Algebra I and II Semester Final Solutions

The solutions to each of the reviews is below. The parts of each question are separated by semicolons (;) - i.e. 1) a; b; c

A few topics to look at:
Algebra I: slope-intercept form, the slope formula, writing the equation of a line, point-slope form, definition of slope and what it looks like if the slope is +, -, 0, and undefined
Algebra II: exponent properties (table on p 246), general form of exponential and power functions, solving exponential functions by getting common bases, difference between exponential and power functions

Algebra I:
5.1 A Formula for Slope
1) 3; -1/3; undefined
2) 4/5; -0.76; -3; undefined
3) (0, -1), (6, 3); (3, 1), (5, 3); (1, 8), (9, -2); (1, 6), (2, 6); (-5, -5), (-3, -9); (1, -8), (15, -2)
4) y = 2 + x; y = 4 - x; y = 2 - 2x; y = -0.25x

5.3 Point-Slope Form of a Linear Equation
1) m = 2, (1, 3); m = -3/4, (-1, -7.4); m = 6/7, (-5, -4.1); m = -1, (2, 0)
2) y = 3 + 2(x - 4); y = 7 - 2/3(x + 6); y = 4
3) 1.5; y = -10 + 1.5(x + 4); y = -5.5 + 1.5(x + 1)
4) 6/5; y = 81 + 6/5(x - 80) or y = 75 + 6/5(x - 75) or y = 69 + 6/5(x - 70); no, no
5) y = 3+2(x-1) or y = 7+2(x-3); y = 7; y=7-2(x-5) or y=3-3(x-7); y=3

Algebra II:
5.1 Exponential Functions
1) 31.25; 20.189; 10.63; 219.62; 427.963; 21.9282; 3305.07; 2515.0376
3) 5, 15, 45; 250, 125, 62.5; 15.5, 17.05, 18.755; 0.75, 1.65, 3.63; 575, 46, 3.68; 66, 66.66, 67.3266
4) decay; growth; growth; decay; growth; decay
5) 0.75, 25% decrease; 1.125, 12.5% increase; 2.25, 125% increase; 0.888, 11.1% decrease; 0.88, 12% decrease; 1.6, 60% increase
6) 1 = 14700, 2 = 12348, 3 = 10372, 4 = 8713, 5 = 7319; y = 17500(0.84)^x or y = 17500(1 - 0.16)^x

5.2 Properties of Exponents & Power Functions
1) 1/9; 1/64; 1/625; 1/25; 1/343; 1/1000000; -1/256; 1/256; -1/125; 32; -25/9; 36/25
2) x^13; x^7; x^-15; 36x^8; 120x^-11; -120x^-20; x^18; 11x^7; 1.4x^5; x^2; 125x^15; -0.008x^18
3) x = -5; x = 2/3; x = -4; x = -7; x = -2; x = 4/3
4) 3.89; 116.55; 0.09; 5.62; 0.39; 578703.70; 0.91; 1.5; 0.79

Week of 14 December 2009

5 more days and counting!

This is what's happening this week:

Algebra I:
Monday - 5.3 Point Slope Form of a Line
Tuesday - Finish up 5.3 and work on the assignment (p 272 1-3, 7-9, 13; bonus 6) due 12/16
Wednesday - Review for Final Exam
Thursday - Final Exam
Friday - Grade Final Exams/Benchmark/Clean out Notebooks

Algebra II:
Monday - 5.2 Properties of Exponents and Power Equations
Tuesday - Finish up 5.2 and work on the assignment (p 248 1-6, 10, 13, 15, 16; bonus 14) due 12/16
Wednesday - Review for Final Exam
Thursday - Final Exam
Friday - Grade Final Exams/Benchmark/Clean out Notebooks

Junior ACT Math Practice Solutions

Correct Answers are as follows:

1. D
2. G
3. E
4. K
5. A
6. F
7. D
8. K
9. D
10. K
11. D
12. F
--------
1. D
2. H
3. C
4. J
5. B
6. H
7. D
8. H
9. C
10. G
11. C
12. F

I'd be more than happy to help you work these if you're not sure how to get the answer! I'm in the library for tutoring on Wednesdays and usually in my room after school for a while.

Week of 7 December 2009

On the downhill slide, now, towards Winter Break! Hooray!
(If we made a graph, would the slope be positive or negative?)

