Hmk. Section 0 Math 1050-­‐003 Instructor: Katrina Johnson  Things you already know from Math 1010.  1. (a) Evaluate/simplify these expressions then graph and label each number. (Place a dot on the number line with the letter above it, refer to the example.) (b) Complete the second column in the table identifying the smallest set the number belongs to. (Choose from these sets: R = real numbers, Q = rational numbers, I = irrational numbers, Z = integers, W = whole numbers.) Number to evaluate and graph: Smallest Set it belongs to… 8
2
Example: A. B. − 2 C. – 22 €
D. 50 €
E. π −1 F. – 0.3 € G. 0.3 H. 7 − 3 € I. 3 − 6 x
€ J. IF x is negative x
x
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K. IF x is positive x
L. €
Additive Identity €
M. € Additive inverse of €
3
4
N. Multiplicative Identity O. Multiplicative inverse of €
0
P. 6
6
Q. 0
0
€ R. 0
3
4
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€ €
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
0
1
2
3
4
5
2. List all the integers in these intervals. (a) (-­‐3, 4] (b) [1, 5] (c) (5, ∞) (d) (3, 4) (e) (-­‐∞, 1] 3. Using 5x 3 − 2x + 4 = 0 , fill in an example of each of these questions, to practice your understanding of the vocabulary words. (For instance, if I asked for “degree”, you’d write 3 is the degree.) €
Equation €
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Vocabulary Word Example Expression Term Constant Coefficient Exponent 4. Use the order of operations to evaluate these expressions. (a) 3 • 5 − 6 ÷ 4 + 2 (b) 4 + 3 • 2 3 ÷ 4 − 2 2x 3 − x
(c) IF x = -­‐2, y = 3, and z = -­‐6 yz + y
5. Evaluate these power (exponent) expressions. 2
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(a) 64 3 3
2
(b) 64 −2
3
(c) 64 −3
(d) 64 2 3
(e) −64 2 2
(f) (−64) 3 6. Simplify, by rationalizing the denominator. 5
(a) 10
3
(b) 5 −2
2x 3
(c) 8x 6
7. Simplify and write each expression with positive, rational exponents. −
(a) 1
2
5
2
5 (5x )
(5x)
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(b) 3
3
2
8x 3 y 6 32⋅ 8⋅ 2 4
(c) (Hint: Rewrite this as 2 to some power.) 64⋅ 16⋅ 2 −3
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8. Factor completely. (a) 90 x 2 + x − 2 (b) 2y 3 − 7y 2 −15y € (c) € (d) 4q 2 − 4qr + r 2 z 3 + 27 (e) €
x 3 − 27 (f) € 9u 2 − 4v 2 € (g) 9x 2 −12x + 4 € (h) €