Download Name____________________________________________________________ Final Review Packet Algebra 2 Final Exam

NO OMITS ON THE PRACTICE FINALS!!
Name____________________________________________________________
Final Review Packet
Algebra 2 Final Exam
Practice Final 1
Part I
Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits.
1. Which function is NOT one-to-one?
(1) {(12,-3), (4, 15), (0, 8), (2, -11)}
(3) {(5, 7), (9, 11), (3, 1), (4, 11)}
(2) {(2, 0), (-1, 6), (8, 4), (3, -10)}
(4) {(1,-5), (2, 2), (8, 6), (1, -4)} (5) OMIT
2. If 𝑓(𝑥) = 6𝑥 − 5 and (𝑥) = −𝑥 + 1 , what is the value of 𝑓(𝑔(−3)).
(1) 24
(2) 19
(3) −17
(4) −22
(5) OMIT
3. What is the solution of the equation log 3 3𝑥 = 3 ?
1
(1) 9
(2) 3
(3) 3
(5) OMIT
(4) 0
4. The expression 6ab 18b  4a 72b3  9ab 10b is equivalent to
(1) 3ab 10b
(5) OMIT
(2) 3ab 12b
(3) 6ab 2b  9ab 10b
(4) 6ab  9ab 10b
3
5. If 𝑠𝑖𝑛𝑥 = 5 , what is sin(2𝑥) ?
7
(1) 25
9
(2) 25
24
(3) 25
6
(4) 25
(5) OMIT
6. Which graph represents the solution set of |4𝑥 − 1| ≤ 7 ?
(5) OMIT
7. Factored completely the expression 3𝑥 2 + 𝑥 − 2 is equivalent to
(1) (3𝑥 − 2)(𝑥 + 1)
(2) 3(𝑥 − 2)(𝑥 + 1)
(3) (3𝑥 + 2)(𝑥 − 1)
(4) 𝑥(3𝑥 + 1)(𝑥 − 2)
(5) OMIT
8.
Ten students compared their grades on their last math test. Their scores were:
77,55,68,92,85,80,91,94,78,89
To the nearest tenth, what is the sample standard deviation for this set of data?
(1) 12.2
(2) 11.6
(3) 10
(4) 12.3
(5) OMIT
9. If a function is defined by the equation f(x) = 3𝑥 , which equation represents the inverse of that
function?
(1) 𝑦 = log 3 (𝑥)
(2) 𝑦 = log (𝑥) 3
(3) 𝑦 = log(3)
(4) 𝑦 = (𝑥)3 (5) OMIT
10. The expression (6-i)2 is equivalent to
(1) 37 + 12𝑖
(2) 35 − 12𝑖
(3) 37 − 12𝑖
(4) 35+12i
(5) OMIT
NO OMITS ON THE PRACTICE FINALS!!
11. Factored completely the expression 4𝑥 − 64𝑥 is equivalent to
(1) x2 (4x + 16)
(2) 8x(x+2)(x-2)
(3) 4x(x+4)(x-4)
(4) 8x2(x - 4)
(5) OMIT
3
12. If side a=6 and angle A = 62°, find side b correct to two decimal places when angle B = 41°.
(1) 4.46
(2) 4.45
(3) 9.64
(4) 9.65
(5) OMIT
13. What are the values of 𝜃 in the interval 0° ≤ 𝜃 ≤ 360° that satisfy the equation 2𝑐𝑜𝑠𝜃 − 1 = 0?
(1) 30°, 330°
(2) 150°, 210°
(3) 60°, 300°
(4) 120°, 240°
(5) OMIT
14. Which graph does not represent a function?
(1)
(2)
(3)
(4)
(5) OMIT
15. In ∆XYZ, m<X = 67o , side y = 3 and side z = 10. What is the area of ∆XYZ to the nearest square
inch?
(1) 13
(2) 14
(3) 28
(4) 6
(5) OMIT
16. Express (𝑐𝑜𝑠𝑥)(𝑡𝑎𝑛𝑥) as a single trigonometric function.
(1) sinx
(2) cscx
(3) 1
17. The expression 𝑙𝑜𝑔4 16 is equivalent to
(1) 1/4
(2) 1/2
OMIT
(4) cosx
(3) 4
(5) OMIT
(4) 2
(5)
18. What change will be made to the graph of the equation 𝑦 = 𝑥 2 if the equation is changed to 𝑦 =
(𝑥 + 5)2 − 3?
(1)shift right 5, up 3
(2)shift right 5, down 3
(3)shift left 5, down 3 (4)shift
up 5, left 3 (5)OMIT
19. In simplest form the expression
1
(1) 𝑥+𝑦
1 1
−
𝑥
𝑦
𝑦 𝑥
−
𝑥 𝑦
1
(2) 𝑥−𝑦
20. The solution set of √𝑥 − 6 + 4 = 7
(1) {15}
(2) {12}
equals
−1
−1
(3) 𝑥+𝑦
(4) 𝑥−𝑦
(5) OMIT
(3) {9}
(4) {-15}
(5) OMIT
NO OMITS ON THE PRACTICE FINALS!!
21. A circle has a radius of 8 inches. In inches, what is the length of the arc intercepted by a central
angle of 2 radians?
1
(1)16
(2) 4
(3) 4
(4) 10
(5) OMIT
𝑥 2 −3x+2
22. What is the domain of the function (𝑥) = 𝑥 2 −9 ?
(1) 𝑥 ≠ 3, −3
(2) 𝑥 = 2, 1
(3) 𝑥 ≠ −3
(4) 𝑥 ≠ 3
(5) OMIT
23. What is the equation of the axis of symmetry of the graph of 𝑦 = 2𝑥 2 − 8𝑥 + 4
(1) 𝑥 = −4
(2) 𝑥 = 4
(3) 𝑥 = −2
(4) 𝑥 = 2
(5) OMIT
24. Which formula can be used to determine the total number of different 5 letter arrangements
that can be formed using the letters in the word PIZZA?
