Description
In This collection, we will go deep into math.
This collection will help all math and high school students.
Study Set Content:
Luttrell 2012
141
Name: ______________________
Date: _____
8 - Irrational Functions
Answer the following questions based on
f x
x
( )
= −
−
4
3
.
1. What is the domain?
2. What is the range?
3. When will
f(x)
= 2?
4. Where does the maximum occur?
Simplify:
5.
3 125
2 80
405
−
+
6.
(
)(
)
2 3
2 2 3
2
−
+
7.
7
49
4
Solve:
8.
x
x
+ − =
6
4
9.
2
4
3
1
4
3
x
x
x
−
− =
−
10.
x
x
x
−
+ =
−
−
1
3
1
1
1
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Name: ______________________
Date: _____
9 - Polynomials of any Degree
1. Describe the difference in the shape of the curves between even-powered polynomials and
odd-powered polynomials.
2. Complex solutions come in _____________. They are ________________ to each other.
Use synthetic division to rewrite as linear (or non-reducible quadratic) factors:
3.
x
x
x
3
2
4
4
−
−
+
4.
5
3
8
20
3
2
x
x
x
−
−
+
5.
x
x
x
x
4
3
2
5
6
+
−
+ −
6. How many possible positive and negative zeros does
y
x
x
x
x
=
−
−
+
+
4
3
2
11
9
8
have?
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Final Exam
Let me say a word about this final exam. This is an excerpt of an exam where grades seven through twelve had a
common portion of questions. The pages were broken down by subject material so that everyone always had to
show competence on their basics. This allowed me as a teacher to assess students’ progress. This also allowed for
reducing my exam writing so I didn’t have six completely different exams to write, on top of the other courses I
taught. The idea was continue to drill the basics as they learned more concepts each year. This was essential as I
noted when arriving at my school a lot of students were weak in their arithmetic and oblivious to their need to shore
up their weak areas before graduating.
Thus the exam starts off where everyone has the same pages but slowly different grades will drop out. The bonus
page is numbered in base 2 so that it can be attached at any point of the exam. For example the first five pages are
for grades seven and eight. So I would attach the bonus page at the end of the fifth page, and not bother printing the
rest of the exam for them. I would circle the grade at the top of the page after correlating and stapling the pages.
Then I would ask students when passing out the test to verify they had the correct exam by checking the grade level.
You will also note that the first two pages were to be done without a calculator. The students would have to submit
it before receiving the rest of the exam and allowing calculators to be used. I would color code the exam sheets so
the non-calculator pages were different. Then I would have a visual reminder when scanning the examinees for
calculator misuse. I got this idea of having a calculator/non-calculator parts from my colleague Dr Keith Calkins,
who would also color code.
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Final Exam
Name: __________________________
Your grade level: 7, 8, 9, 10
Date: ____________
Follow directions!
No calculator
is allowed on this part of the exam. Show work for full
credit. One 8.5" by 11" sheet of notes is allowed on the entire exam.
Real Numbers and Their Operations
1. Simplify:
a. 15 - 7
b. 3 -17
c. -5(-21)
d. -120 ÷ -3
2. Simplify, leaving answer as proper fraction (mixed number):
a.
4
5
3
5
+
b
.
4
5
2
3
−
c.
3
4
2
15
×
d.
− ÷
14
15
2
5
3. Simplify:
a. 3.4 - 5.25
b. - 4.1 - 3.001
c. 0.011(3.5)
d. 5.46 ÷ 0.6
4. Simplify:
a.
4
2
b. 75% of 88
c. ___ % = 0.241
d.
16
Bonus (2 pts): Simplify, exactly:
32
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Basic Algebra
Final Exam 7, 8, 9, 10
Leave answers as exact or proper fractions (mixed numbers). Demerits given for not leaving
answer in correct form.
