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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