1. Algebra CP

2.  Evaluate each expression if x = 2, y = 3, z = –4. 1. = 360 2. = 12 3. = 256 4. = 1

3.  Which number is irrational ? Explain. a) b) c) d)

4.  Simplify the two expressions. Will there be a difference in your final simplified expressions? Explain why or why not. 1. (–5) 2 2. –5 2  According to PEMDAS, the first expression’s negative is applied within the parentheses before simplifying the exponent. The second expression’s negative would be applied after simplifying the exponent.

5.  (2 x 2 y –3 / x 4 ) 3 (4/ x 6 y 9 ) –1 22  (5 y –2 z 4 / x 3 ) –2 (50 x –5 y –3 / z –9 )  2 xyz

7.  (6 x 2 y 3 ) 2  36 x 4 y 6  (–3 x 4 ) 3 (2 x 4 )  –54 x 16  (12 x 4 /6 x 2 ) 4  16 x 8  (2 x 5 / y 2 z 4 ) 5 (1/ x 6 )  32 x 19 / y 10 z 20

8.  First, simplify: (36 x 3 y 7 /9 y 4 z 5 ) 3 * z 14 / x 8 y 8  (4 3 x 9 y 21 / y 12 z 15 )( z 14 / x 8 y 8 )  64 xy / z  Then, evaluate if x = 2, y = 3, and z = 4.  64(2)(3) / 4  384 / 4 = 96

9.  Is this written in scientific notation?  45.2 * 10 3  No, because the first term isn’t between 1 and 10.  Convert to standard form:  1.68 * 10 –5 .0000168

10. 1. (2.4 x 10 14 ) + (4.1 x 10 13 ) 1. 2.81 x 10 14 2. (4.5 x 10 6 )/(7.5 x 10 –2 ) 1. 6.0 x 10 7 3. (3.5 x 10 4 )(4.2 x 10 3 ) 1. 1.47 x 10 8

11. 1. The distance from the Sun to Earth is 1.5 x 10 8 km. The distance from Earth to Neptune is 4.35 x 10 9 km. How far in total is it from the Sun to Neptune?

13.  9 x 2 √(3 x )  (3√6)/(10 x 2 )

14. Simplify:  4 x 8 /3 y 2 Evaluate:  –2.799999519 x 10 27 Simplify:  4 x 2 y 2 √6 yz /15 z 4

16.  A friend owes you $100. They offer to pay you 10% of the remaining balance every week until the debt is paid off. How long will it take for them to pay you back?

17. f ( x ) = 4(2) x f ( x ) = 1 / 2 (2) x f ( x ) = 125(5) x f ( x ) = 1 / 9 (3) x

18.  Mr. S purchased a stock for $11.20 on 4/7/00. On 4/7/14, the price is $58.26. If the stock grew at an exponential rate, what was the rate of growth?

19. 15 4 5x35x3 Base Exponent Coefficient

20.  Example #1  3 2 * 3 4  3 2+4  Keep common base, add exponents 3636  Example #2  x 7 * x  x 7+1  Keep common base, add exponents x8x8  Example #3  5 x 2 * 3 x 3  (5*3) x 2+3  X coefficients, keep common base, + exponents  15 x 5

22.  Example #1  (2 4 ) 3  2 4*3  Keep original term, multiply exponents  2 12  Example #2 (x5)2(x5)2  x 5*2  Keep original term, multiply exponents  x 10  Example #3  [( x + 3) 3 ] 6  ( x + 3) 3 * 6  Keep original expression, multiply exponents  ( x + 3) 18

24.  Example #1  (2 2 * 3 2 ) 3  2 2*3 * 3 2*3  Keep original terms, multiply exponents  2 6 * 3 6  Example #2  (4 x 2 y 3 ) 3  4 3 x 2*3 y 3*3  Keep original term, multiply exponents  64 x 6 y 9  Example #3  –(5 x 2 ) 2  –(5 2 x 2 * 2 )  Keep original terms, multiply exponents  –(25 x 4 )  Simplify within parentheses  –25 x 4

26.  Example #1  8 10 /8 4  8 10–4  Keep original base, subtract exponents 8686  Example #2 x7y4/x3y3x7y4/x3y3  x 7–3 y 4–3  Keep original bases, subtract exponents x4yx4y  Example #3  35 x 9 /7 x 5  5 x 9–5  ÷ coefficients, keep original base, – exponents 5x45x4

28.  Example #1  (5/3) 2  5 2 /3 2  Apply exponent to numerator & denominator  25/9  Example #2 (x2/y)3(x2/y)3  x 2*3 / y 3  Apply exponent to numerator & denominator x6/y3x6/y3  Example #3  (3 x 6 / x 3 ) 2  3 2 x 6*2 / x 3*2  Apply exponent to numerator & denominator 9x69x6