5!
5!
2!
(1) 2!
(2) 5!
(3) 3!2!
(4) 5!
(5) OMIT
25. The graph at the right represents which of the following equations?
(1) 𝑦 = 1/2𝑐𝑜𝑠𝑥
(2) 𝑦 = 𝑠𝑖𝑛𝑥
(3) 𝑦 = 𝑐𝑜𝑠𝑥
(4) 𝑦 = 1/2𝑠𝑖𝑛𝑥
26. What is the third term in the expansion of (x + y)4?
(1) x2y2
(2) 2x2y2
(3) 6x2y2
(5) OMIT
(4) 4x2y2
(5)OMIT
2𝑥 7 𝑦 −3
27. Simplify the expression 10𝑥 9 𝑦 −6 and only use positive exponents.
𝑥2
𝑦3
(1) 5𝑦 9
(2) 5𝑥 2
𝑦9
(3) 5𝑥 2
28. The solution set of 4|10-2x| = 8 is
(1) { }
(2) {6}
(3) {4}
𝑥2
(4) 5𝑦 3
(5) OMIT
(4) {4,6}
(5) OMIT
29. Find the sum of the roots S, and the product of the roots P of the quadratic equation
𝑥 2 + 5𝑥 − 6 = 0
(1) S = -5, P = -6
(2) S = 5, P = 6
(3) S = -5, P = 6
(4) S = 5, P = -6
(5)OMIT
30. Given the equation sin(2𝑥 + 18)° = cos (5𝑥 − 12)° solve for the value of x
(1) 42
(2) 12
(3) 10
(4) 0
(5) OMIT
PART II
Answer all 5 questions from this part. Show work in your notebook.
[Four credits each]
6
31. Find the value of the expression ∑𝑥=2(4𝑥 + 5)
32. Using the formula V = Pert find the value V for an investment of $7200 at an annual rate of 5.8%
compounded continuously after 7 years.
33. Express
18
6−√2
with a rational denominator, in simplest radical form.
NO OMITS ON THE PRACTICE FINALS!!
34. Find the center and radius of the circle with the equation:
(x – 8)2 + (x + 1)2 = 81
35. Solve the fractional equation for x:
6
5
11
+
=
𝑥−1
2
𝑥−1
PART III
Answer 3 out of the 4 questions in this section. All work necessary to the solution of the
question must be written in your notebook. [Each question selected is worth 10 points]
36.
a) Solve 4x2 + 6x + 10 = 0 expressing the result in simplest a + bi form.
b) Solve for all values of x by factoring by grouping.
x3 + 6x2 – 25x – 150 = 0
37. a) The table below summarizes the average revenue in thousands of dollars for the annual ticket
sales for the local basketball team.
Year
1
2
3
4
5
6
7
8
9
Cost
18.0
18.2
18.5
18.9
19.2
19.6
20.0
20.3
20.7
1) Find the linear equation of best fit for the given data. Round decimals to three places.
2) Find the correlation coefficient “r” correct to 4 decimal places for part a.
3) Use the equation of best fit in part a to estimate the average revenue for the local basketball team
in year 15. Round to the nearest dollar.
37. b) St. Francis Prep’s hockey team has 4 games left in the season. The probability that the team
will win a game is 0.65. What is the probability to the nearest hundredth, that they will win at least
three out of the four games?
38.
a) Two forces have magnitudes of 72 pounds and 98 pounds respectively, and act upon a
body at an angle of 85° between them. Find, to the nearest whole pound, the resultant force.
b) In ∆ABC, side a = 12.5, side b = 16.4, and the measure of angle A = 48°. Find the nearest
degree, the measure of <B.
39.Solve the equation below for all values of 𝜃 on the interval 0o < 𝜃 < 360o. Round your answer to
the nearest whole degree.
6𝑡𝑎𝑛2 𝜃 − 7𝑡𝑎𝑛𝜃 − 20 = 0
NO OMITS ON THE PRACTICE FINALS!!
Name____________________________________________________________
Final Review Packet
Algebra 2 Final Exam
Practice Final 2
Part I
Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits.
1. If 𝑓(𝑥) = 5𝑥 + 1 and g(𝑥) = −2𝑥 − 3 , what is the value of 𝑓(𝑔(4)).
(1) −54
(2) −45
(3) 26
(4) −56
(5) OMIT
2. What are the values of 𝜃 in the interval 0° ≤ 𝜃 ≤ 360° that satisfy the equation 2𝑡𝑎𝑛𝜃 + 2 = 0?
(1) 45°, 225°
(2) 30°, 210°
(3) 135°, 315°
(4) 150°, 330°(5) OMIT
3. Express (𝑠𝑒𝑐𝑥)(𝑠𝑖𝑛𝑥) as a single trigonometric function.
(1) tan x
(2) cot x
(3) 1
(4) csc x
(5) OMIT
8
4. If 𝑐𝑜𝑠𝑥 = 15 , what is cos(2𝑥) ?
−97
(1) 225
16
(2) 15
16
64
(3) 225
(4) 225
(5) OMIT
5. Which graph represents the solution set of |3𝑥 − 6| > 9 ?
(5) OMIT
6. Ten students compared their grades on their last math test. Their scores were:
66,75,89,93,95,100,78,65,80,90
To the nearest tenth, what is the sample standard deviation for this set of data?
