Algebra II Chapter 5 Review SOLUTIONS

Solutions are listed below with work provided for some questions. Answers for different parts of one question are separated by semicolons - i.e. for 1) a, b, c the solutions would be written 1) solution to a; solution to b; solution to c. So, without further ado:

Solutions
1) 0.82^6 = 0.3
2) 5*4^2.4 = 139.3
3) for t = 0, y = 4^7; for t = 3/2 = 1.5, y = 4^7 * 4^1.5 = 4^8.5 = 131,072
4) y = 50(2)^x (exponential function with starting value 50 and a growth rate of 2)
5) (xz/w^5) + (x^2/w^3)
6) x = -4
7) x = 4; x = 2
8) 2
9) 4
10) 12x^6
11) Use the points to write two equations in point-ratio form, then solve for b to get y = 0.277(3)^(x+1) or y = 0.031(3)^(x+3)
12) y = 6(2)^x
13) put 70 in for p to get s =45.68; put 50 in for s to get p = 120.43
14) y = 4800(2)^t; y = 4800(2)^4 = 76,800
15) y = 6x + 9
16) y = (x^2 + 6x + 1)/(-8)
17) y = (x - 2)/3; yes - there is only one output for each input
18) The graphs should be reflections about the line y = x. The inverse function should be y = (x + 2)/3
19) Find the inverse function, then put 6 in for x. You should get -2. Put -2 in the original function for x. The end result should be what you started with: 6. This is because composing a function with its inverse will undo itself.
20) -8
21) 8
22) x = 1.97 (remember that 4.7 should be the base and 21 should be a)
23) 4
24) -7
25) 3.17
26) To begin, take the log of both sides then use the power property of logarithms to bring the exponent down. You should get x = 5.03
27) 2.2694 (d)
28) Use your logarithm properties to simplify! Remember that taking the antilog of something leaves you with what you started with - i.e. if I had log x, then 10^log x = x. If I had log 2, 10^log 2 = 2, and so on. So if I had log (x-6)/(x-1), 10^log (x-6)/(x-1) = (x-6)/(x-1) and if I do it to one side, I have to do it to the other, too! x = 36
29) True - this is the quotient property of logarithms
30) log (base p) 4. You should use the power property and quotient property to simplify.
31) 3rd root of m squared; 4logb; logx / log7; y/x^2; 2^(3x + 3y); log10/3
32) 4.19; 0.001; 0.4; -8.46; 2.40, -2.40; 6
33) Write an exponential equation with a = 23000, b = 1 - 0.17. Set it equal to 10000, then solve for x. x = 4.47 years (about 4 years, 6 months)
34) ((x + 1)/2)^2 - 3; 13/4; 6
35) a = 7.44, b = 22.89; 0.47; $48.94; 2.14 hours (2 hours, 8 minutes)
36) y = ((x-3)/5)^2 + 2; 51/25; 5

Please email me at mpatchin@hardingfinearts.org if you have any questions!! I should be at school until around 4:30 today.

Week of 25 January 2010

Remember this is a B Week!!

Algebra 1
Monday - Quiz; Start Section 6.1 Systems of Equations
Tuesday - Finish Section 6.1 and do assignment (p 311 1, 2, 5, 8, 11, 13, 16; bonus 6) due 1/27
Wednesday - Section 6.2 Subsitution
Thursday/Friday - Finish Section 6.2 and do assignment (TBD)

Algebra 2
Monday - Chapter 5 Review (solutions posted at 3:00 pm)
Tuesday - Chapter 5 Test
Wednesday - Section 7.1 Polynomial Degree and assignment (TBD)
Thursday/Friday - Section 7.2 Equivalent Quadratic Forms and assignment (TBD)

Have a great week!!

Algebra I Chapter 5 Test Review SOLUTIONS

The solutions to each question are listed below. Each part of a question is separated by semicolons - i.e. If there was 1) (a) (b), the answer would be listed 1) answer to a; answer to b.