5. Solve for x:
a. 4x = -10
b. 4x - 3 = 7
c. 3(x + 2) = 9
6. Simplify:
a. (6x
3
+ 24x
2
) ÷ (3x)
b. - 6x
2
(2x + 5x
2
)
7. Simplify:
a. (x
3
+ 3x
2
) + (5x - 4x
2
)
b. (5x
3
- 4x) - (3x
3
- x)
8. Write a proportion for the similar triangles below. Solve for x.
14
x
8
2
14
9. Paul eats twice as fast as Nathan, who eats eats three times slower than Ms Luttrell. She
finishes eating her lunch in 12 minutes, how quickly does Paul eat?
Bonus (2 pts): An $56 sweater is on sale for $42. What is the percent of discount?
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Name: __________________________
Final Exam 7, 8, 9, 10
Basic Geometry
Calculator is allowed from this point onward. You must show work for full credit!!
10. What is the perimeter of the rectangle?
4.2 cm
3.1 cm
11. A rectangle with dimensions
x
and 3
x
- 4 has a perimeter of 24. Find
x
. Then find its area.
12. If the diameter of a circle is 6 cm, what is its circumference? What is its area?
(Leave the answer in terms of π.)
13. What is the area of the triangle?
6
9 cm
14. If a cube has surface area of 150 cm
2
, then what is the volume of the cube?
15
Bonus (2 pts): Find the area of the right triangle: 12
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Basic Statistics
& Probability
Final Exam 7, 8, 9, 10
Use the following test scores to answer the questions #14 to #16:
61 65 68 71 71 73 77 78 78 82 82 82 87 89 91 91 95 98.
15. Construct a stem-and-leaf plot.
16. What is the mode? The median? The mean?
17. Create a histogram, labeling the axes.
18. The class has 3 boys and 5 girls. What is your chance of randomly picking a boy’s name
from the list?
19. There are 4 pants (beige, blue, green, black) and 2 matching shirts (white, yellow). How
many ways can you match a pants with a shirt? Write out the combinations if you must.
Bonus (2 pts): A class average on an exam is 85 where the boys in the class averaged 90. The
class of eight students has only three boys. What is the girls’ average?
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Miscellaneous Arithmetic & Geometry
Final Exam 7, 8, 9, 10
20. Factor the following numbers using a factor tree:
a. 48
B. 144
21. Complete the chart:
Scientific Notation
Standard form
2 1 10
7
.
×
0.0000456
2,456,000,000,000
22. Identify the type of angle:
a.
b.
c.
d.
23. Find the volume:
6
12
5
24. Circle whether true or false:
true false If all the sides of one triangle equal to all the sides of another triangle, then the
triangles are congruent (equal).
true false
If two sides of an isosceles are equal to two sides of another isosceles, then the
triangles are congruent (equal).
true false
An equilateral triangle has three equal angles as well.
true false
The angles in a triangle sum to be 180
̊
.
true false
The cube with side length of 4 cm has a surface area of 64 cm
2
.
Bonus (3pts):
A regular (all sides and angles are equal) octagon has perimeter of 96 cm. Find its area.
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Algebra: Linear & Quadratics Systems
Final Exam 9, 10
25. Write the equation of a line that passes through (2,5) and (4, 6).
Bonus (3 pts): Write the line perpendicular that passes through (3,4).
26. Solve the system:
2x + 3y = 3
Bonus (3pts each) for doing
- 3x - 3y = -9
two other methods.
27
. Graph the solutions to the system: y ≤ 3x - 2 and y < x + 1.
28. Answer the questions based on the equation: y = 5x + 6.
a. Slope = _____
b. y-intercept = ______
C. x-intercept = ______
Bonus (1 pt):
f
(7) = ______
Bonus: Solve by one method (3 pts), by an additional method (2pts): 2x
2
- 7x + 5 = 0
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Miscellaneous Algebra
Final Exam 9, 10
29. Simplify each:
a.
(
) (
)
4
3
0
3 2
2
0 2
x y
x y
b.
3
3
3
3
×
−
c. (3 - 2i) + (1 + 3i)
D. (3 - 2i)(1 + 3i)
30.