(1) 12.2
(2)12.1
(3) 11.5
(4) 10
(5) OMIT
7. If a function is defined by the equation f(x) = 7𝑥 , which equation represents the inverse of
that function?
(1) 𝑦 = (𝑥)7
(2) 𝑦 = log(7)
(3) 𝑦 = log 7 (𝑥)
(4) 𝑦 = log (𝑥) 7(5) OMIT
8. Factored completely the expression 8𝑥 3 − 32𝑥 is equivalent to
(1) 8x(x+2)(x-2) (2) 8x2(x-4)
(3) 8x(x2 – 4)
9. The expression 8√8𝑥 5 − 2𝑥√18𝑥 3 is equivalent to
(1) 22𝑥 2 √2𝑥
(2) 10𝑥 2 √2𝑥
(3) 22𝑥√2𝑥 3
10. Which graph represents a function?
(1)
(2)
(3)
(4) 8x(x+4)(x-4)
(4) 15𝑥 2 √2𝑥 (5)OMIT
(4)
(5) OMIT
NO OMITS ON THE PRACTICE FINALS!!
11. Which function is NOT one-to-one?
(1) {(3,0), (4, -5), (10, 1), (10, 5)}
(3) {(1, 8), (-3, 9), (2, -2), (12, 9)}
(2) {(4, 1), (-5, 10), (2, -7), (8, 9)}
(4) {(6,2), (1, -3), (5, -2), (7, -1)} (5) OMIT
12. In ∆XYZ, m<X = 48o, side y = 5 and side z = 9. What is the area of ∆XYZ to the nearest
square inch?
(1) 17
(2) 16
(3) 15
(4) 33
(5) OMIT
13. The expression 𝑙𝑜𝑔2 4 is equivalent to
(1) 8
(2) 1/2
(3) 4
(4) 2
(5) OMIT
14. The expression (5 + 3i)2 is equivalent to
(1) 34+30i
(2) 34 – 30i
(3)16 – 30i
(4) 16+30i
(5) OMIT
15.What change will be made to the graph of the equation 𝑦 = 𝑥 2 if the equation is changed to
𝑦 = (𝑥 − 1)2 + 2?
(1)shift left 1 down 2
(2)shift right 1,up 2
(3)shift up 1 left 2
(4)shift right 1,down 2
(5)OMIT
16. Find the sum of the roots S, and the product of the roots P of the quadratic equation
𝑥 2 − 3𝑥 − 1 = 0
(1) S = 3, P = 1 (2) S = -3, P = 1
(3) S = 3, P = −1
(4) S = −3, P = -1
(5)OMIT
17. In simplest form the expression
(1) 1
(2)
1
𝑎
1
𝑎
1
1− 2
𝑎
1−
equals
(3) -
1
𝑎
18. What is the solution of the equation log 2 (𝑥 + 1) = 4 ?
(1) 7
(2) 8
(3) 15
(4)
𝑎
𝑎+1
(4) 16
(5) OMIT
(5) OMIT
19. A circle has a radius of 15 inches. In inches, what is the length of the arc intercepted by a central
angle of 3 radians?
1
(1) 5
(2) 45
(3) 5
(4) 18
(5) OMIT
2𝑥
20. What is the domain of the function (𝑥) = 3𝑥+1 ?
(1) 𝑥 ≠ 1
(2) 𝑥 = 1/3
(3) 𝑥 ≠ 0
(4) 𝑥 ≠ −1/3 (5) OMIT
21. What is the equation of the axis of symmetry of the graph of 𝑦 = 𝑥 2 − 6𝑥 + 5
(1) 𝑥 = −3
(2) 𝑥 = 3
(3) 𝑥 = −6
(4) 𝑥 = 6
(5) OMIT
22. Which formula can be used to determine the total number of different 7 letter arrangements
that can be formed using the letters in the word ALGEBRA?
7!
2!
7!
(1) 2!
(2) 7!
(3) 7!
(4) 2!5!
(5) OMIT
NO OMITS ON THE PRACTICE FINALS!!
23. Factored completely the expression4𝑥 + 7𝑥 + 3 is equivalent to
(1)(4𝑥 − 3)(𝑥 − 1)
(2) 4𝑥(𝑥 − 3)(𝑥 − 1)
(3)(4𝑥 + 3)(𝑥 + 1)
(4) 4(𝑥 + 1)(𝑥 − 3)
(5) OMIT
2
24. The graph at the right represents which of the following equations?
(1) 𝑦 = 3𝑠𝑖𝑛𝑥
(2) 𝑦 = 3𝑠𝑖𝑛3𝑥
(3) 𝑦 = 𝑠𝑖𝑛3𝑥
(4) 𝑦 = 𝑐𝑜𝑠3𝑥 (5) OMIT
25. What is the fourth term in the expansion of (x – 1)7?
(1) 35x4
(2) 35𝑥 3
(3)−35𝑥 4
(4) −35𝑥 3
(5)OMIT
6𝑥 2 𝑦 −4
26) Simplify the expression 2𝑥 −3 𝑦 2 and only use positive exponents.