Solutions:
1) add 9 to both sides; multiply by 8 on both sides
2) R = D/2; w = (P/2) - l; r = d/t; h = 2A/b
3) h = 3.5
4) k = 4
5) x = -2.45 (rounded to 2 decimal places)
6) rate of change ~ -167 dollars per year
7) C
8) plot points; connect using line segments; 1994 to 1996
9) -3/4; use the slope formula (6-9)/(2+2) = -3/4 so yes it is on the line; (10, 0)
10) -0.5; 1; 1
11) (9, 15) and (17, 22)
12) undefined
13) 0
14) y = 2x + 7
15) y = 26x + 800; $3192 for 92 people
16) y = -8 + 6(x - 3) or y = 6x - 26
17) y = 7 + 8(x -5) or y = -1 + 8(x - 4)
18) y = 2x - 10
19) y = 2x - 8
20) yes
21) no
22) no
23) (18 - 5) - v or 13 - v
24) y = 2x + 4; y = 0.5x - 2.5; y = -4x - 5
25) y = 30300 + 900(x - 11) or y = 900x + 20400

Week of 19 January 2010

Algebra 1
Monday - NO SCHOOL
Tuesday - Chapter 5 Review (answers will be posted after 3:00 pm 1/19)
Wednesday - Chapter 5 Test
Thursday - Section 6.1 Solving Systems of Equations
Friday - Finish Section 6.1 and do assignment (p 311 1, 2, 5, 6, 8, 13, 16; bonus 10) due 1/25

Algebra 2
Monday - NO SCHOOL
Tuesday - Section 5.6 Logarithmic Functions
Wednesday - Finish Section 5.6 and do assignment (p 276 1-7, 10, 13; bonus 12) due 1/22
Thursday - Section 5.7 Properties of Logarithms
Friday - Finish Section 5.7 and do assignment (p 282 1-5, 8; bonus 12) due 1/25

Week of 11 January 2010

How about that weather last week?! Since we were out of school Friday, the schedules from this week and last will appear to overlap, but... they didn't.

Don't forget this is a B Week!
Algebra 1:
Monday - Section 5.4 Equivalent expressions
Tuesday - Finish Section 5.4 and do assignment (p 279 1-10; bonus 14) due 1/13
Wednesday - More practice solving Equations (WS)
Thursday/Friday - Algebraic Scavenger Hunt

Algebra 2:
Monday - Section 5.3 Rational Roots and Exponents (p 256 1-4) due 1/12
Tuesday - Finish Section 5.3 and do assignment (p 256 1-5, 11, 13-15; bonus 10) due 1/13
Wednesday - Section 5.5 Building Inverse Functions
Thursday/Friday - Finish Sectino 5.5 and do assignment (p 269 1-4, 6, 8, 9, 12, 15, 16, 18; bonus 14) due 1/15

Have a great week, everyone!
<3 Miss P

Week of 5 January 2010

Algebra 1:
Monday - NO SCHOOL
Tuesday - Benchmark 2
Wednesday - Short review of 5.1 & 5.3, in class assignment (3 questions)
Thursday - 5.4 Equivalent Expressions
Friday - Finish 5.4 and assign p 279 1-10 (bonus 14) due 1/11

Algebra 2:
Monday - NO SCHOOL
Tuesday - Benchmark 2
Wednesday - Short review of 5.1 & 5.2, in class assignment (5 questions)
Thursday - 5.3 Rational Roots and Expressions
Friday - Finish 5.3 and assign p 256 1-5, 11, 13-15 (bonus TBD) due 1/11

Gotta hit the ground running to get everything done!

Welcome Back!!

Hey everyone! I hope you all had a great break, I know I did. Here's a summary as evidence:

1. The HFAA Faculty Christmas party - such fun people and yummy food! It was a blast!
2. Sleeping in as late as I wanted
3. Christmas with my extended family - 4 generations!
4. Not getting up early
5. Keeping my nephew for 3 days
6. Devon (my fiance, remember) bought a new truck! It's a Hybrid... hello better gas mileage!
7. Getting up late
8. THE BLIZZARD - how awesome was it?! Our fence blew over. Dogs are safe, though, which is good. Oh and can you say 14 INCHES OF SNOWY GOODNESS? I like the snow. Especially when I'm inside with a cup of hot chocolate!
9. Going to visit my parents - we stayed 2 nights, our dogs had a great play-date with my mom's dogs. Picture this if you will: 1 German Shepherd (~100 pounds), 1 Australian Shepherd (~40 pounds), 1 Aussie/Border Collie (~50 pounds), and 1 Maltese (~10 pounds) and 4 grown adults, then adding a 9 year-old the second night ALL in a 2 bedroom house :-) It's amazing I didn't fall and break something with all the dogs underfoot!
10. SLEEPING as much as I wanted
11. Getting a new classroom with ENOUGH DESKS for everyone! Hooray!!!
12. Did I mention that I liked sleeping in?

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All kidding aside, I hope that we're all ready to hit the ground running this semester because we still have a lot to cover before the EOIs in April.

Also, remember that I'm now located in room 407, which is the old Spanish room. You can't miss my letters above the door, though, so hopefully no one will be too lost! See you guys then!!

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