Here's this week's agenda:

Algebra I:
Monday - Section 5.1 A Formula for Slope
Tuesday - Finish Section 5.1 (p 256 1 - 3, 5 - 7, 9, 12, 15; bonus 8) due 12/9
Wednesday - Extension for p 256, due to Online Book malfunction Tuesday night
Thursday/Friday (B week) - Chapter 4 Test Corrections

Algebra II:
Monday - Section 5.1 Exponential Functions
Tuesday - Finish Section 5.1 (p 240 1, 3*, 4, 5bcd, 6, 8, 10; bonus 16; *do not write a recursive formula) due 12/9
Wednesday - Extension for p 240, due to Online Book malfunction Tuesday night
Thursday/Friday (B week) - Chapter 4 Test Corrections

Chapter 4 Review Keys (Algebra I and II)

Algebra I - Chapter 4 Review Key
Each answer is listed below. For questions with more than one part, the answers are separated with a semicolon (;).
[1] 2 x 3 / (4 - 5); (2 + 4) / 2 x 7
[2] (1 x 12 + 5) / 9 or 17/9
[3] $40,768
[4] $4.05; $5.79; $6.45
[5] Starting Numbers: 9, 1, -2.5, x
Subtract 3: 6, -2, -5.5, x-3
Multiply by 2: 12, -4, -11, 2(x - 3)
Add 4: 16, 0, -7, 2(x-3) +4
Divide by 2: 8, 0, -3.5, (2(x-3) + 4)/2
Subtract original number: -1, -1, -1, (2(x - 3) + 4)/2 - x
[6] 64
[7] x = 34
[8] 7
[9] [C]
[10] 2
[11] 12, 14, 16; 22
[12] 520
[13] 16.9, 10, 3.1, -3.8, -10.7, -17.6
[14] {Ans + 1, Ans + 2} Enter, Enter
[15] Graph with points at (0, -5), (1, -3), (2, -1), (3, 1), and (4, 3)
[16] Graph of a line with points at (0, 2), (2, 5), (3, 7), etc
[17] [B]
[18] (-2, 4), (0, 2), (2, 0), (4, -2) and (6, -4); (0, 2)
[19] y = -1 - 2x
[20] y = -5 - 3x
[21] The y-intercept is the constant.
[22] y = 15 + 2x, y-intercept = 15
[23] Input: -3, 4, 6
Output: -7, 0, 2
[24] Row 2: 5, -16.7, 2, 0.92, 0.46
Row 3: 9, -14.86, 4, 1.84, 0.46
Row 4: 16, -11.64, 7, 3.22, 0.46
Row 5: 19, -10.26, 3, 1.38, 0.46
Row 6: 25, -7.5, 6, 2.76, 0.46
Row 7: 26, -7.04, 1, 0.46, 0.46
[25] Start at 1. Rule: +2
[26] 4 = 2x; 2 = x
[27] add 9 to both sides; multiply both sides by 8
[28] h = (2A)/b
[29] a = 8.9
[30] j = 6
[31] x = -3
[32] x = 343

Algebra II - Chapter 4 Review KEY
[1] 6:40 pm
[2] Sample answer: most people buy plants in the spring and early summer. The sales for the nursery rise in the spring and summer and fall off dramatically in the fall and winter.
[3] The car's speed is first measured at 3 mph, then the car increases speed to 5 mph, decreases speed to 2 mph, and then stays at that speed.
[4] graph Kim's distance v time or speed v time.
[5] no relation
[6] linear; y = 5x - 4
[7] 20
[8] x = 3, x = 5
[9] Yes
[10] Yes
[11] y = x + 2
[12] -7; -12; -7x - 12
[13] [B]
[14] 4x - 3y - 21 = 0
[15] It is translated right 3 units and down 2 units.
[16] g(x) = x - 13; The graph of g(x) is the graph of f(x) translated down 18 units.
[17] (0, 0)
[18] y = (x + 7)^2
[19] Right 2, up 4
[20] Graph of the square root of x moved down 2 units
[21] The graph of the square root of x moved left 3 and down 2; the graph of the square root of x reflected across the x-axis, reflected across the y-axis, then moved down 4.
[22] The graph of the line reflected across the x axis. The new lines equation would be y = 2x + 4
[23] g(x) = -(x + 1)
[24] the graph of the absolute value of x moved left 2 and down 5
[25] g(x) is the reflection of f(x) across x-axis.
[26] graph of the absolute value of x reflected across the x-axis and translated down 5
[27] vertical stretches by a factor of 5 and translated down 5 units
[28] (-9, -6)
[29] x^2 + y^2 = 1
[30] (x^2)/16 + (y + 3)^2 = 1
[31] x^2 + ((y - 15)^2)/25 = 1
[32] Sample answer: When written in standard form, the equations have the same terms, one involving the square of x and the other involving the square of y, added together. In both equations, the values of h and k indicate the center of the graph, and the values of a and b indicate the vertices. The equations are different in that the terms of the ellipse equation have unequal scale factors, while the terms of the circle equation have equal scale factors.
[33] (x^2)/9 + (y^2)/25 = 1
[34] g(f(x)) = 5 - 6x
[35] -2/3; 2704; -(2x^2)/9 - 8x/3 - 8
[36] y = sqrt(1 - x^2); y = |x|; y = sqrt(x); y = |x|
[37] x = 1 or x = 13
[38] g(f(x)) = (3x^2)/25 - 6x/5 + 3
[39] graph translated up 2 and left 3; graph translated down 3 and shrunken horizontally by a scale factor of 2 (it's half as wide); graph reflected across the x-axis, stretched vertically by a scale factor of 2 (twice as tall), translated down 1 and left 1
[40]

