4x  6y  2
6 x  9 y  3