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Review Assignment 1. Evaluate/simplify these expressions and place the letter corresponding to each one on the number line below. (Place a dot on the number line and the letter above it, as shown in the example.) If the number does not simplify to some defined value, i.e., it is undefined, then just state that and you will not be able to plot that on the number line. Also fill in the table telling the smallest set the number belongs to. Choose from these number sets: R real numbers, Q = rational numbers, I = irrational numbers, Z = integers, W = whole numbers. NUMBER TO EVALUATE AND PLOT: A. SET: -V B. c 5° D. it-i E. —0.3 F. 0.3 G. V7E H. 3—6! i. J. J2_[. if x is negative x! ii xis postive . — K. Additive Identity L. Additive Inverse of M. Multiplicative Identity N. Multiplicative Inverse of n ..—. 4 P. Q. R. 0.9 EXAMPLE: S. = 4 W XI REVIEW ASSIGNMENT xii S 3 2 1 0 —1 4 2. List all the integers in these intervals. (a) (b) (c) (d) (e) (—3,4) [1,5] (5, o) (3,4) (oo, 1] 3 2x + 4 = 0, fill in an example of each of these questions to practice your understanding of 3. Using x the vocabulary words. (For instance, if I asked for “degree,” you’d say 3 is the degree.) — EXAMPLE VOCABULARY WORD Equation Expression Term Factor Constant Coefficient Exponent 4. Use the order of operations to evaluate these expressions. (a) 3 5 — 6÷4 + 2 (d) (2 (—2) — (—2)) ÷ (5 (—2) . + 3) a a (b) 4÷32÷4—2 (c) x 2x — 3 I if x=—2,y=3,z=—6 a 5. Evaluate these power (exponent) expressions. 2 —3 (a) 64 (d) 642 (b) 642 (e) _642 -2 (c) 64 (f) (—64) I a I a I a I 4 REVIEW ASSIGNMENT 6. Simplify, by rationalizing the denominator, 5 (a) 3 (b) 7. Simplify and write each expression with positive, rational exponents. (a) 52 i,5x2 (5xi (1) /J8x3y6 (c) 32 82 64 16. (Hint: Rewrite this as 2 to some power.) . 8. Decide which expression, from each pair, cannot be evaluated and explain why not. (a) (b) 4 1 0 V ± (d) —16 V (c) (4)2 (—16) (e) (4)2 9. Simplify each expression, if possible. /÷V (a) (e) (b).--.- (f) (c)-.- (g)V’J (d)-÷ (h)\/÷\/ 10. Factor these quadratic polynomials. (a) x 2 — 2x — 15 (d) 32 — 3x — 60 (b) .x —13x÷36 2 ÷14x÷6 2 (e) 4x (c) 2x 2 2 (f) 12x + 17x —9 — 7x — 10 xiii Review Assiment Key •‘:‘:z 1. A. I B. —4;Z C. 1;W D. I E.Q F. 1/3; Q G. 2;W H. 3;W I. -1;Z J. 1;W K. 0;W L. —3/4; Q M. 1;W N. 4/3; Q 0. 0;W P. undefined Q. undefined R. 1;W 2. (a) (b) (c) (d) (e) 5x3 2x 5x3 — 2x —2x 5 (or x ) 3 4 —2 3 — + 16 512 1/16 1/512 —512 16 9. (a) 6. (a) —i- (c) (d) - (c) (e) + (c) 0 3V (g) 4 z 4 8. (a) -; cannot divide by zero = 17 (b) 3(V’+2) ) (2y 4 4 I I (d) (—16); because (—16) ‘/i and no real num bei raised to the fourth power gives —16 (e) \/; no real number squared gives —64 5. (a) (b) (c) (d) (e) (f) 7. (a) —2,—1,O,1,2,3,4 1, 2, 3,4,5 6,7,8,9,... there are none ...,—2,—1,O,1 3. Equation Expression Term Factor Constant Coefficient Exponent xiv 4. (a) 15½ (b)8 (c) 14/3 (d) 2 (b) V; no real number squared gives —2 I I (c) (_4)2; because (4)2 V and no real num ber squared gives —4 (h) 10. (a) (b) (c) (d) (e) (f) (x—5)(x+3) (x—4)(x—9) (2x—1)(x÷9) 3(x+4)(x—5) 2(2x + 1)(x + 3) (4x—5)(3x+2)