Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
Practice Final #2
Part I: Multiple Choice. On the final all of these questions will be multiple choice questions. You will have to
answer 25 out of 30 questions (omit 5).
1. The expression (2 + 𝑖)2 is equivalent to
(1) 3 − 0𝑖
(2) 5 + 4𝑖
(3) 3 + 4𝑖
(4) 5 + 0𝑖
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
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°
4. Express csc 𝑥 ∙ tan 𝑥 as a single trigonometric function.
(1) tan 𝑥
(2) sec 𝑥
(3) cos 𝑥
(4) csc 𝑥
5. Which graph represents the solution set of |𝑥 − 3| ≤ 5
(1)
(3)
-2
8
(2)
-2
8
-2
8
(4)
-2
8
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)}
(2) {(2,1), (4,2), (6,2), (8,4)}
(4) {(5,1), (4,2), (3,3), (2,4)}
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
8. Which graph does NOT represent a function?
(1)
(2)
9. *The expression log 4 64 is equivalent to
(1) 2
(2) 3
(3)
(3) 4
1
(4)
1
(4) 3
Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
Practice Final #2
3
10. If cos 𝑥 = 5, what is cos 2𝑥?
(1)
24
(2)
25
4
(3)
5
7
(4)
25
−7
25
11. What change will be made to the graph of the equation 𝑦 = 𝑥 2 if the equation is changed to 𝑦 =
(𝑥 + 2)2 − 5
(1) shift right 2, up 5
(3) shift up 2, left 5
(2) shift left 2, down 5
(4) shift down 2, left 5
−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
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
14. The expression
(1)
3𝑞 5
𝑝7
6p−2 q4
2p5 q−1
is equivalent to
(2)
𝑞5
3𝑝−7
(3)3𝑝7 𝑞 5
4)
3𝑞 3
𝑝7
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 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?
(1) 𝑓(𝑥) = 𝑙𝑜𝑔𝑥 4
(2) 𝑓(𝑥) = 𝑙𝑜𝑔4 𝑥
(3) 𝑓(𝑥) = 𝑥 4
(4) 𝑓(𝑥) = 𝑙𝑜𝑔𝑥
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)
2
Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
Practice Final #2
18. The expression 2√3𝑎3 − 4𝑎√27𝑎 is equivalent to
(1) −8𝑎√3𝑎
(2) −10𝑎√3𝑎
(3) −8√3
(4) 10𝑎√3𝑎
19. *What is the second term in the expansion of (4 – x)4?
(1) 96x2
(2) 256𝑥
(3)−256𝑥
(4) −16𝑥 3
𝑥2
−1
16
20. In simplest form the expression 𝑥 1 equals
−
8 2
(1) −2
(2)
𝑥+4
𝑥−4
(3)
𝑥−4
2
21. *What is the solution of the equation 𝑙𝑜𝑔5 (3𝑥) = 2 ?
3
(1) 75
(2) 50
(3)
25
(4)
𝑥+4
(4)
2
25
3
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
23. What is the domain of the function 𝑓(𝑥) = √4𝑥 − 12 ?
(1) x ≥ 3
(2) x > 3
(3) x ≤ 3
(4) x < 3
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
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)
(3)
(4)
6!
2!+2!+2!+3!
2!2!2!3!
26. Express 𝑥 3 − 5𝑥 2 − 24𝑥 in factored form.
(1) 𝑥(𝑥 + 8)(𝑥 − 3)
(2) 𝑥(𝑥 − 6)(𝑥 + 4)
27. The solution set of |3x - 5| = 7 is
−2
(1) { 3 }
(2) {4}
(3) (𝑥 2 + 12)(𝑥 − 2)
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}
(4) { 25 }
29. Given the equation sin(2𝑥 − 30)° = cos(3𝑥 + 10)° solve for the value of x.
(1) 40
(2) −22
(3) 22
(4) − 40
30. *If side a = 13 and < 𝐴 = 56°, find side b correct to two decimal places when <𝐵 = 29°
(1) 20.33
(b) 7.21
(3) 7.60
(4) 10.78
3
Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
Practice Final #2
Part II: Answer all 5 questions from this section. Show all work, including formulas. [4 pts each]
31. Find the value of the expression ∑3𝑘=0(2𝑘 − 1).
32. Using the formula V = Pert find the value of V for an investment of $2000 at an annual rate of 4%,
compounded continuously after 7 years.
33. Express
4
1+√3
with a rational denominator, in simplest radical form.
34. Find the center and radius of the circle with the equation: (x – 3)2 + (y + 5)2 = 49.
35. Solve the fractional equation for x:
7
=
𝑥−3
5
𝑥−3
+
2
3
Part III: Answer 3 out of the 4 questions in this section. All work necessary to the solution must be
written in the space provided and on the graph when necessary. [10 points each]
36. Answer both parts a and b.
a) Solve 𝑥 2 + 4𝑥 + 5 = 0 expressing the result in simplest 𝑎 + 𝑏𝑖 form.
b) Solve 𝑥 3 − 5𝑥 2 − 4𝑥 + 20 = 0 by factoring by grouping.
37. *The number of items sold based on the weekly selling price in dollars is summarized in the table
below.
Quantity
Price
30
28
47
22
38
29
28
32
49
20
23
35
47
21
46
20
39
24
42
29
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 price to the nearest dollar if
the quantity sold was 55 items.
38.* Answer both parts a and b. a) Two forces have magnitudes of 70 pounds and 120 pounds respectively,
and act upon a body at an angle of 83° between them. Find, to the nearest pound, the resultant force of these
two forces. b) In ∆XYZ, side x = 8.4, side y = 11.3, and the measure of angle X = 47°.Find, to the
nearest degree, the measure of angle Y.
39. Solve the equation below for all values of 𝜃 on the interval 0° ≤ 𝜃 ≤ 360°
2tan2  - 3tan  – 5 = 0
4