Algebra II Pre-Chapter Test
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1. Given these two points: (-2, 6) and (6, 9), find:
a. Slope
b. Midpoint
c. Distance
d. Equation in Slope-Intercept Form
e. Equation in Standard Form
2. Graph the line y = -4x + 2
3. Spencer can complete a job in half the amount of time
that Zach can complete the job. Together they
complete the job in five hours. How long does Zach
take to complete the job?
4. Complete the Square using Factoring:
a. 2x2 – 6x + 3 = 0
b. -5x2 + 6x + 9 = 0
Algebra II Pre-Chapter Test
5. Factor and Solve: 8x3 – 27 = 0
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6. Simplify the Rational Expression. State all restrictions.
a.
b.
3
𝑥−1
−
𝑥 3 −8
𝑥 2 −4
2
𝑥
÷
+
𝑥+3
𝑥 2 −1
𝑥 2 +2𝑥+4
𝑥 3 +8
7. Simplify the complex fraction. State all restrictions.
2
( −3)
𝑥
a.
1
(1−
)
𝑥−1
b.
(4− 𝑥 2 )1/2 + 𝑥 2 (4− 𝑥 2 )−1/2
4− 𝑥 2
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Algebra II Chapter 1 Test
Solve the quadratic-type equations:
1. 6x4 + 7x2 – 5 = 0
𝑥 2
)
𝑥+1
2. 2(
𝑥
�−
𝑥+1
+ 3�
5=0
3. 3x - 4√𝑥 + 1 = 0
Solve the absolute value equations. Check for extraneous solutions.
4. |3x| = 5
7. Find the equation of the
line that passes through
(2,5) and slope is
undefined.
5. |2x + 1| = 4x
6. |3x + 2| = 5x – 7
8. Find the equation of the
line that passes through
(2,5) and is perpendicular
to 2x – 5y = 10.
10. Given the relation {(3,0), (3,2), (1,5),
(7,4)}, is this a function? Explain why or
why not.
Page 1 of 5
9. Find the intercepts of 2x –
5y = 10.
11. Given the relation
graphed, is this a
function? Explain
why or why not.
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Algebra II Chapter 1 Test
12. Can the relation {(6,-1), (5,-2), (4,-3), (3, 2)} be considered one-to-one? Explain
why or why not.
13. Given the relation
graphed, can it be
considered one-toone? Explain why or
why not.
14. Find the inverse of f(x) = 5√3 − 𝑥
Given the functions f(x) = 3x – 2, g(x) = x2 – x, and h(x) = √𝑥, find:
15. g(-2) =
17. (g/h)(x) =
19. (g o f)(x)
16. (f + g)(x) =
18. (f o g)(x)
20. (h o g)(x)
21. (f o h)(529)
Determine if the function is even, odd, or neither:
22. f(x) = 3x4 – 2x3 + 1
23. g(x) = 2x5 – 3x3 + 1
24. h(x) = -2x6 + 7x4 + 3x2
Find the difference quotient and simplify your answer.
25. f(y) = -4y2 + 6y ;
𝑓(1+ℎ)−𝑓(1)
;
ℎ
h≠ 0
26. Explain what a difference quotient is helping us find on a graph of a curve.
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Determine if the following two functions are inverses by using composition.
27. f(x) = 9x – 8 and g(x) = 8/9 + x/9
28. g(x) = 3x – 2 and h(x) = -2 + x/3
29. _____
30. Determine the intervals in which the function:
increases:
decreases:
constant:
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31. Given the function 𝑓(𝑥) = �
A) f(0)
−𝑥, 𝑥 < 0
, find:
𝑥2, 𝑥 ≥ 0
B) f(-5)
2, −5 < 𝑥 ≤ −2
32. Graph the function 𝑔(𝑥) = �2𝑥 + 1, −2 < 𝑥 < 2
−𝑥 2 + 3, 𝑥 ≥ 2.
33. Graph ℎ(𝑥) = ⟦𝑥 − 4⟧ + 1
34. Find the domain and range of 𝑓(𝑥) =
2𝑥
√6−𝑥
35. Given the graph g(x), complete the following
transformations on the same graph. Differentiate by
different types of lines or colors.
g(-x)
-g(x)
g(2x) - 3
g( ½x) + 1
2g(x) - 4
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36. What type of relationship does this scatter plot appear to have?
37. When the State of Arizona projects how many prison beds it will
need, it factors in the number of kids who read well in fourth
grade (Arizona Republic (9-15-2004)). Evidence shows that
children who do not read by third grade often fail to catch up and
are more likely to drop out of school, take drugs, or go to prison. So many nonreaders wind up
in jail that Arizona officials have found they can use the rate of illiteracy to help calculate future
prison needs. Describe the type of correlation the officials have found in this data set.