30.  Example #1  (–25) 0  (–25) 0 = 1  Apply definition of zero exponent to base  Example #2 6x0y46x0y4  6(1) y 4  Apply definition of zero exponent to variable 6y46y4  Example #3  (6 x 3 y 5 ) 0  (6 x 3 y 5 ) 0 = 1  Apply definition of zero exponent to term

31.  Example #1  7 –2  7 –2 = 1/7 2  Apply definition of negative exponent to base  7 –2 = 1 / 49  Example #2  5 x –7 y –2 z 4  5 z 4 / x 7 y 2  Apply definition of negative exponent to variable  Example #3  (4 y –6 / x 3 ) –2  4 –2 y 12 / x –6  “Distribute” negative exponent  x 6 y 12 /16  Apply definition of negative exponent to term

33.  What is a rational number?  Any number that can be written as the ratio of two integers  When used as an exponent: 9 1/2 Base Exponent

34.  Coefficient – Number preceding the radical  Radical – Square root symbol  Radicand – The number within the radical  Index – The number outside the radical

35.  Multiplying Radicals:

36.  Adding/Subtracting Radicals:

37.  Radical expressions are in simplest form when: 1. No fractions are in the radicand 2. No perfect square factors other than 1 are in the radicand 3. No radicals appear in the denominator of a fraction  Tools to simplify a radical:  Product Property of Radicals  Quotient Property of Radicals  Rationalizing the Denominator

38.  Simplify:  Factor out perfect square  Product Property of Radicals  Evaluate perfect square

39.  Simplify:  Factor out perfect square  Product Property of Radicals  Evaluate perfect square  Simplify

40.  Simplify:  Factor out perfect squares  Product Property of Radicals  Evaluate perfect squares

41.  Simplify:  Quotient Property of Radicals  Simplify perfect squares

42.  Simplify:  Quotient Property of Radicals  Simplify perfect square

43.  Simplify:  Quotient Property of Radicals  Rationalize the denominator  Product Property of Radicals  Simplify perfect square

44.  Simplify:

45. xf(x)

46.  Exponential Function  a ≠ 0(Initial Value)  b > 0 and b ≠ 1(Constant Ratio)  x is a real number

47.  Graph the following function: xf(x) -2 0 1 2

48.  Graph the following function: xf(x) -2 0 1 2

49.  Graph the following function: xf(x) -2 0 1 2

51.  The value of a 1909 Honus Wagner baseball card increases at a rate of 5% per year. If the value of the card was $2,100,000 in 2008, how much would the card be valued at in 2016?

52.  Determine the growth rate of the function pictured in the table. xf(x) 2$2,016.00 3$2,419.20 4$2,903.04 5$3,483.65 6$4,180.38

53.  Determine the growth rate of the function graphed.

55.  Determine the decay rate of the function graphed.

56.  Determine the decay rate of the function pictured in the table. xf(x) –5948.0383 –4616.2249 –3400.5462 –2260.3550 –1169.2308

57.  Geometric Sequence – a series of numbers where the ratio of any term to its preceding term is a constant value  20 200 2,000 20,000 200,000  2 4 6 8 10  5 -5 5 -5 5

58.  Write an Exponential Function: xf(x) -225 5 01 1 1/51/5 2 1 / 25

59.  Write an Exponential Function: xf(x) -2 3/43/4 3/23/2 03 16 212

61.  Evaluate: (1.5 x 10 3 ) + (2.4 x 10 5 ) (.015 x 10 5 ) + (2.4 x 10 5 )  Convert to Similar Power of 10 10 3 (.015 + 2.4)  Factor (Reverse Distributive) 2.415 x 10 3  Evaluated Expression

62.  Evaluate: (8.5 x 10 2 )(1.7 x 10 6 ) (8.5 x 1.7)(10 2 x 10 6 )  Commutative Property (14.45)(10 8 )  Evaluate (1.445 x 10 1 )(10 8 )  Rewrite first term in S.N. (1.445)(10 1 x 10 8 )  Associative Property 1.445 x 10 9  Evaluated Expression

63.  Evaluate: (1.2 x 10 4 )/(1.6 x 10 –3 ) ( 1.2 / 1.6 )(10 4 /10 –3 )  Product Rule (0.75)(10 7 )  Quotient of Powers (7.5 x 10 –1 )(10 7 )  Rewrite first term to S.N. (7.5)(10 –1 x 10 7 )  Associative Property 7.5 x 10 6  Evaluated Expression