(1)
3𝑥 5
1
(2) 3𝑥𝑦 6
3
(4) 3x5y6
(5) OMIT
27. The solution set of 3|2x-3| = 15 is
(1) {1, 4}
(2) {-1, -4}
(3) {-1,4}
(4) {1, -4}
(5) OMIT
28. The solution set of √3𝑥 − 5 + 1 = 6
(1) {40/3}
(2) {10}
(4) {10/3}
(5) OMIT
𝑦6
(3) 𝑥𝑦 6
(3) { }
29. Given the equation sec(3𝑥 + 10)° = csc (2𝑥 + 15)° solve for the value of x
(1) 31
(2) 13
(3) 5
(4) 1
(5) OMIT
30. If side a=7 and angle A = 58°, find side b correct to two decimal places when angle B = 39°.
(1) 10.27
(2) 10.26
(3) 5.20
(4) 5.19
(5) OMIT
31.
PART II
Answer all 5 questions from this part. Show work in your notebook.
[Four credits each]
Find the value of the expression ∑5𝑥=1(8𝑥 − 6)
32.
Using the formula V = Pert find the value V for an investment of $8800 at an annual rate of
6.9% compounded continuously after 7 years.
33.
Express 7+√5 with a rational denominator, in simplest radical form.
34.
35.
18
Find the center and radius of the circle with the equation:
(x + 12)2 + (x + 5)2 = 121
Solve the fractional equation for x:
6
5
13
+ 2 = 𝑥+4
𝑥+4
NO OMITS ON THE PRACTICE FINALS!!
PART III
Answer 3 out of the 4 questions in this section. All work necessary to the solution of the
question must be written in your notebook. [Each question selected is worth 10 points]
36.
a) Solve 2x2 – 2x + 6 = 0 expressing the result in simplest a + bi form.
b) Solve for all values of x by factoring by grouping.
x3 – x2 – 49x + 49 = 0
37.
a) The table below summarizes the average revenue in thousands of dollars for the annual
ticket sales for the local basketball team.
Year
1
2
3
4
5
6
7
8
9
Cost 10.2 10.5 10.9 11.3 11.7 11.8 12.1 12.3 12.6
1) Find the linear equation of best fit for the given data. Round decimals to three
places.
2) Find the correlation coefficient “r” correct to 4 decimal places for part a.
3) Use the equation of best fit in part 1 to estimate the average revenue for the local
basketball team in year 15. Round to the nearest dollar.
b) St. Francis Prep’s hockey team has 8 games left in the season. The probability that the
team will win a game is 0.85. What is the probability to the nearest hundredth, that they will
win at least seven out of the eight games?
38.
a) Two forces have magnitudes of 74 pounds and 102 pounds respectively, and act upon a
body at an angle of 63° between them. Find, to the nearest whole pound, the resultant force.
b) In ∆ABC, side a = 20.1, side b = 22.4, and the measure of angle A = 36°. Find the nearest
degree, the measure of <B.
39.
Solve the equation below for all values of 𝜃 on the interval 0o < 𝜃 < 360o. Round your answer
to the nearest whole degree.
6𝑐𝑜𝑠 2 𝜃 + 5𝑐𝑜𝑠𝜃 − 4 = 0
NO OMITS ON THE PRACTICE FINALS!!
NAME:_________________________________________________________________
Final Review Packet
Algebra 2 Final Exam
Practice Final 3
June 2013
Algebra 2 Final Exam
Part I
Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits. Write your
answers on the scantron sheet provided. FOR EACH OF THE 5 QUESTIONS YOU OMIT ON PART I,
FILL IN CHOICE (5) ON THE SCANTRON SHEET.
1. If 𝑓(𝑥) = 2𝑥 + 3 and (𝑥) = −3𝑥 + 2 , what is the value of 𝑓(𝑔(2)).
(1) 7
(2) −4
(3) −5
(4) −7
(5) OMIT
2. What are the values of 𝜃 in the interval 0° ≤ 𝜃 ≤ 360° that satisfy the equation 2𝑠𝑖𝑛𝜃 + 1 = 0?
(1) 210°, 330°
(2) 60°, 300° (3) 30°, 300° (4) 30°, 150°
(5) OMIT
3. Express (𝑐𝑜𝑡𝑥)(𝑠𝑖𝑛𝑥) as a single trigonometric function.
(1) csc x
(2) cos x
(3) sin x
(4) sec x
(5) OMIT
24
(5) OMIT
4
4. If 𝑠𝑖𝑛𝑥 = 5 , what is sin(2𝑥) ?
8
12
(1) 5
(2) 25
7
(3) 25
(4) 25
5. Which graph represents the solution set of |2𝑥 − 1| ≥ 7 ?
(1)
(2)
(3)
(4)
6.Ten students compared their grades on their last math test. Their scores were:
76, 84, 91, 75, 83, 82, 94, 90, 84, 89
To the nearest tenth, what is the sample standard deviation for this set of data?
(1)
84.8
(2)6.3 (3)
5.9
(4)
84.0 (5)
OMIT
7. If a function is defined by the equation f(x) = 5𝑥 , which equation represents the inverse of that
function?
(1) 𝑦 = (𝑥)5 (2) 𝑦 = log(𝑥)
(3) 𝑦 = log 5 (𝑥)
(4) 𝑦 = log (𝑥) 5
(5) OMIT
8. Factored completely the expression 6𝑥 3 − 24𝑥 is equivalent to
(1) (6𝑥 2 − 12)(𝑥 + 2)
(2) 6𝑥(𝑥 2 − 4)
(3) 6𝑥(𝑥 + 2)(𝑥 − 2)
(4) (𝑥 − 6)(𝑥 + 2)(𝑥 − 2)
9. The expression 3𝑥√12𝑥 − 5√3𝑥 3 is equivalent to
(1) 2𝑥√9𝑥 2
(2) 𝑥√3𝑥
(3) −𝑥√3𝑥 (4) (3𝑥 − 5)√36𝑥 2
(5) OMIT
(5)OMIT
NO OMITS ON THE PRACTICE FINALS!!
