Name: ____________________
Date: _____________
Algebra 2 Quarter III Test (2022)
Part I. Multiple Choice. Circle the right answer.
1.
a. 7
b. –1
c. 2
d. –2
2.
a.
c.
b.
d.
3. Solve
a. 365.878
2
5
. Round to the nearest thousandth.
b. 1,095.633
c. 365.211
d. 1,096.966
4.
a.
b.
c.
d.
5.
a.
c.
b.
d.
6. Solve
a. 4
.
b.
 13
8
c.
1
2
d.
5
4
11.
a.
b.
c.
d.
a.
c.
b.
d.
a.
b.
c.
d.
12.
13.
14.
a.
c.
b.
d.
15. Is i (iota) a root of 1+x2=0?
a) True
b) False
16. What is the complex conjugate of 20−9i?
a)−20+9i
b) 20+9i
c)−20−9i
d)20−9i
17. What happens to the result of the expression (a+bi)+(c+di) when it changes to
(a+bi)−(−c−di)?
a) Nothing, they are the same.
b) The value of the real part decreases
c) Both the values of the imaginary and real parts decrease.
d) The value of the imaginary part decreases
18. Which of the following is a true conclusion about the result of evaluating the
expression (−3+4i)+ (5−2i)?
a) The real part will be positive and the imaginary part will be negative.
b) The real part will be negative and the imaginary part will be positive.
c) Both the real and imaginary parts will be positive.
d) Both the real and imaginary parts will be negative.
19.
20.
Part II. Solve. Show all your work
Simplify, rationalize all denominators.
1.
2.
Expand each logarithm.
3. ln
a 2 b3
c4
4. log
x 7
y2
Condense. Write as a single logarithm.
5. log 7 x + log7 y – log7 z
6.
1
(ln x  ln y )  4 ln z
3
Use change of base formula to evaluate.
7. log2 7
8. log4 1.116
Solve each equation.
9. log (5 – 2x) = 0
10. e2x = 10
11. ln (t – 1)2 = 3
12. log2 (x – 4) = 3
Write the following complex numbers in standard form
(2  2i) 2
14.
15. (3  2  32 )( 2  3  8 )
3  4i
16. (-8 + 3i) – (2 + 7i)
17.
5  3i
4  2i
Describe the transformations on the given function.
Find the discriminant. State the number and nature of the solutions.
19) x2 – 8x = -14
Solve using the quadratic formula.
20) -3x2 + 6x +12 = 0
Bonus Questions:
If i   1 and z  1  i 3 , simplify the expression

1 2
z  2z
i