38. Is there a relationship between Math SAT scores and the number of hours spent studying for the
test? A study was conducted involving 20 students as they prepared for and took the Math
section of the SAT Examination.
a.)
Graph a scatter plot on Excel or your TICalculators. Determine a linear regression
model equation to represent this data.
b.)
c.)
Graph the new equation.
Decide whether the new equation is a "good fit"
to represent this data.
d.)
If a student studied for 15 hours, based upon
this study, what would be the expected Math
SAT score?
e.) If a student obtained a Math SAT score of
720, based upon this study, how many hours did
the student most likely spend studying?
f.) An example of extrapolating about the data
would be to evaluate the SAT score for a student
who studied for 100 hours. Explain why this
would be considered as extrapolation.
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Hours Spent
Studying
4
9
10
14
4
7
12
22
1
3
8
11
5
6
10
11
16
13
13
10
Math SAT
Score
390
580
650
730
410
530
600
790
350
400
590
640
450
520
690
690
770
700
730
640
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Chapter 3 Practice Test: Exponential & Logarithmic Functions
Will the exponential function be increasing or decreasing?
1. y = 3(5.1)-x
2.
y = -2(5/4)x
Graph the following function. Show at least five points in the table. Create your graph’s axis such that it
fits your functions’ needs.
3. y = 7(1/3)x
5. y = 5 – log2x
4. y = 4x + 1
6. y = log(x – 3)
Create an exponential function of the form y = abx that includes the given points.
7. (0,2), (2,4)
8. (1, ½), (2,1)
Switch into logarithmic form:
9. 34 = 81
10. 7-3 = 1/343
Switch into exponential form:
11. 0 = log151
12. -2 = log4(1/16)
Evaluate:
13. log5125
14. ln1
15. Show how to evaluate by changing bases (show what you’ll plug into your calculator): log76
16. Show how to rewrite the given logarithm with a base of 2: log85
Expand the following expressions:
17. log3xy5
√
18. log5( )
Write each expression as a single logarithm:
19. 3log7x – 5log7y
20. ln ab + 6ln b
Solve the following equations to the nearest thousandth:
21. 2ln x – ln 3 = 2
23. 6e2x – 4 + 1 = 13
25. 2xe2x + e2x = 0
22. log5(x + 2) + log5(x – 2) = 0
24. e2x - 7ex = -10
26. 50/(1 – 2e-0.001x) = 1000
27. If $10,000 is invested in a savings account that pays 8.65% interest compounded continuously,
in how many years will the balance be $250,000? Round to the nearest tenth.
28. A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count
has increased to 80. If this rate of growth continues, how much more time will it take for the
bacteria count to reach 100?
29. The demand, x, for a 32-inch plasma television depends on price. The demand is modeled by
(
). Find the demand for prices of p = $450.
30. The half-life of radioactive actinium (227Ac) is 22 years. What percent of a present amount of
radioactive actinium will remain after 19 years?
31. The table shows the annual revenues R (in millions) for Daktronics from 2001-2008. Determine
the model that best fits the data. Use the model to predict the revenue of Daktronics in 2015.
2001
148.8
2002
177.8
2003
209.9
2004
230.3
2005
309.4
2006
433.2
2007
499.7
2008
581.9
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RIT
Chapter 4 Practice Test
1. Label the positive and negative degrees and radians with their coordinates.
2. Describe what a radian is and how it was created. Why is it used?
3. List the three Pythagorean Identities. Show how to create the last two from the first.
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4. Sketch -120° in standard position.
5. Sketch 7π/2 in standard position.
6. Sketch 6.02 in standard position.
7. Convert 34π/15 to degrees.
13. The diameter of a DVD is 12cm. The
drive motor of the DVD player is
controlled to rotate precisely between
200 and 500 revolutions per minute,
depending on the track.
A) Find the interval for the angular
speed of a DVD as it rotates.
B) Find an interval for the linear speed
on a point on the outermost track as
the DVD rotates.
8. Convert -20° to radians.
9. Give two co-terminal angles (pos/neg)
to -15°.
14. Given sec Ɵ = 6, find the remaining five
trigonometric functions of Ɵ.
10. Give two co-terminal angles (pos/neg)
to 3π/4.
15. Given tanƟ = 5, find csc(90° - Ɵ).
11. Find the arc length of a central angle of
120° of a circle with a radius of 4 inches.
16. Prove: secƟcotƟ = cscƟ.
12. A car’s rear windshield wiper rotates
125°. The total length of the wiper
mechanism is 25 inches and wipes the
windshield over a distance of 14 inches.
Find the area covered by the wiper.
