(1) Assignment # 1 Absolute Value. (2) Assignment # 2 Compound Absolute Values. (3) Assignment # 3 Exponents. (4) Assignment # 4 Simplifying Radicals
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1 Alg_0 Packet # The beginning of our Quest () Assignment # Absolute Value () Assignment # Compound Absolute Values () Assignment # Eponents () Assignment # Simplifying Radicals (5) Assignment # 5 Fractional Eponents (6) Assignment # 6 Review Worksheet (7) TEST (8) Assignment # 7 Factoring (9) Assignment # 8 Factoring (0) Assignment # 9 Factoring Review Worksheet () QUIZ () Assignment # 0 Multiplying/Dividing Rational Epressions () Assignment # Adding/Subtracting Rational Epressions () Assignment # Dividing polynomials (5) Assignment # Comple Numbers (6) Assignment # Review Worksheet (7) TEST
2 Alg_0
3 Alg_0 Absolute Value A) Notes: a a if a 0 coordinate = distance from origin = - a if a 0 B) If you are given a distance, then what are the coordinates? = 5 Eample: = 0 cases _ + Let s look at the graph Case : Case : Domain Domain If 0-0 If 0 ( ) = 0 neg pos 7
4 Alg_0 Inequalities a if a is positive Is this a union or intersection? What if a was negative? - a a Eample: + Case : Case :
5 Alg_0 5 a if a is positive - a a What would happen if a was negative? Eample: () 5
6 Alg_0 6 () 5 9 () 7 > +
7 Alg_0 7 ) + = 6 5) + = 6) >
8 Alg_0 8 7) < Summary Powerpoint
9 Alg_0 9 Algebra Assignment # Absolute value inequalities Solve for please. () + 8 (6) 9 () + 5 (7) < () < 9 (8) 8 + = 5 () 5 + (9) + 8 > 8 (5) 7 5 (0) + 8 > 5 () 5
10 Alg_0 0
11 Alg_0 Algebra Assignment # Answers () (6) 5 () =, or = (7) < or > 6 () < < (8) () or (9) 5 (5) 8 (0) 5 5 () All Real Numbers
12 Alg_0 Compound Absolute Values More than one absolute value in the sentence Can you find one solution for in this inequality? 7 Test some numbers In order to solve for all possible values for we need to eliminate the absolute value symbols. Can we use two cases like before? Find the critical points. - Case : Case : Case : Case : If + 0 If + 0 If 0 0
13 Alg_0 Domain: the set of real numbers for which an algebraic epression is defined Eample: Cases?
14 Alg_0 Practice: () + + *() +
15 Alg_0 5 () Notes:
16 Alg_0 6 Algebra Assignment # Compound Absolute Values Solve for please. () 5 () () 5 () (5) (6) 5 (7) = 7
17 Alg_0 7 Algebra Assignment # Answers () () 5 or () or () 5 and (5) 5 (6) 9 and 0 (7) or =
18 Alg_0 8 Etra Practice Compound Absolute Values ) < + ) = 9 ) + > 5 ) ) + 6 >
19 Alg_0 9 Eponents Review of the Basics A) Come up with as many rules for eponents as possible. B) Smartboard C) = = = repeated addition 0 = repeated multiplication E. ( ) = ( ) = ( y) = (y) = Practice problems Simplify each epression, remember that no negative eponents can appear in a final answer n n
20 Alg_0 0. y 5. y (-) (-) 7. (- y) (- y ) 0 ( y ) ( -5 y ) a a 8. 7( y) (y ) Solve for :. 8 5.
21 Alg_0 Algebra Assignment # Eponents Simplify each of the following please. Epress answers without negative eponents. () 5 y () yz z () y 6y () 6 y z 7 y z (5) 0 0 y + 6 (6) t t + (7) 8 8 n n (8) y z (9) () + c y (0) 5 () 8 n n m m y y () () y y (5) y + y 5y 8 + y (6) 5 y 9 0 y y (7) (9) (8) (0) n y y + y
22 Alg_0 Solve for please. () 6 = () 7 =
23 Alg_0 Algebra Assignment # Answers () 7 0 y () 0 08 y z () 9y () z y 7 (5) 9 (6) t + (7) 8 (8) y z (9) + c y (0) 6 9 () 5 () n y m () 9 () y 8 6 (5) (7) + y (6) + (8) 9y 9 + (9) + (0) n 6y + 6 y () = 9 () =
24 Alg_0 Radicals I What is a radical? Brainstorm. II Vocabulary: n a = n = root or inde a = radicand = root Perfect Roots What must a be to be a perfect root? A a B a C a What if a < 0?