A. Expand: (x - 3)(x - 5)
B. Solve for x: 3 - 2(1 - x) = -5.
C. Solve for x: 3 - x < 6
D. Solve for x: | x - 3 | > 3
E. Expand: (x - 3)(x²-5x + 6)
31. Do the matrix operations:
a. [ 2 3] + [-1 2]
b. [ 2 -2] × [4 3]
c. 2[4 -1]
32. Simplify:
x
x
x
x
2
2
4
5
8
9
−
−
−
−
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Algebra: Graphing & Evaluating
Final Exam 10
33. Graph: y = 3x
2
- 6x - 4, labeling the intercepts, vertex and symmetry point.
34. Graph
x
y
2
2
9
+
=
35. A. Evaluate f(x) = 8 - 2x³ + 4x + 7x² when f(-2).
B. Evaluate f(x) = 3x³ + 4x² when x = -1.
36. Solve:
x
− =
1
7
37. Solve
x
− + =
1 4
6
3
Bonus: (3 pts) Solve
3
1
5
1
3
x
x
−
−
+ =
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Algebra: Series & Logarithms
Final Exam 10
38. Write the next three terms for the sequence: 2, 8, 14, ____, ____, ____ ... and then write a
general equation to represent the terms of the sequence.
39. Write in summation notation: 2+8 + 14 +... 236.
40. Evaluate:
(
)
k
k
k
2
3
6
−
=
∑
41. A. Expand this logarithm:
log
4
2
3
x
B. Simplify into one logarithm log(x-1) + log(x+1) - log 4
42. Solve:
e
x
=
6
Bonus (2 pts): Find the zeroes of the equation:
y
x
x
x
=
−
+
−
3
6
8
16
4
2
.
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153
Basic Trigonometry
Final Exam 10
43. A right triangle has a hypotenuse of 60 and leg of 24. What is the measure of the other leg?
What are the angle measures?
44. The oldest tree in town casts a shadow of 52 m long on level ground. At the same time, a
boy 2 m tall casts a shadow 4 m long.
A.
How tall is the tree?
B.
If the boy, standing 60 m away, looks into binoculars at an osprey at the top of the
tree, what is the angle of elevation?
45. In a right triangle where sin x =
3
2
, find cos x.
46. A surveyor is measuring the distance across a small lake. He has set up his transit on side of
the lake 150 meters from a piling that is directly across from a pier on the other side of the lake.
From his transit, the angle between the piling and the pier is 72
̊
. What is the distance between
the piling and the pier to the nearest foot?
Bonus (2 pts): For what angle is sinθ = ½ and tanθ =
−
3
?
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Bonus
Final Exam 7, 8, 9, 10
Each bonus question is worth 4! ÷ 3!. Show work for full credit!!
0. How can 7 + 8 = 12? One possibility is that the number system being used is to the base 13.
However, what we are looking for here is a different digit to be substituted for each of the letters in the
following example in order to give a correct addition.
S E V E N
+ E I G H T
T WE L V E
01. If the city of
A
is 9000 miles from
B
, and
B
is 9000 miles from the city of
C
, what is the probability
that
C
is closer to
A
than to
B
?
10. What number should be replace the x?
7
8
9
4
6
8
1
x
7
11. With the weights given below, find x so the weights balance the scale.
6 10 12 x
100. What is X?
131
517
192
X
I have been careful not to allow others to see my work and the work on the examination is completely my own. This examination
may be returned for my own personal use and I will not share it except with concurrent classmates. Other uses are not condoned.
I will properly dispose it. I will not talk about the exam until after June 30.
Signature/Date: ____________________________________
Luttrell 2012
155
Answer Key
A select portion of the answers are given below. Any answer with graphics was not included.
Sheet 1a:
1. 17, Four less than a number is thirteen.
2. 3, Five more than a number is eight.
3. 3, A number less than eight is five.
9. 18, A number divided by three is six.
12. 9, A number times six is fifty-four.
Sheet 1b:
2. 3.1234322...
3. 3.040040004...
