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Algebra Midterm Study Guide
Evaluate Expressions
1.
Find the value of 3 x 2  4 x  2 when x= -3
Set Notation
Represent all real numbers greater than 0 and less than or equal to 4 using the following
notations:
2.
Interval Notation:
3.
Graph:
Properties
4.
5.
6.
7.
8.
9.
Provide an example
Commutative
Associative
Distributive
Additive identity
Additive Inverse
Multiplicative identity
10. Multiplicative
inverse
a+b=b+a
(a + b) + c = a + (b + c)
a(b + c) = ab + ac
a+0=a
a + (-a) = 0
ax1=a
1
ax
=1
a
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Verbal expressions
11.
12.
10 more than 3 times a number:
________________
6 less than 2 times a number is the product of 3 and the number: ______________
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Polynomials: Review any other exponents laws.
13. Simplify
x 2  x  6  2x 2  4
14. Simplify
( x 2  2 x  3)  (4 x 2  2 x  3)
15. Simplify
(4 x 2  3x  2)  (3x 2  7 x  6)
16. Simplify
( x  6) 2
17. Simplify (4 x 2  3x  2)( x 2  7)
Solve Equations: Solve for the given variable and write solution in set notation
18. )
3( x  2)  4  47  4 x
20. Solve for x: ax – 2b = b + q
19)
.6x  8  .25x  10
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Inequalities: Solve and graph on a number line. (Make sure you reverse the inequality sign when
multiplying or dividing by a negative number.)
21. -3x + 6 > 18
22. 2x < 6 or x + 2 > 10
23. Your local garden shop has plants on sale for $1.50 each. You are planning a vegetable
garden. You have $20 to spend on tomato plants.
a. Write an inequality to find the greatest number of plants (p) you can buy.
b. What is the greatest number of plants you can buy?
Word Problems
24. Sally has quarters and dimes in her pocket. She has 20 coins in all and has $3.65 in all. How
many quarters and dimes does she have?
25. Dominick has twice as many nickels as pennies and 5 times as many dimes as pennies in his
talking cow bank. He has total of $ 1.22. How many of each kind does he have?
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Statistics
26. A. The weekly salaries of seven employees at McDonalds are $140, $220, $90, $180, $140,
$200, $1200. For these seven salaries, find:
(a) the mean
(b) the median
(c) the mode
(d) the range
B) Construct a box plot based on the salaries. Make sure you state the 5 statistical data
summary.
C) How do you describe the distribution? Is there an outlier?
27. Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on the
next test to have an average of exactly 80 for the four tests?
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28. The scores for a class of 20 students are as follows:
93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95
a) Copy and complete the table shown at the left.
Test
Scores
91-100
Frequency
b) Find the modal interval. The "modal interval" is the interval
containing the greatest frequency. It is not the mode.
81-90
71-80
61-70
c) Find the interval that contains the median
51-60
d) Construct a histogram, label, label, label
Vocabulary: Circle one
29. Jed's new horse is 15.2 hands high, 1250 pounds, costs $2,200, and is 3 years, 4 months. Is
this quantitative or qualitative data?
30. The tree has rough brown bark, red berries, wandering branches, and small, sharply edged
leaves. Is this quantitative or qualitative data?
31. Is a study of whether the number of hours a student studies will improve his/her final
examination scores and an example of univariate or bivariate data?
32. In a study that was conducted to determine whether office workers have high blood
pressure, when the participants in the study were friends of the researcher who shared the
same doctor, biased or unbiased?
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Systems:
33. Solve the following system of equations algebraically:
4x + y = 11
x+y=2
34. Solve algebraically, using two variables.
At a store, Justin bought three notebooks and two pencils for $2.80. At the same prices, Nina
bought two notebooks and five pencils for $2.60. Find the cost of one notebook and one pencil.
Linear Equations:
35. Given the equation y – 2x + 6 = 0
a) Would the graph of this equation be a line, a parabola, or something different?
b) What is the slope of this function?
c) What is the y-intercept of this function?
d) Explain in words how you would graph the equation?
e) Graph it.