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.