4. ½
Sheet 1c:
2. 3600
3. 86400
6. A. 315/100
6. B. 104/33
Sheet 1d:
6. A. < B. >
C. <
D. <
Sheet 1e:
2. -13
3. -12
4. 0
5. -8
6. -2
7. -14
11. 9
12. 0
13. 6
Sheet 1f:
1. 10
2. -9
3. -14
4. 3
5. 3
6. -15
7. -2
8. 2
25. 11
26. 5
27. 7
28. 16
33. 2
34. - 4
35. -3
36. 1
38. $43
40. 11
Sheet 1g:
1. 24
3. -45
5. 18
7. -60
9. -85 11. -217
13. -24
15. 70
17. 3
19. -4
21. 10
23. 9
25. -5
27. 8
29. 9
31. -1
Sheet 1h:
1. Hundred
3. Million
6. Tens
8. (5×1000) + (3×100) + (4×10) + (5×1)
13. 453,800
15. 76,876
Sheet Test review:
1. A. 40
2. A. 1
3. A. 8 C. 7 D. -20
4. C. 9
5. 406,530
6. 4(10,000) + 3(100) + 5(100) +7(1)
Chapter 1 Test: 2. A. 501,072
3. A. x – 3
4B. 900,300
5. A. 3
Sheet 2a:
4. 3∕4
5. 9∕10
6. 3∕4
Sheet 2b:
1. 3 ⅔
2. 3 7∕12
8. 2⅓
9. 23∕8
11. 72∕7
15. 53∕10
16. 66∕5
Sheet 2c:
1. 1 1∕12
3. 1 1∕4
5. 1 23∕26
7. 3∕4
9. 1 21∕45
11. 1 1
3∕24
Sheet 2d:
1. ⅔
3. ¼
5. 6∕7
7. 12 1∕10
9. 2¼
11. -2
13. 15
15. 40
17. 2∕5
19. 2∕7
21. 1 25∕27
Sheet 2e:
1. 43 ½
3. 6⅞
7. 37
8. 6⅓
Sheet 2f:
3. –x
2
+ 4xy + y
2
5. 4x
2
+ 2x + 2
7. 8x
3
– 15x
2
+ 3x + 8
11. x + 4
12. x + 4
Sheet 2g:
1. -7
3. 7
5. -17
7. 24
9. -30
11. -96
13. 98
15. -324
17. -18
19. 3
21. 0
23. 10
Luttrell 2012
156
Answer Key, chapters 2-3
Sheet 2h:
1. 2
3. 3
5. -5
7. 1
9. 4
11. 4
13. 0
15. 3
Sheet 2i:
1. 4
3. ¾
5. 3
7. -140
9. 108
11. 4
13. 21
15. -9
17. 3
Sheet 2j:
1. 5
3. -5
5. ½
7. 3.5
9. -2
Sheet 2k:
1. -2
3. -25
5. 3
7. {}
Sheet 2L:
1. -1
3. 2
5. -5
7. 4
9. 1
11. 24
13. 10
15. 4 1∕5
Sheet 2m:
1. 80 by 44
3. 5
5. 1 by 2
7. 32
9. 3
Sheet 2n:
1. 80
3. 97⅜
5.
14 61∕64
7. 110 5∕6 ft
2
or 12 17∕54 yd
2
Sheet 2o:
1. 4
3. 4
5. 1¼
7. 2⅓
9. -
5 2∕5
11. -
1⅔ 13. -6
15. 14 27∕32
Sheet 2p:
1. 2 7
∕34
3. 5 5∕7
5. 9∕22
7. 3 3∕14
9. 8 19∕64
Sheet 2q:
1. 6 ½
3. 1 2∕7
5. 12
7. 21⅓
9. 1¼
11. 15∕32
13. 8
Sheet 2r:
1. A. 13⅞
B. 29⅓
C. 12 23∕24
3. A. 24 ½
B. 17 ½ C. 12 ¼
5. 16
7. 12 4∕5
9. W = 1 ½, area = 8¼
Chapter 2 Test:
2. 27∕4; 2⅞
4. A.
12 4∕9, B. 2 5∕8
6. A.
6∕7, B. 2 1∕8
8. 10 1∕6
Sheet 3a:
1. 351.008
3. 4800.40335
9. 47∕100
11. 5 63∕100
13. 2.3
Sheet 3b:
1. 40.5 3. 61.0625
5. 0.8
7. 2.1
9. 16.4
13. 4, 7
Sheet 3c:
2. 2.11, 2.111, 2.112, 2.121
5. 2.418
7. 81.364
9. 14.6917
11. -0.82
13. -44.55
15. -4.255
17. 5.251
Sheet 3d:
1. 39.18’
3. 39.84’
5. 13.2’
7. 11.6”
9. 6.5’
Sheet 3e:
1. 30.03
3. -0.0483
5. 18.7068
7. -18.13
9. -85.86
11. 0.003611
13. $86.50
15. P=21.2 ft, A=28.09 ft
2
17. 171.91 ft
2
Sheet 3f:
1. 33.784
3. 28.4889
5. 22.14
7. 46.7
Sheet 3g:
1. 0.0135
3. 40
5. 14.592
7. 0.023
9. 100.21
11. 6
13. 9
15. $16.67
17. 3.4 (4)
Sheet 3h:
1. 8.99
3. 0.27
5. 45
7. 8
9. 9
11. 22.72
13. 3.2
Sheet 3i:
1. 56.52
2. 6.28
5. 2.00
6. 1.50
Sheet 3j:
1. 254.3
2. 3.1
5. 3
6. 4
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157
Answer Key, chapters 3-4
Sheet 3k:
1. SA=880, V = 1600
3. SA≈ 628, V ≈ 1,177.5
Sheet 3L:
1. 60
3. 3840
5. 4 times, 64 times
7. 32π
9. double, 8 times
11. K → K
3
Sheet 3m:
1. 200
3. 6.93
5. 810
7. 267.9
9. 198.4
Sheet 3n:
1. 25
3. 10
5. 80
7. 300
9. 4187
11. 1000
13. 54
15. 60
Sheet 3o:
1. 12
3. 2
5. 100.5
Sheet 3p:
1. 235.5
3. 60
5. 1130
Chapter 3 Test: 1. A. 6.001, 6.01, 6.1, 6.11
B. -3.3, -3.22, -3.2
3. A. 11.3
B. 18
3. C. 12.307
7. 11.1
8. 44.33
10. V = 500π cm
2
, SA = 250π cm
Sheet 4a:
1. -5/8
2. A(b+c) = Ab+Ac
3. 3
4. 1/x
5. 5+(-5) = 0
Sheet 4b:
1. 3×3 = 9
3. 5×5×5 = 125
5. 4×4 = 16
7. 8×8 = 64
9. 1000
11. 0
13. 81
15. -243
19. 1∕27
21. 1∕27
23. 1∕216
Sheet 4c:
1. 441
3. 0
5. -15
7. 5x – 5x
2
9. 3x + 3
Sheet 4d:
3. -2
5. ½
7. -180
9. -2
11. -2
Sheet 4e:
1. 1
3. -6
5. 1
7. 23
9. 1 4/7
Sheet 4f:
1. Seventy-five
3. Four hundred
5. Ten thousands
7. Hundreds
9. 3(100,000) + 4(10,000) + 5(1,000) + 6(100) + 4(10) + 5(1)
13. 4,083,700
Sheet 4g:
1. 10
4
3. 10
7
5. 49,506
7. 7,860,000
9. 87,401
11. 4(10
2
) + 3(10
0
)
13. 5(10
7
) + 5(10
5
)
Sheet 4h:
2. 5(10
4
) + 3(10
3
) + 1(10
2
)
5. 3(10
1
) + 2(10
0
)
9. 7,426
11. 8,121,530
10. 23
11. 5
12. 53
13. 64,206
Sheet 4i:
3. 1(10