Evaluate:
18. tan(-π/3) =
19. csc(π) =
17. Prove cosƟ(secƟ – cosƟ) = sin2Ɵ.
20. sin(210°) =
21. cos(2π/3) =
22. cot(-3π/4) =
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Chapter 6 Practice Test Part II
1. Graph
y = cosx
y = tanx
y = cscx
y = sinx
y = secx
y = cotx
2. Create a graph to fit
two full periods of
y = -3 – 2six(3x + π)
3. Fit y = 7 + 3cos5x
between [-2π, 2π]
5. Graph y = 3cot(πx/2)
7. Graph y = arctanx
6. Graph y = -secπx + 1
8. Graph y = arcsinx
4. Fit y = -4 + 6six(2x) to this
generic curve:
9. Graph y = arccosx
Evaluate:
10. csc[arctan(-5/12)]
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11. sin[arcsin(-5)]
12. cos[arctan2]
13. Find the altitude of an isosceles triangle whose base angles are 45° and base side is 11 meters.
Round to two decimal places.
14. The angle of elevation of the sun is 26°. Find the length, l, of a shadow cast by a tree that is 53
feet tall. Round to two decimal places.
15. A jet is traveling at 580 miles per hour at a bearing of 51°. After flying for 1.5 hours in the same
direction, how far north will the plane have traveled? Round answer to nearest mile.
16. Two lifeguards, Natalie and Jack, are 16 miles apart and Jack is directly due south of Natalie on
the beach. A stranded boat offshore is spotted by both lifeguards, and the bearings from Jack
and Natalie are N 30° E and S 11°E. Determine the distance the stranded boat is from the beach.
Round answer to nearest tenth of a mile.
17. While traveling across the flat terrain of Nevada, you notice a mountain directly in front of you.
You calculate that the angle of elevation to the peak is 4°, and after you drive 6 miles closer to
the mountain it is 7°. Approximate the height of the mountain peak above your position. Round
your answer to the nearest foot.
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Chapter 5-6.2 PRACTICE Test
Verify the following proofs:
1.
1
1−𝑠𝑖𝑛𝜃
= 𝑠𝑒𝑐 2 𝜃 + 𝑡𝑎𝑛𝜃𝑠𝑒𝑐𝜃
𝜋
2
2. 𝑠𝑖𝑛𝜃 csc � − 𝜃� = 𝑡𝑎𝑛𝜃
3.
𝑠𝑖𝑛𝜃−𝑠𝑖𝑛3 𝜃
𝑐𝑜𝑠4 𝜃+𝑐𝑜𝑠2 𝜃𝑠𝑖𝑛2 𝜃
= 𝑠𝑖𝑛𝜃
4. Use the cofunction identities to evaluate the expression below without the aid of a calculator:
sin256o + sin225o + sin234o + sin265o
5. Solve: cos3x = cosx
6. Find tan2x given that cosx = -1/2 in Q3.
7. Find the exact value using the sum or difference formula: sin255o.
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Chapter 5-6.2 PRACTICE Test
5𝜋
8. Find the exact value using the sum or difference formula: tan .
12
9. Find the exact value of sin(u + v) given that sinu = 5/13, in Q2, and cosv = -4/5, in Q2.
𝜃
2
10. Find sin� � given cot𝜃 =
30
16
𝜃
2
11. Solve in the interval: [0,2𝜋), cos( ) − 𝑠𝑖𝑛𝑥 = 0
12. Use the product to sum formula to write the given product as a sum or difference:
𝜋
𝜋
12sin(10)sin(10)
13. Use the sum-to-product formulas to find the exact value of the given expression:
sin1500 + sin30o
14. Given C = 128o, a = 13.9, and c = 9.3, final all possible solutions to solve the triangle. Round
answer to two decimal places if needed.
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Chapter 5-6.2 PRACTICE Test
15. Determine the area of the triangle such that A=119o, b = 6, and c=12. Round your answer to two
decimal places.
16. Determine a range of values for b such that a triangle with A=50o and a = 10 has no solution.
17. After a severe storm, a tree was leaning 3o from vertical toward the house. From the house, 93
feet away from the base of the tree, they noticed that the angle of elevation to the top of the
tree was 31o. Approximate the height of the tree. Round answer to two decimal places.
18. Given a = 4, b = 10 and c = 11, find the area. Then solve the triangle.
19. Given A=54o, b = 6, and c= 11, solve the triangle.
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Alg II Chapter 7 Practice Test: Matrices
Determine the order of the matrix.
1)
1) _______
Perform the matrix operation.
2) Given A =
and B =
3) Given A =
, find -3A2. 3) _______
Find the product, if possible.
4)
4) _______
5)
5) _______
Solve using Cramer's rule.