[41]
the order matters for A and B but not for C and D. The final equations when A is applied irst are different from the final equations when B is applied first, but the final equations when C are applied first are the same as the final equations when D is applied first.

30 November 2009

I hope that everyone had a great Thanksgiving! We're now on the downward slope toward Winter Break and we still have quite a bit to accomplish. I'm hoping to be finished with chapter 5 for Algebra I and II, that's the midway point!!

Here's the breakdown for this week:
Algebra I:
Monday - Section 4.8 Solving Equations Using the Balancing Method (p 237 1-7, 9-12; bonus 14) due 12/2
Tuesday - Working on Section 4.8 assignment due 12/2
Wednesday - Review Chapter 4 (With Alg-eopardy if all goes well!)
Thursday - Review Chapter 4
Friday - Chapter 4 TEST

Algebra II:
Monday - Section 4.8 Composition of Functions (p 228 1-4, 6, 9, 10, 16; bonus 12) due 12/2
Tuesday - Working on Section 4.8 assignment due 12/2
Wednesday - Review Chapter 4
Thursday - Review Chapter 4
Friday - Chapter 4 TEST

<3 Miss P

Week of 23 November 2009

Thanksgiving is almost here! Hooray!!

Also, I had a great time in Nashville at the NCTM Regional Conference - which has been rumored to be the largest (most-attended) NCTM Regional conference to date! There were about 5,000 math teachers (PreK-higher ed) attending... it was awesome!

Anyway, on to this week:

Algebra I:
Monday - Section 4.7 Linear Equations and Rate of Change (p 229: 1-3, 5-9, 11; bonus: 12) due 11/24
Tuesday - it's a surprise!

Algebra II:
Monday - Reveiw Section 4.7 Transformations and the Circle family
Tuesday - p 220 1-5 and WS 4.7 all

I hope everyone has a great Thanksgiving. I'm very thankful for all of my students, who made sure to tell me how much they missed me while I was gone and who inspire me every day to be better at what I do. I'm thankful for the parents who are working with me constantly to ensure their student's success at school and in my class. I'm thankful for my family who have been with me every step of the way to where I am today. I'm thankful for an amazing HFAA faculty/staff/administration - who would want to work anywhere else?!

<3 Miss P

Week of 16 November 2009

Remember, everyone, that I will be in Nashville, TN at the National Council of Teachers of Mathematics (NCTM) Regional conference from 18 - 20 November (Wednesday through Friday). The substitute we will have WILL be able to assist with math homework, so never fear! We will keep moving!

This is the plan:
Algebra I: B WEEK
Monday - Section 4.3 (Recursive Sequences) (p 202: 1-5, 7) due 11/17
Tuesday - Section 4.4 (Linear Plots) notes, etc
Wednesday - Section 4.4 assignment (p 209: 1-5, 11-13, 15) due 11/19
Thursday/Friday - Section 4.6 (Linear Equations - Intercept Form) (p 220: 1-4, 6, 7, 11, 13) due 11/23

Algebra II: B WEEK
Monday - Start Section 4.6 (Stretches/Shrinks and the Absolute Value Family)
Tuesday - Finish Section 4.6 (p 214: 1-5, 7, 10, 11) due 11/19
Wednesday - Section 4.7 (Transformations and the Circle Family) notes from book
Thursday/Friday - Section 4.7 assignment (p 220: 1-8, 15 and WS 4.7: all) due 11/24

I will miss all of your bright, smiling faces while I'm in Nashville!!!

Miss P

Week of 9 November 2009

Two more weeks till Thanksgiving Break! We can make it!!