3
)
5. 4(10
16
)
11. 1(10
1
) + 2(10
0
) + 5(10
-3
)
15. 8,450,001
Sheet 4j:
1. 1.23×10
-4
3. 3.45×10
-8
5. 7.6×10
10
7. 2.3×10
13
9. 4.56×10
14
11. 23,400
13. 67,000,000
15. 0.000 034
17. 0.000 003 25
Sheet 4k:
1. 4%
3. 45%
5. 100%
7. 0.23
9. 0.003
11. $3.20
13. $4.80
15. $4.20
17. $6.30
19. $88
21. $14.25; 33.3%
23. $68.80; $72.93; $91.16
Sheet 4L:
1. 500; 5000; 0.005
3. 0.045; 0.000045
5. 3; 300
1. 1440
3. 0.081
5. 1
7. 0.000145
9. 96.75
11. 0.0004005
13. 480
Luttrell 2012
158
Answer Key, chapters 4-6
Sheet 4m:
1. 9
3. 16
5. 50
7. 12
9. 12; 14; 108; 42
11. Quadrilateral
12. Hexagon
13. 105
Sheet 4n:
1. 20.8
2. 2300m; 2,300,000 mm
3. 4.2 classes
4. 90%
5. 25%
Chapter 4 Test: 1. <; <; =
2. 7/3; 2/3
3. 15; 4; 40
4. 9; 25; 5.42
5. 1600; 420
6. $3.20 is cheaper; 326.7 km
7. 28; 10; 150; 64; 39%
8. 247,026
9. 80%
10. 37%
11. A. 234000
11. C. 6,304
11. D. -6
11.E. 8
Bonus Jar I: 350 red, 50 white; Jar II: 360 red, 40 white
Sheet 5a:
1. H = 3V/(
πr
2
)
2. m = (y-b)/x
5. Y
1
= m(x
1
-x
2
) + y
2
7. h= 2A/b
Sheet 5b:
1. S = 2T-5
3. 3R
5. S+T = 50,000
7. x + y
9. H = 4 + y
11. H = ½ L
13. T = 1.25S
15. D = 8
Sheet 5c:
1. x = 5
3. x = 6
5. w > -4
7. z < -6
Sheet 5d:
1. | 6 - 4 | = 2
3. | 7 – (-3)| = 10
5. | x – (-2)| = 4
7. |x – (-2)| < 4
9. 5, 11
11. -8, 4
Sheet 5e:
1. 2
3. -4, 4
5. x < 3
7. -
3 ≤ x ≤ 3
9. -2, 8
11. -1, 11
12. -1, 5
Sheet 5f:
1. -1< x < 5
3. -8 < x < -6
5. x < -4 or x > 6 7. -
2≤ x ≤ 6 9. x > 1 or x < -1/2
10. 0 < y < 4
14. 9 ≤ x ≤ 15 15. -5 ≤ x ≤ -1
Sheet 5g:
4. The figure is a line.
Sheet 5h:
1, 6, 4, 2, 7, 8, 5, 3
9. y = kx
11. y = k/x
12. y = k
15. y = kx + b
Sheet 5i:
1. Yes, Domain: -
1 ≤ x ≤ 4; Range: -5 ≤ y ≤ 6
2. Yes
3. No
4. Yes
5. Yes
6. Yes
7. Yes
8. No
9. No
Chapter 5 Test: 1. 7.5; 8; 6
2. T = 180B + 14000; 16,340
3. h = 2A/b; h = V/(πr
2
)
4. y < -3…
5. -2 < x < 8; -
7 ≤ x ≤ 5; 2, -⅔
Sheet 6a:
Fill in blanks: 3, 6, 1, 3, 6, 4
1. x = {-1, 0}, y = {4, -2.5}
2. x = {7, 14}, y = {3, 9, 15}
3. x = {6, 10}, y = {7.96, 23.88}
Sheet 6b:
Graphs are not included.