10. Which function is NOT one-to-one?
(1) {(2,3), (-4, 5), (7, -6), (9, 11)} (2) {(6, 0), (-3, 9), (3, 5), (8, -6)}
(3) {(-10, 2), (6, 1), (9, -5), (8, 12)} (4) {(0,7), (2, -1), (8, 3), (11, -1)} (5) OMIT
11. In ∆XYZ, m<X = 52o , side y = 4 and side z = 11. What is the area of ∆XYZ to the nearest square
inch?
(1) 44
(2) 17
(3) 35
(4) 18
(5) OMIT
12. Which graph does not represent a function?
(1)
(2)
(3)
(4)
(5) OMIT
13. The expression 𝑙𝑜𝑔3 81 is equivalent to
(1) 1/4
(2) 5
(3) 27
(4) 4
14. The expression (2 + 4i)2 is equivalent to
(1) −12 + 0𝑖 (2) −12 + 16𝑖
(3) 20 + 0𝑖
(4) 20 + 16i
(5) OMIT
(5) OMIT
15.What change will be made to the graph of the equation 𝑦 = 𝑥 2 if the equation is changed to 𝑦 =
(𝑥 + 3)2 − 1?
(1)
shift left 3, down 1 (3)
shift up 3, left 1
(2)
shift right 3, up 1
(4)
shift right 3, down 1 (5)OMIT
16. Find the sum of the roots S, and the product of the roots P of the quadratic equation 𝑥 2 − 4𝑥 −
7=0
(1) S = 7, P = 4
(2) S = 4, P = 7
(3) S = 4, P = −7
(4) S = −4, P = 7
(5)OMIT
17. In simplest form the expression
2𝑥−8
(1) 𝑥 2 −4
2𝑥 2 −8𝑥
(2) 2𝑥 3 −4𝑥
2
𝑥
8
− 2
𝑥
1−
4
𝑥
equals
2
(3) 𝑥
18. What is the solution of the equation log 5 4𝑥 = 2 ?
5
25
(1) 4
(2) 8
(3) 4
(4) −2
4
(4) 25
(5) OMIT
(5) OMIT
19. A circle has a radius of 12 inches. In inches, what is the length of the arc intercepted by a central
angle of 4 radians?
1
(1) 3
(2) 24
(3) 3
(4) 48
(5) OMIT
NO OMITS ON THE PRACTICE FINALS!!
𝑥−3
20. What is the domain of the function 𝑓(𝑥) = 2𝑥+8 ?
(1) 𝑥 ≠ 3
(2) 𝑥 = 3
(3) 𝑥 ≠ −4
(4) 𝑥 ≠ 4
(5) OMIT
21. What is the equation of the axis of symmetry of the graph of 𝑦 = 3𝑥 2 + 6𝑥 + 2
2
2
(1) 𝑥 = 3
(2) 𝑥 = − 3 (3) 𝑥 = −1
(4) 𝑥 = 1
(5) OMIT
22. Which formula can be used to determine the total number of different 12 letter arrangements
that can be formed using the letters in the word CIRCUMFERENCE?
13!
13!
13!
(1) 7!
(2) 3!+2!+2!
(3) 13!
(4) 3!2!2!
(5) OMIT
23. Factored completely the expression 2𝑥 2 + 5𝑥 − 3 is equivalent to
(1)(2𝑥 + 3)(𝑥 − 1) (2)(2𝑥 − 1)(𝑥 + 3) (3)𝑥(𝑥 − 1)(𝑥 + 3)
(4)(2𝑥 + 1)(𝑥 − 3) (5) OMIT
24. The graph at the right represents which of the following equations?
(1) 𝑦 = 2𝑠𝑖𝑛𝑥
(3) 𝑦 = 2𝑠𝑖𝑛2𝑥
(5) OMIT
(2) 𝑦 = 𝑠𝑖𝑛2𝑥
(4) 𝑦 = 2𝑐𝑜𝑠2𝑥
25. What is the third term in the expansion of (x – 6)5?
(1) 360x3
(2) −360𝑥 3
(3)−30𝑥 4
(4) 30𝑥 4
(5)OMIT
12𝑥 2 𝑦 −5
26) Simplify the expression 15𝑥 4 𝑦 −6 and only use positive exponents.
4𝑥 6
(1) 5𝑦 11
4𝑦
(2) 5𝑥 2
(3)
4𝑦 11
5𝑥 2
27. The solution set of 2|4x +8| = 56 is
(1) {−9, 5}
(2) {-5, 9}
(3) {5}
28. The solution set of √2𝑥 + 3 − 5 = 2
(1) {2}
(2) {23}
(3) {3}
(4)
4𝑥 2
5𝑦
(5) OMIT
(4) {9} (5) OMIT
(4) {-26}
(5) OMIT
29. Given the equation tan(2𝑥 − 8)° = cot (4𝑥 − 16)° solve for the value of x
(1) 30
(2) 4
(3) 34
(4) 19
(5) OMIT
30. If side a=16 and angle A = 42°, find side b correct to two decimal places when angle B = 35°.
(1) 13.7
(2) 7.48
(3) 34.25
(4) 36.15
(5) OMIT
JUNE 2013 ALGEBRA 2 PART II
Answer all 5 questions from this part. Show work in your notebook.
[Four credits each]
31. Find the value of expression: ∑1𝑥=−1(3𝑥 − 7)
NO OMITS ON THE PRACTICE FINALS!!
32. Using the formula 𝑉 = 𝑃𝑒 find the value of V for an investment of $5800 at an annual rate of
2.6% compounded continuously after 7 years.
