Download Unit #1 Study Guide (Self-test) - New Paltz Central School District

Name: __________
Date:_______
Review Unit #1 Study Guide (Self-test)
Check your notes for additional help!!
Radicals: ALL answers MUST be in simplest radical form!!!!
1) Simplify: 7 45
2) Simplify: 2 20


Multiplication:
3)
 12  3  

4)  2 2
 12  
5)
3 2 4 5 
6) A rectangular flower garden is shown at the right. It has a length given by
15 yards and a width given by 10 yards. Find the area of the figure below.
(Area= length times width)


Division:
7)
96
3
8)
36
3
9) 3
75
5

1
Addition:
10)
2 3 2
11) 5 45 2 20
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
Subtraction:
12) 2 27  5 12
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Mixed operations:
13) 13 5  125  2 45
14)
18  5 300  2 48
Exponents:
Simplify the following:
15) x2 x7
 10 x 2 y 7
19)
5 xy
16) (3x2y4)2
20)
17) x-6
21)
18) 5-3
22)
x 
x 
4 0
4 3
y 3  y  y 2
2
Scientific Notation:
23] Express each in scientific notation:
a.)
92,960,00 (miles between Earth and the Sun)
b.)
300 million (Population of the US)
c.)
0. 000000000753 (kg-mass of a dust particle)
24] Perform the indicated operation. Express answers in scientific notation.
5 x 10-2  3 x 107
25] The Population density of a region is the number of people per square mile and
is calculated by finding the ratio (fraction) of the population to the land area. The
Earth’s population is 6.5 x 109 and has a land area of 5.8 x 107 square miles. Find the
population density. Include units.
Venn Diagrams:
26] Central High School has 480 freshmen. Of those freshmen, 333 take Algebra,
306 take Biology, and 188 take both Algebra and Biology. How many freshmen at
Central High School take neither Algebra nor Biology?
3
27] A high school surveyed 260 of its students regarding participation in either
track or cross country. The result of the survey showed that 92 students
participated in track only, 38 students participated in cross country only, and 86
students participated in neither sport. Of those surveyed, how many students
participated in both track and cross country?
Set Theory:
28] A = {apples, bananas, oranges,}
B = {lemons, peaches, apples}
A B=
A
 B=
29] If A={(1,2),(2,3),(3,4),(4,5),(5,6)} and B ={(4,7),(3,5),(2,3),(1,2),(0,1)},
then find
A  B.
30] Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8}
B = {3, 5, 7}
a) Find A  B
_____________________
b) Find A  B
_____________________
c) Find Ac
d) (A  B)c
_____________________
_____________________
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31] For each of the following, the graphs of two sets, A and B, are shown
below. Graph their union and intersection. Then write each using set-builder
notation.
32] In the set of real numbers, express the set [-∞, -2] or [3, ∞in the
following ways:
Set-builder ______________________
Graph on a number line:
33] In the set of real numbers, express the complement of the set [5, ∞in
the following ways:
Interval notation ___________________
Set-builder ______________________
5
34] In the set of real numbers, express the set of integers which are greater
than -1 and less than or equal to 3 in the following ways:
Interval notation ___________________
Set-builder ______________________
Roster:_________________
Real Number System:
35] Write a roster for each set of numbers.
36] Which of the following is a rational number, but not an integer?
(1)
12
(2) 
3
7
(3)
15
3
(4) -6

Evaluating Expressions:
37] Evaluate the following expressions when,
X = -2, r = -1,
a2 b2
a = 6,
b = -8
x2 + 4
-x2 + 4
x- b
-x- b

4 3
r
3
6