Sheet 6c:
1. y = ⅔x – 7
2. y = 3x – 2
3. y = -
⅓x + 2
4. y = -x + 3
5. y = -2x + 5
6. y = 2
7. -4x + 9y = 51
Sheet 6d:
1. y = -3x + 2
2. y = ⅔x + 2⅓
4. y = x + 5
6. y = -2x + 5
7. y = 4x – 11
8. y = -3
Graphs are not included (#9-#17)
9. x = 6
10. x = 6
11. x = -3
12. y = 4
Sheet 6e:
1. A & C
2. y = ⅓x + ⅔
3. 5x – 3y = -26
4. 4x + 9y = -2
Luttrell 2012
159
Answer Key, chapters 6-8
Sheet 6f:
1. A&B, B&C
2. D
3. 3x + 5y = 22
4. 3x + 4y = -1
Sheet 6g:
Graphs are not included. Simplified equations: 1. y < -2x -4
2. y > -3x + 5
3. y < x – 4
4. y ≤ 2x + 4
5. y ≥ - ½ x + 2.5
6. y > 4/3 x - 3
Sheet 6h:
1. (2.5, 0.5)
2. (2, 4)
3. (2,-1)
4. (-3, -4)
5. (-3, -2)
6. (3, 5)
Sheet 6i:
1. (3, 2)
2. (1, 1)
3. (2, -3)
4. (2,4)
5. (3, 1)
6. (3, -2)
Sheet 6j:
1. (½, ⅓)
2. (1, 3)
3. (4, 7)
4. (-6, 5)
5. (2, -5)
6. once
Sheet 6k:
1. Y = 0.49x; $36.75
2. Y = 64x + 5500; $21,500
3. Y = 25x + 65; $127.50
4. y = 8x; $96
5. Y = -1360x + 17000; $-3400 (cost you to get rid of it!!!)
Sheet 6L:
1. 161.6°F
2. $270
3. 36 ft
4. 46,875 ft
2
5. 2 ⅔ cups
6. 1⅓ cup
7. Keith = 48, Shirleen = 32, Rachel = 16
Chapter 6 Test: 1. -9, ½, -10
2. C = 60, A = 480
5. (4, 3)
6. 6x – 9y = 8; -x + 2y = 10
7. y = -6x + 27 9. Y = 0.75x + 2.75
10. 2x – 3y = 17; 3x + 2y = 6
Bonus: 32; -1
Sheet 7a:
1. 12
2. 36
5. 16
6. {}
8. 8y + 49y
2
9. 176x
2
11. 4x
4
12. ½
14. Z
3
y
6
x
9
15. 1
Sheet 7b:
1. Y
11
2. –x
8
y
6
3. Z
6
4. A
18
b
11
5. X
8
6. a/2
Sheet 7c:
1. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
2. 3 and 5
3. 11
4. 3 and 9
5. 6, 9, and 11
Sheet 7d:
1. 2
2
×29
2. 5
2
×7
5. GCF = 7; LCM = 105
7. GCF = 3, LCM 378
9. GCF = 6; LCM = 168
11. GCF = 5; LCM = 350
13. GCF = 8; LCM = 448
Sheet 7e:
1. 2√6
2. 5√3
3. 4√6
5. 12
6. 15
7. 25
Sheet 7f:
1. 16
3. 32
4. 16
6. 49
10. √3
11. 9
Sheet 7g:
1. 0
2. 3√3
3. 9√3
4. 1
5. -6x
6. 10√2
7. 6√2
8. 8√2
9. 54
10. 24√6
11. √6
12. 75
Sheet 7h:
1. √3
2. 3√(5)/5
3. √(30)/6
4. √(6)/3
5. √(2)/2
Sheet 7i:
1. ±4
2. ±5
3. 2
4. 144
5. 225
6. 30
7. 50
8. 22
Chapter 7 Test: 1. 8; 48
2. 2; 504
3. 8∕27; -256
4. -
⅓; 9261
5. 20; y
4
∕x
6. 1∕512; x
15
7. 3.4×10
-11
; 5×10
9
8. 3; 5; 28
bonus: 909; -1982
Sheet 8a:
1. x
2
– xy – 6y
2
3. –x
2
+ 5x – 6 5. 2a
2
– 7ab – 15b
2
7. W
2
– 4
9. –x
2