𝑟𝑡
15
33. Express 4−√3 with a rational denominator, in simplest radical form.
34. Find the center and the radius of the circle with the equation:
(𝑥 − 3)2 + (𝑦 + 7)2 = 169
8
3
5
35. Solve the fractional equation for x: 𝑥−2 + 4 = 𝑥−2
JUNE 2012 ALGEBRA 2
PART III
Answer 3 out of the 4 questions in this section. All work necessary to the solution of the question
must be written in your notebook. [Each question selected is worth 10 points]
36. a) Solve 3x2 + 4x + 8 = 0 expressing the result in simplest a + bi form.[5 points]
b) Solve for all values of x by factoring by grouping. [5 points]
𝑥 3 + 5𝑥 2 − 16𝑥 − 80 = 0
37. Answer both parts A and B
a) The table below summarizes the average cost in thousands of dollars for annual tuition and fees
at a public college. [5 points]
Year
Cost
1
12
2
12.6
3
13.1
4
13.4
5
13.9
6
14.2
7
14.6
8
15.2
9
15.5
10
16
1) Find the linear equation of best fit for the given data. Round decimals to three places.
2) Find the correlation coefficient “r” correct to 4 decimal places for part a.
3) Use the equation of best fit in part a to estimate the cost of tuition and fees at the college in year
12. Round to the nearest dollar.
b) St. Francis Prep’s soccer team has five games left in the season. The probability that the team
will win a game is 0.75. What is the probability, to the nearest hundredth, that they will win at least
four of the five games? [5 points]
38. a) Two forces have magnitudes of 46 pounds and 116 pounds respectively, and act upon a body
at an angle of 73° between them. Find, to the nearest whole pound, the resultant force. [5 points]
b) In ∆𝑅𝑆𝑇, side 𝑟 = 18.7, side 𝑠 = 14.3, and the measure of angle 𝑅 = 51° .
Find to the nearest degree, the measure of angle S. [5 points]
39.
Solve the equation below for all values of 𝜃 on the interval 0° ≤ 𝜃 ≤ 360° Round your
answer to the nearest whole degree. [10 points]
𝑡𝑎𝑛2 𝜃 − 𝑡𝑎𝑛𝜃 − 12 = 0
NO OMITS ON THE PRACTICE FINALS!!
NAME:_________________________________________________________________
Final Review Packet
Algebra 2 Final Exam
Practice Final 4
June 2014
Algebra 2 Final Exam
Part I
Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits. Write your
answers on the scantron sheet provided. FOR EACH OF THE 5 QUESTIONS YOU OMIT ON PART I,
FILL IN CHOICE (5) ON THE SCANTRON SHEET.
1. Factor the expression 5𝑥 3 − 20𝑥 2 + 15𝑥 completely:
(1) (6𝑥 2 − 15𝑥)(𝑥 + 2)
(2) 5𝑥(𝑥 2 + 𝑥 − 3)
(3) 5𝑥(𝑥 + 1)(𝑥 − 3)
(4) 5𝑥(𝑥 − 3)(𝑥 − 1)
(5) OMIT
2. If a function is defined by the equation y = 𝑙𝑜𝑔3 𝑥, which equation represents the inverse of that
function?
(1) 𝑦 = (𝑥)3
(2) 𝑦 = log(𝑥 3 )
(3) 𝑦 = 3𝑥
(4) 𝑦 = 𝑙𝑜𝑔𝑥 3
(5) OMIT
3. The expression (3- 5i)2 is equivalent to
(1) 9 + 25𝑖 2 (2) −16 + 15𝑖
(3) −16 − 30𝑖
1
4. The expression 𝑥1
𝑥
(1) 1
+1
−1
(4) 34 + 30i
(5) OMIT
is equivalent to
(2) 1 − 𝑥 2
(3)
1+𝑥
(4)
1−𝑥
𝑥
1−𝑥 2
(5) OMIT
5. Which graph represents the solution set of |2𝑥 + 3| < 9
(1)
(3)
(2)
(4)
(5) OMIT
6.Ten students measured their heights in inches. Their results were:
58,58,61,62,62,65,66,68,70,72
To the nearest tenth, what is the sample standard deviation for this set of data?
(1)
64.2
(2) 4.6
(3) 4.8 (4) 61
(5) OMIT
𝑥−2
7. What is the domain of the function 𝑓(𝑥) = 2𝑥+10?
(1) 𝑥 ≠ −2 (2) 𝑥 ≠ 2 (3) 𝑥 ≠ −5
(4) 𝑥 ≠ 5
(5) OMIT
8. . If 𝑓(𝑥) = 4𝑥 − 5 and 𝑔(𝑥) = −2𝑥 + 7, what is the value of 𝑔(𝑓(5))?
(1) -17
(2) -23
(3) 12
(4) 37
(5) OMIT
9. The expression 4𝑥√20𝑥 − 5√5𝑥 3 is equivalent to
(1) −𝑥√25𝑥 3
(2) 3𝑥√5𝑥
(3) −𝑥√5𝑥 (4) (4𝑥 − 5)√15𝑥 2
(5)OMIT
NO OMITS ON THE PRACTICE FINALS!!
10. Which relation IS a one-to-one function?
(1) {(2,3), (-4, 5), (2, -6), (9, 11)} (2) {(6, 0), (-3, 9), (3, 9), (8, -6)}
(3) {(-10, 2), (6, 1), (9, -5), (8, 12)} (4) {(0,7), (2, -1), (8, 3), (11, -1)} (5) OMIT
11. In ∆ABC, 𝑚∠𝐴 = 71° , side b = 23 and side c = 14. What is the area of ∆ABC to the nearest tenth
of a square inch?
