Math 1090
Homework 1
9 January, 2011
Name:
1. Decide which category or categories each number belongs to. Check the appropriate
box(es) in the chart.
W (whole numbers) Z (integers) Q (rational numbers) R (real numbers)
√
2
3
4
1
−6
8, 462
π
− 53
2. Use the order of operations to evaluate each expression.
(a) 3 · 5 − 12 ÷ 4 + 2
(b) 4 + 3 · 23 ÷ 4 − 2
(c) (2 · (−2)3 − (−2)) ÷ (5 ∗ (−2) + 3)
3. Decide which expression from each pair cannot be evlauated and explain why not.
(a)
4
0
(b)
√
2
0
4
√
−2
(c)
1
(−4)2
(−4) 2
−161/4
(−16) 4
(d)
1
(e)
4
0
(f)
√
−64
0
4
√
3
−64
4. Drawing your examples from the mathematical statement
5x3 − 2x + 4 = 0
give an example of each of the following:
(a) Equation
(b) Expression
(c) Term
(d) Factor
(e) Constant
(f) Coefficient
(g) Exponent
5. Evaluate each expression. (Hint:
√
√
64 = 8 and 3 64 = 4)
2
(a) 64 3
(d) 64
−3
2
2
(e) (−64) 3
(b) 64
3
2
(c) 64
−2
3
3
(f) −64 2 (Remember order of operations!)
6. Simplify each expression, if possible.
(a)
3
4
+
2
3
(e)
(b)
3
4
−
2
3
(f)
(c)
3
4
·
(d)
3
4
÷
2
3
(g)
2
3
(h)
√
√
√
√
2+
2−
2·
√
√
8
√
2÷
8
8
√
8
7. Simplify each expression, if possible.
(a) x5 + x3
(e) x3 ÷ x5
(b) x5 − x3
(f) (x3 )5
(c) x5 · x3
(g) (x5 )3
(d) x5 ÷ x3
8. Simplify each expression by rationalizing the denominator.
(a)
√5
10
(b)
√3
5−2
(c)
√
3
√2x
8x6