+ 8x + 33
Sheet 8b:
1. (x + 1)(x + 3) 3. (x + 4)(x + 2) 5. (x – 2)(x – 12)
7. (x + 3)(x + 6) 9. (x + 4)(x + 5)
Luttrell 2012
160
Answer Key, chapter 8 & appendix
Sheet 8c:
1. (x - 2)(x + 3) 3. (x + 2)(x – 10)
5. (x + 2)(x – 8) 7. (x-4)(x+4)
9. (x - 9)(x + 2)
Sheet 8d:
1. (2x + 7)(x – 1)
4. (x + 1)(4x – 5)
7. (3x – 4)(x + 1) 10. (3x + 2)(2x – 3)
Sheet 8e:
1. {1, 6}
2. {2, 1}
3. {3, 4}
4. {4, -1}
5. {-1, -4}
6. {-12, -1}
7. {-7, 2}
8. {2, 6}
9. {-2, -6}
10. {1.5, -2}
Sheet 8f:
(ax ± b)
2
; (ax –b)(ax + b) 1. {±3}
2. {±4}
3. {±5}
4. {±6}
5. {0, ±2}
6. {0, ±4}
7. {±3}
8. {±3}
9. {±0.6}
Sheet 8g:
1. (5x+3)(5x–3) 2. (2-9x)(2+9x) 3. 16(c-2)(c+2) 4. 3(3-n)(3+n) 5. 3c(c-3)(c
2
+3c+9)
6. x(x-1)(x
2
+x+1)
7. 5x
2
(x-10)(x
2
+10x+100)
9. ab(a-b)(a
2
+ab+b
2
)
Sheet 8h:
1. {0.6, -1}
2. {1.75, -1}
4. {-
3⅓, 1}
5. {2, 3}
6. {⅓, -4} 7. {6,-1}
Sheet 8i:
1. {2⅔, -1}
2. {-6, 1}
3. {1, -8}
5. {3, -1} 6. {-3.5, 1} 8. {1.5, 1}
Sheet 8j:
1. {0, -8, -8, -5, 0, 16}
2. {4, -3, -6, -5, 0, 9}
3. {2, 0, 0, 2, 6, 12}
Sheet 8k:
2. Up; y-int (0,8); vertex (3,-1); sym (6,8) 5. Down; y-int (0,-2); vertex (1.5, 0.25); sym (3,-2)
Sheet 8L:
1. 27 ft
2. C = 50.5; Wind speed
3. 365.8 parts per million 4. 14 mph
Sheet 8m:
1. -6
2. 0
3. 8 – 4i
4. -13 + 10i
Sheet 8n:
1. 12 + 5i
2. 13
3. -3 – 4i
4. 4
7. √5
8. 13
Chapter 8 Test: 2. –x
2
– x – 4; x
2
y
2
+ 3xy
3
3. 12b; -6p
5
4. 4x
2
+ 6x; -36 - 24t
5. 5a(5 + 6a); 3c(c
2
- 5)
6. (a+7)(a+6); 32(x-2)
7. a
2
-2a – 3; 6x
2
– x –12
8. 2a – 4; 4(a – 1)
9. {2, -7}; {-11}
10. {-1, -
1⅔}
11. up; vertex (1.25; -0.125), y-int (0, 3); sym (2.5; -0.125) 12. 49; two real bonus. 1
Cumulative Review:
1. 1.2x
5
y
3
2. 3
3. P = I/(rt)
5. -
5 < x < ⅓
6. -2x + 15y = -12
7. y = -7.5x + 1
9. y = 3x – 7
10. 4x
2
– 20x + 25
11. ⅔, 1
13. 0.6 ± 0.8i
14. (4y + 5)/(xy)
A-1
4. x < 3
5. x > 1
8. {3, -1.8}
9. x
3
+ 3x
2
y + 3xy
2
+ y
3
10. {-4, 5, -1.5}
A-2
1. {4}
2. 5061/990
5. Range {y| y ≤ 8}; 8, 0
6. No. There are two values for y for an x.
A-3
3. Slope is 3 and y-intercept is 5. 4. 3x – 4y = -27
6. Inconsistent 7. y = 2x - 5
A-4
1. (1, 1)
2. (3, -5)
3. (4, 2)
4. (2, -3, 1)
5. (-1, 4, 2)
A-5
1. y = 3(x – 2)
2
– 7
3. y > 5(x + 1)
2
+ 7
5. 33; 2 real
7. y = 3x
2
– 3x + 1
8. {-
1, ⅔}
10. {78}
