Name__________________________Period______
Another Module 3 Test Review
1.) Match the following quadratics with their roots:
_____ x2 + 10x + 11
a. x = -11, 1
_____ x2 + 10x – 11
b. x = 3, 7
_____ x2 – 10x + 11
c. x = −5 ± √14
_____ x2 – 10x – 11
d. x = 5 ± √14
_____ (x - 5)2 = 4
e. x = 11, -1
Simplify.
2. 𝑖 23
3. 𝑖 20
4. 𝑖 30
5. 𝑖 17
6. 5 + √8 -4√2 -7√5 – 9 +3√5
7. √125 -7√2 + 3√5
8. (5i)2
9. (-4i)(3i)
10. (√−27 ) (√−2 )
11. (4 – 5i) (4 + 5i)
12. (7 + 3i) + (6 –5i)
14.
13. -5(3 + 2i) – 5(4 + i)
4+3𝑖
15.
3−𝑖
2+𝑖
5−2𝑖
16. Solve this quadratic equation ALL three ways. Make sure you get the same answers!
𝑥 2 − 8𝑥 = 9
FACTORING
COMPLETING THE SQUARE
QUADRATIC FORMULA
17. Use any method you’d like to solve. Remember, not all quadratics can be factored!
3𝑥 2 + 4𝑥 − 4 = 0
𝑥 2 + 4𝑥 − 8 = 0
𝑥 2 + 8𝑥 + 16 = 0
Decide which method is the fastest. Solve the equation using that method. Explain why that
particular method is the fastest.
18. 𝑥 2 + 13𝑥 + 12 = 0
Solutions: _______________
Method: _______________
Reason for Method: _______________
19. 𝑥 2 + 13𝑥 − 12 = 0
Solutions: _______________
Method: _______________
Reason for Method: _______________
20. (𝑥 + 13)2 − 12 = 0
Solutions: _______________
Method: _______________
Reason for Method: _______________
Find the discriminant. Describe the nature of the roots.
21. f(x)=𝑥 2 + 2𝑥 − 3
21.________________________
22. f(x)=𝑥 2 − 2𝑥 + 3
22.________________________
23. f(x)=𝑥 2 − 2𝑥 − 1
23.________________________
24. Factor the following:
a. x2 – 10x + 21
b. 6x2 + 13x - 5
c. x2 – 49
a. 12x2 +11 x – 5
3
25. Write 174 in radical form (you do not have to simplify it) _______________
9
26. Write √45 in exponential form ____________
27. Simplify
12 ± √20
2
_________________
3
28. Simplify 204 ___________________
29. Simplify (√−27)2 __________________
30. Simplify (2𝑥 4 )3 = ____________