6)
6) _______
7) 2x
+ 8z = 58
-3x + 4y + 3z = 39
9x - 3y
= 18 7) _______
, find 2A + B.
2) _______
Solve for x in the determinants.
8)
= -2
9)
A) 4
8) _______
=4
B) 2
C) -2
9) _______
D) No solution
Find the inverse of A.
10) A =
10) ______
Find the inverse of B.
11) B =
11) ______
Write the augmented matrix for the system. Then solve.
12) 3x + 9y = 90
5y = 45
12) ______
13) 3x + 7y + 6z = -20
2x + 8y + 9z = -30
2x + 9y + 9z = -32
13) ______
14) Determine if the following points are collinear. If they are not, find the area of the triangle that they create.
(-2,-2)(1,1), and (7,5).
15) Determine if the following points are collinear. If they are not, find the area of the triangle that they create.
(1,0)(2,2),and (4,3).
16) Find the equation of the line that passes through (2,4) and (-1,3) using matrices.
17) (You may use your calculator.)
1
The following message as encoded by �−1
1
Decode the following message:
−2 2
1 3� using a standard 0-26 => A-Z
−1 4
31 -56 179 17 -17 75 7 -12 18 10 -15 93 30 -37 106 -16 15 74 7 -15 47
Chapter 8: Sequences and Series
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1. Explain why -34,-28, -22, -16, … is a finite/infinite sequence/series.
2. Given 3, 6, 12, 24, 48, …
a. Is this arithmetic, geometric, or neither. Then identify the common difference/ratio.
b. Write the recursive formula:
c. Write the explicit formula:
d. Find a 10.
3. On October 1, a gardener plants 20 bulbs. On October 2, she plants 23 bulbs. On October 3, she
plants 26 bulbs. She continues this until October 15, on which she plants the last bulbs.
a. Is this arithmetic, geometric, or neither. Then identify the common difference/ratio.
b. Write the recursive formula:
c. Write the explicit formula:
d. How many bulbs will be planted on October 15?
e. How many total bulbs were planted?
4. Write out each term and evaluate the sum: ∑6𝑛=1(−𝑛 − 3)
5. Write the summation notation for the arithmetic series:
3 + 7 + 11 + … ; n = 10
6. Evaluate the finite geometric series with the formula: 𝑆 =
7
1
� 32( )𝑛−1
4
𝑛=1
𝑎1 (1−𝑟 𝑛 )
(1−𝑟)
7. Evaluate the infinite geometric series with the formula: 𝑆 =
∞
2
� −( )𝑛−1
3
𝑛=1
𝑎1
(1−𝑟)
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Alg II Chapter 9 Practice Test
Part I: Conic Sections
1. Identify the focus and directrix given
x = -6(y - 4)2 + 2
4. Write an equation given that the center is
(5,-1) and circumference is 5π
2. Write an equation given V(-3,5) and F(-3,7)
5. Write an equation of a vertical ellipse
given C (-2,7), major axis of 12, and minor
axis of 4.
3. Find the radius, center, and intercepts of
the circle: 4x2 + 4y2 + 32x -24y + 51 = 0
6. Write an equation of a hyperbola and its
asymptotes given V(3, ±4) and Foci (3,±5).
7. Identify the conic section represented. For a parabola, state the vertex, focus, and directrix. For
a circle, given the center and radius. For an ellipse or hyperbola, give the center and foci.
Sketch the conic sections.
2
a. x – 4y2 + 4x + 8y – 16 = 0
c. x2 + y2 – 4x + 2y + 1 = 0
e. x + 2y2 + 4y – 2 = 0
b. 25x2 + 4y2 – 50x – 24y – 39 = 0
d. x2 – 4x – y + 7 = 0
f. x2 + 9y2 + 8x – 54y + 88 = 0
8. Rotate the axes to eliminate the xy-term in the equation: x2 -4xy + y2 + 1 = 0
a. Determine the conic represented
b. Determine the angle rotated
c. Write the equation in standard form.
d. Sketch the resulting equation, showing both sets of axes.
Part II: Polar Coordinates and Equations
9. Graph the polar coordinate, (
).
Then name three additional points.
10. Convert the polar coordinate to a rectangular coordinate: (-3, ).
11. Convert the rectangular coordinate to a polar coordinate: (6,9)
12. Convert the rectangular equation to polar form: xy = 4
13. Convert the polar equation to rectangular form: r = 2sinϴ.
14. Sketch the graph of the following polar equations:
a. r = 2sinϴ
d. r = 6 + 6sin ϴ
g. r = sin(2 ϴ)
b. ϴ =
e. r = 5 - sin ϴ
h. r = cos(3 ϴ)
c. r = 6 – 4cos ϴ
f.
r = 2 + 5cos ϴ