ALGEBRA 1
Midterm Review
Algebra 1-Midterm Review
3/8/2016
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1) Complete the table of field properties of real numbers below.
Field Properties of Real Numbers
Let a, b, and c represent real numbers
Property
Addition
a + b is a unique real number.
Closure
Commutative
Associative
Identity
Inverse
Distributive
Multiplication
a · b is a unique real number
2) Perform the order of operations to determine the value of the following
expression:
3(5 + 42) ÷ 7 – 7
3) Match the following:
a. Probability of 0
I. Definite event
b. Probability of 1
II. Is not a probability
c. Probability of
1
2
III. Will occur 1 out of 2 times
d. Probability of 2
IV. Impossible event
4) Identify the following as discrete, or continuous.
a)
b)
c)
d)
e)
The floors an elevator stops on in a high rise.
The number of cars in the student parking lot.
The air temperature in a 10 hr. period.
The number of people in a senior class.
The number of books checked out of the library each day for a month.
5) Classify independent and dependent variables.
a) Total cost of gas; number of gallons of gas.
b) Total calories; number of slices of bread.
c) Total cost of an item; change from a $20 bill.
Algebra 1-Midterm Review
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6) Find the mean of the following 92, 91, 84, 86, 87, 91, 75
7) Find the mean, median, and mode of the following:
18, 90, 18, 30, 18, 98, 18, 30
8) Use an equation to model each situation.
A.
Tickets
1
4
6
8
B.
Cost
$7
$19
$27
$35
Hours
8
12
16
20
Pay
$40
$60
$80
$100
9) Evaluate each expression when x = 4, y = 8, z = 12
a) x2 + y2
z2
b) 5x –3y – z
c) 2(x + y)
d) 8x – 2y – z2
10) If x  y = z , then x = ________.
11) The point (5-5) is in which quadrant?
12) If 5% of the students in our class are left handed and there are 25 students in our
class, how many are left handed?
Algebra 1-Midterm Review
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13) Simplify 10 + 8 –14 – (10)
14) Write with numbers and variables.
a) Five more than twice a number
b) 10 less than the square of a number.
15) If 5 lbs. of potatoes cost $1.50, how much would 12 lbs. cost?
16) Identify the following as rational or irrational numbers.
a. π
1
b.
3
c. .589
d.
2
17) Find the function rule
x f(x)
-1 -3
0 -1
1
1
2
3
18) Let f(x) = 2x + 1. What is the range if the domain is (4,5,6)?
19) Which of the following is not a function?
a. (1,7) (2,9) (8,3)
b. (5,2) (-1,3) (5,6)
c. (1,9) (2,5) (3,7)
20) Which graph is not a function?
5
Algebra 1-Midterm Review
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21) Match each graph to the equation.
y = 3x
22) Solve
y = x2 = 4
y= x
2x
=4
3
23) Solve and graph the inequality 5 – 2x > 9
24) A shirt was $30 and went on sale for $22. Find the percent of decrease.
25) An Algebra student’s first grade test was 88% and their second was 93%. Find
the percent of increase.
26) What is the y-intercept of y = 4x –3?
27)
A horizontal line passes through the point (3,2)
a) What is the slope?
b) Name another point on the line
c) What is the equation?
28) A horizontal line pass through (3, -1) which other point does it pass through?
Algebra 1-Midterm Review
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29) What are the slope and y – intercept of the line that passes through (0, -1) (4,1)?
30) What is the y-intercept of:
y =
5
x–2 ?
8
31) Write the equation of the line with
slope = -
3
5
and
y – intercept = 2
32) What is 80% of 140?
33) 15 is what % of 60?
34) 42 is 40% of what number?
35) 60% of 100 is what number?
36) Add
-2 3
L
M
6 -2
N
4
-3
O
L2 - 5 8 O
+ M
P
-7 3 - 3P
Q N
Q
37) Subtract
-3 5 O L
4 -3 O
L
M
-3 - 7 P
N2 9 P
Q M
N
Q
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38) Compare the quantities in Column X and Column Y. What can you conclude?
Column X
Column Y
P (rolling a 5 on
a number cube)
a)
b)
c)
d)
P(rolling a 1 on
a number cube)
The quantity in column X is greater.
The quantity in column Y is greater.
The two quantities are equal.
The relationship can not be determined on the basis of the information
supplied.
39) Evaluate 5(b2-3b)3 + 1 for b= 2
39) Simplify 10.5  15.2
40) Simplify (-2)3
41) A road map has a scale of 4 cm : 1 km. A street is 3.5 km long. How long will
it be on the map?
a. 21.25 cm
b. .50 km
c. 14 cm
d. none of the above
42) Describe the graphs below as:
straight line, V, U, or O
a) y = x  4
b) y = x –10
c) 7x
d) 3x2 + 5
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42) Graph the inequalities below on a number line.
a) 7 < x  10
x
b) x  4 or x  -2
x
c) x < 3 or x > 10
x
d) x < 2 and x > 5
x
43) The opposite of -15 is which of the following?
a) –51
b) 15
c)
1
15
d) -
1
15
44) Which of the following is not an irrational number?
1
4
a.
b.
5
c. 210
d. 0.875
45) The total cost for movie tickets for a family equals the number of adults at
$8.00 each plus the number of children at $5.25 each. Write an equation to
model this.
46) Write a function for each.
x
f(x)
x
f(x)
5
-15
-3
4
2 6
2
-6
-2
3
0 2
-1
3
-1
2
1 4
Algebra 1-Midterm Review
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x f(x)
47) To simplify 10 + 3(4÷ 2), you should first calculate which of the following?
a. 10 + 3
b. 3 x 4
c. 4 ÷ 2
d. 3 ÷ 2
48) Slope as Rate of Change
There is a direct relation between the rate of change of a function and the
slope of its lines.
Study the graph to the left.
Carlos and Maria are on their
way to school. Answer the
following questions with values
of time (t). (For example, AB
includes all t between A and B.)
a) For what values of time (t) are Carlos and Maria stopped?
b) For what values of t do they increase their speed?
c) Which of these increase at the same rate?
d) Explain how this question relates to the slope of the lines?
e) For what values of t do Carlos and Maria decrease their speed?
f) At what time (t) do they achieve their highest speed?
g) For what values of t do Carlos and Maria drive at a constant rate?
49) Would you expect a positive correlation, negative correlation, or no
correlation between the two data sets?
a. A person’s age vs. the number of pets
b. Number of times you brush your teeth vs. number of cavities.
50) Find the slope of the line that passes through (-4, -6) and (8, -2).
Algebra 1-Midterm Review
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51) Find the slope and y-intercept of a line that passes through (-4,10) and
(-9,35).
52) Which of the following matches this graph?
x
a)
b)
c)
d)
x > -3 or
x > -3 and
x  -3 and
x > -3 and
x > 2
x2
x< 2
x =2
Solve the problems below:
53) -32 – 7 – 3
54) 15 – (-3.5)
55)
x
= -21
4
56)
x
-2=5
5
57)
x
+ 9 = 10
4
58) –5(2x –1) + 6x = 21
59)
1
(8x + 12) – 27 =15
2
60) There were three times as many adults as students attending a school
play, if the attendance was 480, how many adults, and students attended
the play?
Algebra 1-Midterm Review
3/8/2016
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Algebra 1-Midterm Review
3/8/2016
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