Download HW worksheet #1

MTH 104 Intermediate Algebra
1st Homework
(do not use a calculator)
Name: ______________________
P. Seeburger
1. Which elements of the given set are (a) natural numbers, (b) whole numbers, (c) integers,
(d) rational numbers, (e) irrational numbers, (f) real numbers, (g) undefined?
Many of these numbers belong to two or more sets of numbers. Include each number in all sets
to which it belongs.
2 6
75
{–9, 13, 8, − 6 , –.7, 0, 3 , , , 10.5,
}
0 7
5
(a) Natural numbers: ___________________
(e) Irrational numbers: _____________________
(b) Whole numbers: ____________________
(f) Real numbers: _________________________
(c) Integers: ___________________________
(g) undefined: ____________________________
(This means it is NOT a number!)
(d) Rational numbers: ___________________
2. Indicate whether each of the following sets of real numbers belong to the Natural numbers, the
Whole numbers, the Integers, the Rational numbers, or the Irrational numbers.
Use the letters N, W, I, R, or Irrational. Write as many as apply to all the numbers in each set.
Ex. {0, 2, 7}
W, I, R
Note: This set does NOT belong to the Natural
numbers because 0 is not a natural number (even though 2 and 7 are natural numbers).
a.
{–1, 4, 7}
_________________
b. {– π ,
c.
{ 11
, 1, – 23 }
8
_________________
d.
3, 7 }
__________________
{3, 5, 8}
__________________
3. Supply the following numbers.
a. The opposite of 7
_________
c. The additive inverse of 5 _________
b. The negative of –12
__________
d. The negative of 1
__________
4. Graph the following numbers on the given number line. Be sure you label them with the numbers.
2, –3, .5, –1.2, π
-4
-3
-2
-1
0
1
2
3
4
5. List the order of operations. (It does not have to be in the same words as the book.)
6. If A = {1, 3, 5, 7}, B = {3, 7, 8, 9}, and C = {2, 4, 6, 8}, determine the following sets.
a.
A∩B =
b.
B∩C =
c.
A∩C =
d.
A∪B =
7. Simplify. (Be sure to use the order of operations.)
a.
−3
b.
c.
8 − 10
d.
e.
− 5
5 − −7
4 − 2⋅3
2 + 2 · 2 + 2
8. Simplify: –5(3x – 2)
9. Evaluate the following expression where x = –2.
–3x3 + 4x
10. Simplify, showing work. Always reduce fractions, but you may leave an answer as an improper
fraction.
a.
−
1 3
+
2 4
b.
1 −
2 5
⋅
3 6
c.
−
4
⋅ (−8)
5
d.
3 −
6
5