Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
Practice Final #1
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 (5 − 3𝑖)2 is equivalent to
(1) 25 + 9𝑖
(2) 16 − 30𝑖
(3) 34 − 30𝑖
(4) 34 + 0𝑖
2. If 𝑓(𝑥) = (𝑥 + 1)2 and 𝑔(𝑥) = 𝑥 − 6, what is the value of (g ⃘𝑓)(3)
(1) −2
(2) 4
(3) 10
(4) 19
3. What are the values of 𝛳 in the interval 0° ≤ 𝜃 ≤ 360° that satisfy the equation
2𝑠𝑖𝑛𝜃 − 1 = 0.
(1) 60°, 240°
(2) 30°, 150° (3) 60°, 120°, 240°, 300°
(4) 30°, 150°, 210°, 330°
5. Which graph represents the solution set of |2𝑥 − 1| < 7
(1)
(3)
-3
4
-3
(2)
4
(4)
-3
4
-3
4
6. Which function is NOT one-to-one?
(1) {(2,4), (3,6), (4,7), (5,10)}
(2) {(3,2), (4,3), (5,4), (6,5)}
(3) {(1,1), (2,2), (3,3),(4,4)}
(4) {(2,3), (4,5), (6,7), (7,7)}
8. Which graph does NOT represent a function?
(1)
(2)
(3)
(4)
11. 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, up 1
(2) shift right 3, up 1
(3) shift down 3, right 1
(4) shift up 3, right 1
12. For which equation does the sum of the roots equal -9 and the product of the roots equal 10?
(1) x2 – 9x + 10 = 0 (2) x2 + 9x – 10 = 0 (3) x2 + 9x + 10 = 0
(4) x2 – 9x – 10 = 0
14. The expression
(1)
3𝑠4
5𝑟 11
12𝑟 −3 𝑠 5
20𝑟 8 𝑠
is equivalent to
(2)
3 11 4
r s
5
(3)
3𝑟 5 𝑠6
5
(4)
3𝑟 5
5𝑠6
Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
17. Simplify: 𝑐𝑜𝑡𝜃𝑠𝑖𝑛𝜃
(1) 𝑠𝑖𝑛𝜃
(2) 𝑐𝑜𝑠𝜃
Practice Final #1
(3) 𝑡𝑎𝑛𝜃
(4) 𝑐𝑠𝑐𝜃
18. The expression 6ab 18b  4a 72b3  9ab 10b is equivalent to
(1) 3ab 10b
(2) 3ab 12b (3) 6ab 2b  9ab 10b
(4) 6ab  9ab 10b
2
1
a
20. For a ≠ 0, 2, -2, the fraction
is equivalent to
4
a
a
1
1
1
(1)
(2)
(3) 
a2
a2
a2
(4) 
1
a2
22. A circle has a radius of 3 inches. In inches, what is the length of the arc intercepted by a
central angle of 4 radians?
(1) 4𝜋
(2) 4
(3) 12
(4) 12𝜋
23. What is the domain of the function 𝑓(𝑥) = √2𝑥 − 8 ?
(1) x ≥ 4
(2) x > 4
(3) x ≤ 4
(4) x < 4
24. What is the axis of symmetry of the quadratic equation y = x2 – 8x + 4
(1) x = 8
(2) x = -8
(3) x = -4
(4) x = 4
26. Express 𝑥 3 + 7𝑥 2 − 18𝑥 in factored form.
(1) 𝑥(𝑥 + 2)(𝑥 − 9)
(2) 𝑥(𝑥 + 9)(𝑥 − 2)
27. The solution set of |3 + 4x| = 1 is
1
(1) {- 2 }
(2) {-2, -1}
(3) (𝑥 2 + 9)(𝑥 − 2) (4) 𝑥(𝑥 + 9)(𝑥 + 2)
1
(3) {- 2, -1}
28. The solution set of √2𝑥 − 1 + 8 = 5 is
(1) { }
(2) { 2 }
(3) { 5 }
(4) {-1}
(4) { 85 }
29. Given the equation sin(2𝑥 − 30)° = cos(3𝑥 + 10)° solve for the value of x.
(1) 40
(2) 22
(3) 44
(4) - 40
Part II: Answer all 5 questions from this section. Show all work, including formulas. [4 pts each]
31. Find the value of the expression ∑4𝑘=1(3𝑘 + 5)is
33. Express
3
2 − √5
with a rational denominator, in simplest radical form.
34. Find the center and radius of the circle with the equation: (x – 5)2 + (y + 2)2 = 16.
Name:_________________________________________________
Date:___________
Algebra II - Pd:_______
35. Solve the fractional equation for x:
Practice Final #1
3
=
𝑥−1
4
−
7
1
𝑥−1
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.
36. Answer both parts a and b.
a) Solve 𝑥 2 + 6𝑥 − 3 = 0 by completing the square, expressing the result in simplest radical form.
b) Solve 9𝑥 3 − 15𝑥 2 + 3𝑥 − 5 = 0 by factoring by grouping.
39. Solve the equation below for all values of 𝜃 on the interval 0° ≤ 𝜃 ≤ 360°
8tan2  = 22tan  – 15