Algebra I:
Monday - Chapter 3 Test!
Tuesday - Section 4.1 (Order of Operations and the Distributive Property) (p 187: 1-9, 11, 13, 17) due 11/11
Wednesday - Section 4.2 (Writing Expressions)
Thursday - Section 4.2 assignment (p 195: 1 - 9) due 11/13
Friday - Questions on homework and grade

Algebra II:
Monday - Section 4.4 (Translations of Quadratics) (p 197: 1-8, 10; bonus 13) due 11/11
Tuesday - Questions on p 197, WS 4.4 all for extra practice; due 11/12
Wednesday - Section 4.5 (Reflections and the Square Root Family)
Thursday - QUIZ (4.1 - 4.5) finish Section 4.5 (p 204: 1-5, 9-12) due 11/16
Friday - Work on Section 4.5 assignment in class

Algebra I Chapter 3 Test Review SOLUTIONS

Check your answers while you study!!

Page 1.

1. direct
2. product
3. inverse
4. ratio
5. constant, variation
6. ratio
7. constant

Page 2.

1. 1.5 minutes per page, 0.67 pages per minute, 60 min, 50 pages
2. 0.83 minutes per piece (rate), so it will take 416.7 minutes or 6.9 hours
3. 24 mph (24 miles), 2.5 hours, 126 miles, 6.25 hours
4. About 2 letters per day, 568 million, 156403000 letters

Page 3.

1. 7.6 m, 13.1 ft, 3.8 m, 23.0 ft
2. 91.4 cm, 15.8 in, 5.9 in, 2.0 cm
3. 21, 33.6, 4, 0.25, 3.15, 0.18
4. 5.63, 47.92, 24.67, 249.69
5. 3, 6.5, 24, 17, 0.19, 4.67

Page 4.

1. 4, 0.25, 8, 6, 0.3, 0.02
2. 2, 0.8, 160, 2.5
3. Some possible answers: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6), (6, 3)
   
4. You should write the equation st = d (s = speed, t = time, d = distance). 0.24 s, 4.88 s, 1505 meters per second

Happy Studying - I hope you all have a good weekend!!!

Week of 2 November 2009

B week everyone!!

Algebra I:
Monday - Section 3.2 (direct variation) (p 149: 1 - 5, 10, 11; bonus 8) due 11/3
Tuesday - grade p 149, Start Section 3.4 (inverse variation)
Wednesday - Finish Section 3.4 (p 168: 1 - 4, 6, 7, 14; bonus 12) due 11/5
Thursday/Friday - Chapter 3 Review - Test on MONDAY 11/9

Algebra II:
Monday - Section 4.2 (function notation) (p 181: 1 - 5, 7, 10; bonus 13, 16) due 11/4
Tuesday - Homework questions, start Section 4.3 (translations of lines)
Wednesday - grade p 181, finish Section 4.3 (translations of lines)
Thursday/Friday - Section 4.3 assignment (p 189: 1 - 6, 12, 13; bonus 8. WS 4.3: 1 - 4) due 11/9

Week of 26 October 2009

Algebra I:
Monday - Chapter 2 Test (corrections due Friday 10/30)
Tuesday - Went over test and started Section 3.1 (Using Rates)
Wednesday - Finished Section 3.1 (p 142: 1 - 4, 6 - 9, 11; bonus 14)
Thursday - Work on assignment in class (Miss Patchin absent for conference)
Friday - Questions on homework, grade, begin Section 3.2 (Direct Variation)

Algebra II:
Monday - Chapter 3 Test (corrections due Friday 10/30)
Tuesday - Went over test
Wednesday - Section 4.1 (Interpreting Graphs) (p 175: 1 - 4, 10, 11; bonus 6, 13)
Thursday - Work on assignment in class (Miss Patchin absent for conference)
Friday - Questions on homework, grade, begin Section 4.2 (Function notation)

Monday, 10/26/09

Here's the rundown for today - pretty simple, as it were:

Algebra I: Chapter 2 Test

Algebra II: Chapter 3 Test

I WILL have all of these graded TOMORROW (I think I can I think I can) and ready to pass back to you. In AlgI, we'll be starting Chapter 3, where we'll learn all about direct and indirect variation. In AlgII, we'll be starting Chapter 4, where we'll learn about transformations.

That's it for now, I guess!

Miss P

Welcome!

I will be using this blog to keep you up to date on happenings in Algebra I and II at HFAA. These are my current goals for the blog:

I would like to post the following things:

• regular updates with assignments listed
• links to copies of (some) handouts
• ANSWERS (*gasp*) to chapter reviews to enable that long-forgotten habit of studying

So - starting 10/26/09, I hope to be updating this at least once a week with helpful information about our classes. Hope you guys have a great night!