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Final Review Packet
Algebra 2 Final Exam
Practice Final 4
JUNE 2011
PART I
Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits.
FOR EACH OF THE 5 QUESTIONS YOU OMIT ON PART I, FILL IN CHOICE (5)
ON THE SCANTRON SHEET.
1. The expression (2 + 𝑖)2 is equivalent to
(1) 3 − 0𝑖
(2) 5 + 4𝑖
(3) 3 + 4𝑖
(4) 5 + 0𝑖
(5)OMIT
2. If 𝑓(𝑥) = 5𝑥 − 2 and 𝑔(𝑥) = 2𝑥 + 7, what is the value of (g ⃘𝑓)(−2)
(1) −17
(2) −1
(3) 13
(4) −9
(5)OMIT
3. What are the values of 𝛳 in the interval 0° ≤ 𝜃 ≤ 360° that satisfy the equation 2𝑠𝑖𝑛𝜃 +
√2 = 0.
(1) 45°, 315°
(2) 45°, 135° (3) 225°, 315° (4) 45°, 135°, 225°, 315° (5)OMIT
4. Express sin 𝑥 ∙ cot 𝑥 as a single trigonometric function.
(1) tan 𝑥
(2) sec 𝑥
(3) cos 𝑥
5. Which graph represents the solution set of |𝑥 − 3| ≤ 5
(1)
(3)
-2
8
-2
(2)
(4)
-2
8
-2
6. Which function is NOT one-to-one?
(1) {(4,3), (3,2), (2,1), (1,0)}
(3) {(0,2), (1,3), (4,5),(2,4)}
(4) csc 𝑥
(5)OMIT
8
(5)OMIT
8
(2) {(2,1), (4,2), (6,2), (8,4)}
(4) {(5,1), (4,2), (3,3), (2,4)}
(5)OMIT
7. In △ 𝑅𝑆𝑇, 𝑚 < 𝑅 = 54°, s = 12 and t = 14. What is the area of △ 𝑅𝑆𝑇 to the nearest square
inch?
(1) 67
(2) 68
(3) 135
(4) 136 (5)OMIT
8. Which graph does NOT represent a function?
(1)
(2)
9. The expression log 4 64 is equivalent to
(1) 2
(2) 3
(3) 4
(3)
(4)
1
(4) 3
(5)OMIT
3
10. If sin 𝑥 = 5, what is cos 2𝑥?
(1)
24
(2)
25
4
(3)
5
7
8
25
11. The value of the expression ∑3𝑘=0(2𝑘 − 1) is
(1) 8
(2) 4
(3) 9
(4) 5
(5)OMIT
(4) -10
(5)OMIT
−1
12. For which equation does the sum of the roots equal 2 and the product of the roots equal 2?
(1) 2x2 – x + 4 = 0
(2) 2x2 + x – 4 = 0
(3) 2x2 – x – 4 = 0 (4) 2x2 + x + 4 = 0
(5)OMIT
13. The graph to the right represents which equation below?
(1) y = sin 2x
(2) y = 2 sin x
(3) y = ½ sin x
(4) y = sin½ x
(5)OMIT
6p−2 q4
14. The expression 2p5 q−1 is equivalent to
(1)
3𝑞 5
𝑝7
𝑞5
(2) 3𝑝−7
(3)3𝑝7 𝑞 5
(4)
3𝑞 3
𝑝7
(5)OMIT
15. Nine students who went to SUNY Albany were asked how many times they withdrew money
from the ATM in the Campus Center over the last month. Their responses are shown below.
3, 9, 2, 2, 6, 4, 1, 0, 7
Determine the population standard deviation for this data to the nearest tenth.
(1) 2.8
(2) 3.0
(3) 34
(4) 3.8
(5)OMIT
16. If a function is defined by the equation f(x) =4𝑥 , which graph represents the inverse of that
function?
17. Factored completely the expression 𝑥 4 − 16 is equivalent to
(1)(𝑥 2 − 4)(𝑥 2 + 4)
(2) (𝑥 − 2)(𝑥 + 4)(𝑥 2 − 4)
(3)(𝑥 − 2)(𝑥 + 2)(𝑥 − 2)(𝑥 + 2) (4) (𝑥 − 2)(𝑥 + 2)(𝑥 2 + 4)
(5)OMIT
18. The expression 2√3𝑎3 − 4𝑎√27𝑎 is equivalent to
(1) −8𝑎√3𝑎
(2) −10𝑎√3𝑎
(3) −8√3
(4) 10𝑎√3𝑎
(5)OMIT
19. What is the second term in the expansion of (4 – x)4?
(1) 96x2
(2) 256𝑥
(3)−256𝑥
(4) −16𝑥 3
(5)OMIT
20. In simplest form the expression
(1) −2
𝑥+4
(2) 𝑥−4
𝑥2
−1
16
𝑥 1
−
8 2
(3)
equals
𝑥−4
(4)
2
𝑥+4
2
(5)OMIT
21. What is the solution of the equation 𝑙𝑜𝑔5 (3𝑥) = 2 ?
3
(1) 75
(2) 50
(3) 25
(4)
25
3
(5)OMIT
22. A circle has a radius of 7 inches. In inches, what is the length of the arc intercepted by a
central angle of 2 radians?