(1) 154.5
(2) 152.2
(3) 52.4
(4) 304.5
(5) OMIT
12. Which graph does not represent a function?
(1)
(2)
(3)
(4)
(5) OMIT
13. The expression 𝑙𝑜𝑔6 216 is equivalent to
(1) 1/3
(2) 36
(3) 3
(4) 4
(5) OMIT
14. Express (1 − cos 𝑥)(1 + cos 𝑥) as a single trigonometric function.
(1) sin2 𝑥
(2) − cos 2 𝑥
(3) sec 2 𝑥
(4) tan2 𝑥
(5) OMIT
15.What change will be made to the graph of the equation 𝑦 = 𝑥 2 if the equation is changed to 𝑦 =
(𝑥 − 2)2 + 6?
(1)
shift left 2, down 6 (3)
shift up 2, left 6
(2)
shift right 4, up 6
(4)
shift right 2, up 6
(5)OMIT
16. What are the sum and product of the roots of the equation: 𝑥 2 − 4𝑥 + 8 = 0?
(1) sum = -8; product = -4
(3) sum = 4; product = 8
(2) sum = -4; product = -8
(4) sum = 8; product = 4
(5)OMIT
9
17. If cos 𝑥 = 41, what is sin(2𝑥)?
1519
(1) − 1681
1519
(2) 1681
18
(3) 41
720
(4) 1681
(5) OMIT
18. What is the solution of the equation log 5 (𝑥 + 4) = 1?
(1) 1 (2) 9 (3) -3
(4) 5
(5) OMIT
19. A circle has a radius of 10 feet. In feet, what is the length of the arc intercepted by a central
angle of 2 radians?
(1) 5 (2) 8 (3) 12
(4) 20
(5) OMIT
20. What are the values of 𝜃 in the interval 0° ≤ 𝜃 < 360° that satisfy the equation 2cos 𝜃 + √2 =
0?
(1) 45o, 315o (2) 135o, 315o
(3) 135o, 225o(4) 225o, 315o(5) OMIT
NO OMITS ON THE PRACTICE FINALS!!
21. What is the equation of the axis of symmetry of the graph of: 𝑦 = 4𝑥 2 − 8𝑥 + 5
5
5
(1) 𝑥 = −1
(2) 𝑥 = 1
(3) 𝑥 = − 8 (4) 𝑥 = 8
(5) OMIT
22. Which formula can be used to determine the total number of different 10 letter arrangements
that can be formed using the letters in the word SMARTBOARD?
10!
10!
10!
(1) 10!
(2) 4!
(3) 2!2!
(4) 2!+2!
(5) OMIT
23. The solution set of |3𝑥 − 4| + 7 = 15 is
−4
(1) {4}
(2) {-4, 4}
(3) { 3 , 4}
19
(4) { 3 }
(5) OMIT
24. The graph at the right represents which of the following equations?
(1) 𝑦 = 2𝑠𝑖𝑛2𝑥
(2) 𝑦 = 2𝑐𝑜𝑠2𝑥
(3) 𝑦 = 2𝑠𝑖𝑛𝑥
(4) 𝑦 = 𝑠𝑖𝑛2𝑥
(5) OMIT
25. What is the fourth term in the expansion of (𝑥 + 4)6 ?
(1) 24𝑥 4
(2) 24𝑥 3
(3) 64𝑥 3
(4) 1280𝑥 3
26) Simplify the expression
4𝑥 8
(1) 7𝑦 5
4𝑦
(2) 7𝑥 2
20𝑥 5 𝑦 −3
35𝑥 3 𝑦 2
4𝑦 2
(5) OMIT
and only use positive exponents.
(3) 7𝑥 5
4𝑥 2
(4) 7𝑦 5 (5) OMIT
27. Factored completely the expression 3𝑥 2 − 10𝑥 − 8 is equivalent to
(1)(3𝑥 + 2)(𝑥 − 4) (2)(3𝑥 − 2)(𝑥 + 4) (3)(3𝑥 + 4)(𝑥 − 2) (4)(3𝑥 − 4)(𝑥 + 2)
28. The solution set of √3𝑥 − 5 + 6 = 8 is:
(1) {2}
(2) {23}
(3) {3}
(4) {-26}
(5) OMIT
(5) OMIT
29. Given the equation cos(3𝑥 − 4)° = sin (5𝑥 + 14)° solve for the value of x
(1) 80
(2) 10
(3) 30
(4) 60
(5) OMIT
30. If side a=23 and angle A = 61°, find side b correct to two decimal places when angle B = 40°.
(1) 16.90
(2) 31.30
(3) 36.34
(4) 37.08
(5) OMIT
JUNE 2014 ALGEBRA 2 PART II
Answer all 5 questions from this part. Show work in your notebook. [Four credits each]
31. Find the center and the radius of the circle with the equation:
(𝑥 + 15)2 + (𝑦 + 1)2 = 196
32. Solve the fractional equation for x:
10
4
2
+ =
𝑥−3 3 𝑥−3
26
33. Express 7+√5 with a rational denominator, in simplest form.
NO OMITS ON THE PRACTICE FINALS!!
34. Find the value of the expression: ∑𝑥=7
𝑥=4(5𝑥 − 12)
35. Using the formula 𝑉 = 𝑃𝑒 𝑟𝑡 find the value of V for an investment of $5200 at an annual rate of
4.1% compounded continuously after 12 years.