25 Alg_0 5 Rules A. n a n b n ab = a a b = b B. n n n 8 m n mn C. a a Practice y
26 Alg_ y z a b 9bc d 6 9
27 Alg_0 7 Algebra Assignment # Epress each of the following in simplified form please. () y z (8) 7 8 () y z (9) 5 8 () y z (0) 6 9 () + 7 () z 8 y (5) 7 () y z (6) () (7) ()
28 Alg_0 8 Algebra Assignment # Answers () 6 y z 6y (8) () 6 y z (9) 0 () 5 yz 7 y z (0) 6 () 0 () z 6y z y (5) 8 () 5 5y z 5y z (6) 6 () + (7) ()
29 Alg_0 9 Radicals (Day ) and Rational Eponents (Day ) What is a rational eponent? III Def: For all real numbers, b and n >, n b b n Practice: ) 8 / vs 8 ) 9 7 vs 9 7 ) 6 uh oh! Do we need to rationalize? Rewrite 6 as a different base
30 Alg_0 0 - ) 5) (-8) 6) 6 8 y 7) 8 7 y 8) 9) y 5 Rationalizing in eponent form 6 0) ) 8 6 ) 6 ) ) ) ) + 8 7
31 Alg_0 Multiply ) ( + 5) ( + ) ) ( a + b )( a ab + b )
32 Alg_0 Algebra Assignment # 5 () Evaluate each of the following numbers please. (a) 6 (e) 9 7 (b) 8 (f) 6 7 (c) (d) 5 (g) 8 (h) () Simplify, epress all answers without negative eponents please. (a) 8 y (b) y z 5 y z () Epress as a single radical in simplified form. () Simplify, epress all answers without radicals. (a) n n (b) n + n + y y n n (5) Epand each of the following please. (a) + + (b)
33 Alg_0 Algebra Assignment # 5 Answers () (a) 8 (e) (b) 9 (f) 9 8 (c) 5 (g) 7 (d) (h) 97 6 () (a) 6 y (b) 5 y z () 9 5 () (a) (b) n y (5) (a) (b)
34 Alg_0 () Solve for please. Algebra Assignment # 6 Review Worksheet (a) = (b) (c) + 5 > 9 (d) + = + 7 (e) + (f) + 5 () Simplify each of the following please. Epress answers without negative eponents. (a) (b) + (c) 5 y 6 5 y 9 y (d) y (e) y y y + y () Evaluate each of the following please. (a) (b) (c) 56 (d) + 8
35 Alg_0 5 () Simplify each of the following please. Epress answers without negative eponents. (a) y z (b) y z (c) 8 8y 6 5 (d) y z (e) n + 7 y n n + 5n y (f) 5 (5) Epress each of the following as a polynomial without negative eponents. (a) + (b) (c) y 8 y + y y (6) Rationalize the denominator and simplify please. (a) (b) 6 (7) Solve for please =
36 Alg_0 6 Algebra Assignment # 6 Answers () (a), (b) < (c) < or > (d) (e) 5 (f) 9 and 0 () (a) + (b) + (c) y 0 (d) y 6 (e) y () (a) 8 (b) 9 50 (c) (d)
37 Alg_0 7 Algebra Assignment # 6 Answers () (a) y z z (b) 6 y y z (c) y y (d) 6 y z y z (e) n y (f) 7 or 7 (5) (a) (b) (c) y + y (6) (a) + (b) + 6 (7) 8, 0
38 Alg_0 8 Etra Review A. Solve for B. Simplify 6. (m y ). ( ) () C. Simplify. 7a 9 b 6 D. Simplify. 0 6y z 9 6. n 7 n y y n 5n. 5 E. Rationalize the denominator and simplify. F. Solve for
39 Alg_0 9 Answers: A. 0, B.. 5. ( ) or 6 or or 6 m y C. 6 9a b. n y D.. y z E F. or. 6
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