(1) 14
(2) 3.5
(3) 21
(4) 21𝜋
(5)OMIT
23. What is the domain of the function 𝑓(𝑥) = √4𝑥 − 12 ?
(1) x ≥ 3
(2) x > 3
(3) x ≤ 3
(4) x < 3
(5)OMIT
24. What is the equation of the axis of symmetry of the graph of y = 3x2 + 12x – 2?
(1) x = -2
(2) x = 2
(3) y = -2
(4) y = 2
(5)OMIT
25. 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 CONSTITUTION ?
12!
12!
12!
(1) 12!
(2) 6!
(3) 2!+2!+2!+3!
(4) 2!2!2!3!
(5)OMIT
26. Express 𝑥 3 − 5𝑥 2 − 24𝑥 in factored form.
(1) 𝑥(𝑥 + 8)(𝑥 − 3)
(2) 𝑥(𝑥 − 6)(𝑥 + 4) (3) (𝑥 2 + 12)(𝑥 − 2)
27. The solution set of |3x - 5| = 7 is
−2
(1) { 3 }
(2) {4}
2
(3) {- 3, 4}
28. The solution set of √3𝑥 + 4 − 2 = 3 is
(1) { }
(2) { 7 }
(3) { -7 }
(4) 𝑥(𝑥 − 8)(𝑥 + 3)
(4) {-4}
(5)OMIT
(4) { 25 }
(5)OMIT
29. Given the equation sin(2𝑥 − 30)° = cos(3𝑥 + 10)° solve for the value of x.
(1) 40
(2) −22
(3) 22
(4) − 40
(5)OMIT
30. If side a = 13 and angle 𝐴 = 56°, find side b correct to two decimal places when
angle 𝐵 = 29°
(1) 20.33
(b) 7.21
(3) 7.60
(4) 10.78
(5)OMIT
PART II
Answer all 5 questions from this part. Show work in the space provided.
[Four credits each]
31. Find the value of the expression: ∑3𝑥=1(5𝑥 − 2)
32. Using the formula 𝑉 = 𝑃𝑒 𝑟𝑡 find the value of V for an investment of $5500 at an annual rate
of 4.8% compounded continuously after 6 years.
5
33. Express 3+√6 with a rational denominator, in simplest radical form.
34. Find the center and the radius of the circle with the equation:
(𝑥 − 12)2 + (𝑦 + 5)2 = 49
35. Solve the fractional equation for x:
6
9
12
+ =
𝑥+4 2 𝑥+4
Part III:
Answer 3 out of 4 questions in this section. All work necessary to the solution must be
written in the space provided and on the graph when necessary. Each question is worth 10
points.
36. Answer both parts a and b.
a. Solve 3𝑥 2 + 2𝑥 + 4 = 0 expressing the result in simplest a + bi form.
b. Solve 𝑥 3 − 3𝑥 2 − 25𝑥 + 75 = 0 by factoring by grouping.
37. A kicker punts a football eleven times at the same velocity but at different angles. The table
below shows the distance the football traveled, in yards, when kicked at each angle.
Angle of
Kick
30
33
36
39
42
45
48
51
54
57
60
(degrees)
Distance
57.74 60.83 63.21 65.07 66.19 66.56 66.20 65.11 63.32 30.85 57.73
(yards)
a) Find the linear equation of best fit for the given data. Round decimals to three places.
b) Find the correlation coefficient “r” correct to 4 decimal places for part a.
c) Find the quadratic equation of best fit for the given data. Round decimals to three places.
d) Find the correlation coefficient “r” correct to 4 decimal places for part c.
e) Use the values of “r” to determine which equation, linear from part a, or quadratic from
part c, is a better fit for the given data.
f) Use the equation of best fit found in part e to estimate the number of times a 20 year old
would post to their social networking site.
38. Answer both parts a, and b.
a. Two forces have magnitudes of 65 pounds and 115 pounds respectively, and act upon a
body at an angle of 75° between them. Find, to the nearest whole pound, the resultant
force.
b. In ΔABC, side a = 5.2, side b = 7.8, and the measure of angle A = 29°. Find, to the
nearest degree, the measure of angle B.
39. Solve the equation below for all values of 𝜃 on the interval 0° ≤ 𝜃 ≤ 360°.
2sin2 𝜃 + sin 𝜃 – 1 = 0