Part III
Answer 3 out of the 4 questions in this section. All work necessary to the solution of the question
must be written in your notebook. [Each question selected is worth 10 points]
36. Answer BOTH parts a and b:
a) Solve 𝑥 2 − 6𝑥 + 34 = 0 expressing the result in simplest a + bi form.
[5 points]
b) Solve for all values of x by factoring by grouping. [5 points]
2𝑥 3 − 10𝑥 2 − 18𝑥 + 90 = 0
37. Answer BOTH parts a and b:
a) The table below represents the average cost in thousands of dollars for automobiles in the USA.
[5 points]
Year
1
2
3
4
5
6
7
8
9
10
Cost
18
19.6
23.1
23.4
23.9
24.2
24.6
25.2
25.5
26
1) Find the linear equation of best fit for the given data. Round decimals to three places.
2) Find the correlation coefficient “r” correct to 4 decimal places for part a.
3) Use the equation of best fit in part a to estimate the cost of an automobile in year 12. Round to
the nearest dollar.
b) A New York baseball team has six games left in the season. The probability that the team will win
a game is 0.63. What is the probability, to the nearest hundredth, that they will win at least five of
the six games? [5 points]
38.
Answer BOTH parts a and b.
a.
Two forces have magnitudes of 42 pounds and 65 pounds respectively, and act upon a body
at an angle of 40° between them. Find, to the nearest pound, the resultant force of these two forces.
b.
In ∆PQR, side p = 16.4, side q = 12.7, and the measure of angle P = 68°. Find, to the nearest
degree, the measure of angle Q.
39.
Solve the equation below for all values of 𝜃 on the interval 0° ≤ 𝜃 ≤ 360°.
Round your answer to the nearest whole degree. [10 points]
𝑡𝑎𝑛2 𝜃 − 4𝑡𝑎𝑛𝜃 − 12 = 0
NO OMITS ON THE PRACTICE FINALS!!
Answers to Practice Final 1
Part I
Part II
1. 3
2. 2
3. 1
4. 3
5. 3
6. 4
7. 1
8. 1
9. 1
10. 2
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3
1
3
4
2
1
4
3
1
1
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
1
1
4
1
3
3
2
4
1
2
31. 105
32. $10,805.78
33.
54+9√2
17
34. 𝐶 = (8, −1) 𝑟 = 9
35. 𝑥 = 3
Part III
36. a) 𝑥 =
−3
4
±
𝑖√31
4
or
3±𝑖√31
b) 𝑥 = −6, 𝑥 = 5, 𝑥 = −5
4
37 a. 1) 𝑦 = 0.347𝑥 + 17.533
2) 𝑟 = 0.9980
3) 23
*Make sure your calculator has diagnostics on
*2nd 0… Scroll to “Diagnostics on”
(You will be reminded of this on test day)
b. 0.56
38. a) 𝑐 = 127 𝑝𝑜𝑢𝑛𝑑𝑠 b) 𝑎𝑛𝑔𝑙𝑒 𝐵 = 77°
39. 𝜃 = 68°, 127°, 248°, 307°
NO OMITS ON THE PRACTICE FINALS!!
Answers to Practice Final 2
Part I
1. 1
2. 3
3. 1
4. 1
5. 1
6. 1
7. 3
8. 1
9. 2
10. 4
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3
1
4
4
2
3
4
3
2
4
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
2
1
3
3
3
1
3
2
2
4
Part II
31. 90
32. $14,264.18
63−9√5
33.
22
34. 𝐶 = (−12, −5) 𝑟 = 11
35. 𝑥 =
−6
5
Part III
1
36. a) 𝑥 = 2 ±
√11
𝑖
2
…or…
𝑥=
1±𝑖√11
2
b) 𝑥 = 1, 𝑥 = 7, 𝑥 = −7
37. a) 1) 𝑦 = .298𝑥 + 9.997
b) 0.66
38. a) 𝑐 = 151 𝑝𝑜𝑢𝑛𝑑𝑠
b) 𝑎𝑛𝑔𝑙𝑒 𝐵 = 41
39. 𝜃 = 60°, 300°
2) 𝑟 = .9918
3) 15
Answer Key
1)3
2) 1
3) 2
4) 4
5) 3
6) 2
7) 3
8) 3
9) 2
10) 4
Practice Final 3
11) 2
12) 4
13) 4
14) 2
15) 1
16) 3
17) 1
18) 3
19) 4
20) 3
21) 3
22) 4
23) 2
24) 1
25) 1
26) 2
27) 1
28) 2
29) 4
30) 1
31. -21
32. $6957.76
60+15√3
33. 13
34. center (3, -7) r = 13
35. x = -2
−2±2𝑖√5
36. A) x =
B) x = ±4, −5
3
37. A) 1) y = .428x+11.693
B) .63
2) r = .9981
3) y = 17
38. A) 137 lbs
B) 36o
39. {76, 108, 256, 288}
19
(June 2013)
Answers to Practice Final 4 (June 2014 Final)
1) 4
2) 3
3) 3
4) 3
5) 3
6) 3
7) 3
8) 2
9) 2
10) 3
11.) 2
12) 3
13) 3
14) 1
15) 4
16) 3
17) 4
18) 1
19) 4
20) 3
21) 2
22) 3
23) 3
24)4
25) 4
26) 4
27) 1
28) 3
29) 2
30) 1
31. center (-15, -1) r = 14
32. x = -3
91−13√5
33. 22
34. 62
35. $8505.04
36. A) 3 + 5i B) x = -3, 3, 5
37. A) 1)y = .774x + 19.093
2) r = .9045
3) 28
B) .28
38. A) 101 lbs
B) 57o
39. 81, 117, 261, 297
20