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Unit 3 Test Study Guide

This document is a study guide for a Unit 3 Test, covering various mathematical topics including factoring, simplifying expressions, solving quadratic equations, and operations with complex numbers. It includes specific problems for students to solve, such as factoring expressions, using the quadratic formula, and completing the square. The guide is structured with numbered questions and spaces for students to write their names and dates.

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15 views4 pages

Unit 3 Test Study Guide

This document is a study guide for a Unit 3 Test, covering various mathematical topics including factoring, simplifying expressions, solving quadratic equations, and operations with complex numbers. It includes specific problems for students to solve, such as factoring expressions, using the quadratic formula, and completing the square. The guide is structured with numbered questions and spaces for students to write their names and dates.

Uploaded by

Hannah
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Unit 3 Test Study Guide Name: _________________________ Date: ___________ Block: ______

1. Completely FACTOR 𝟒𝟒𝟒𝟒𝟐𝟐 − 𝟒𝟒𝟒𝟒 − 𝟐𝟐𝟐𝟐 2. Simplify.

a) √−𝟓𝟓𝟓𝟓

b) −√−𝟐𝟐𝟐𝟐

c) 𝒊𝒊𝟐𝟐 + 𝒊𝒊𝟑𝟑 − 𝟐𝟐𝟐𝟐

3. The expression 𝟗𝟗𝟗𝟗𝟐𝟐 + 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟒𝟒 can be factored into the 4. If 𝒇𝒇(𝒙𝒙) = 𝟐𝟐𝒙𝒙𝟐𝟐 − 𝟏𝟏𝟏𝟏𝟏𝟏, find the value of 𝒇𝒇(𝟑𝟑𝟑𝟑)
form (𝒂𝒂𝒂𝒂 + 𝒃𝒃)𝟐𝟐 where 𝑎𝑎 and 𝑏𝑏 are integers. If 𝒂𝒂 = 𝟑𝟑, then
𝒃𝒃 = ?

5. What is a possible value of b that would make the 6. Solve for x. 𝒙𝒙𝟐𝟐 − 𝒙𝒙 − 𝟏𝟏𝟏𝟏 = 𝟎𝟎
quadratic factorable?
𝟐𝟐𝒙𝒙𝟐𝟐 − 𝒃𝒃𝒃𝒃 + 𝟓𝟓
7. Use the discriminant to determine what type (real or 8. Solve for 𝑥𝑥.
imaginary) and how many solutions there are for the 𝟗𝟗𝟗𝟗𝟐𝟐 + 𝟏𝟏𝟏𝟏𝟏𝟏 = 𝟎𝟎
following equations.

a) 𝟓𝟓𝒙𝒙𝟐𝟐 − 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟒𝟒 = 𝟎𝟎

b) −𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟒𝟒𝟒𝟒 − 𝟏𝟏𝟏𝟏 = 𝟎𝟎

9. A water powered rocket shoots off the ground with an 10. Complete the square to make a perfect square
initial speed of 96 feet per second. The height of the trinomial.
rocket, ℎ, in feet, as a function of time, 𝑡𝑡, in seconds, is
𝒙𝒙² − 𝟐𝟐𝟐𝟐𝟐𝟐 + ____
given by the function: 𝒉𝒉(𝒕𝒕) = −𝟖𝟖𝒕𝒕𝟐𝟐 + 𝟒𝟒𝟒𝟒𝟒𝟒 + 𝟗𝟗𝟗𝟗. After
how many seconds is the rocket at a height of 80 feet off
the ground? (hint: use the Quadratic Formula)

11. Completing the square and then write the factored


form of the following quadratic. (perfect square
trinomial)
𝒙𝒙𝟐𝟐 − 𝟔𝟔𝟔𝟔 + __

12. Solve for 𝑥𝑥. 𝟏𝟏𝟏𝟏𝒙𝒙𝟐𝟐 − 𝟑𝟑𝟑𝟑 = 𝟎𝟎 13. Solve for 𝑥𝑥. 𝟐𝟐𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟏𝟏𝟏𝟏𝟏𝟏 = 𝟎𝟎
14. Solve for 𝑥𝑥. 𝟗𝟗𝒙𝒙𝟐𝟐 + 𝟒𝟒𝟒𝟒 = 𝟎𝟎 15. Solve for 𝑥𝑥. 𝟑𝟑(𝒙𝒙 − 𝟐𝟐)𝟐𝟐 = −𝟐𝟐𝟐𝟐

16. Solve for 𝑥𝑥. 𝟐𝟐(𝒙𝒙 − 𝟐𝟐)𝟐𝟐 + 𝟏𝟏𝟏𝟏 = 𝟎𝟎 17. Solve for 𝑥𝑥.
𝟒𝟒𝟒𝟒𝟐𝟐 − 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟏𝟏𝟏𝟏 = 𝟎𝟎

18. Solve for 𝑥𝑥. 19. Solve for 𝑥𝑥.


𝟐𝟐
𝟑𝟑𝒙𝒙 − 𝟐𝟐𝒙𝒙 + 𝟏𝟏𝟏𝟏 = 𝟎𝟎 𝟓𝟓𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐 − 𝟏𝟏 = 𝟎𝟎
20. Solve for 𝑥𝑥. 21. Solve for 𝑥𝑥.
𝟑𝟑𝒙𝒙𝟐𝟐 − 𝟔𝟔𝟔𝟔 + 𝟏𝟏𝟏𝟏 = 𝟎𝟎 𝒙𝒙𝟐𝟐 + 𝟔𝟔𝟔𝟔 − 𝟏𝟏𝟏𝟏 = 𝟎𝟎

22. Solve for 𝑥𝑥. 23. Find the product. (𝟒𝟒 − 𝟕𝟕𝟕𝟕)(−𝟕𝟕 + 𝟗𝟗𝟗𝟗).
𝟐𝟐
𝟐𝟐𝟐𝟐 + 𝒙𝒙 − 𝟔𝟔 = 𝟎𝟎

24. Perform the following operations. Leave answers in simplest form.

a) (−3 + 5𝑖𝑖) + (2 − 4𝑖𝑖) b) (−3 + 5𝑖𝑖) − (2 − 4𝑖𝑖)

c) (−3 + 5𝑖𝑖)(2 − 4𝑖𝑖) d) 2𝑖𝑖(11 + 6𝑖𝑖) − (4 − 3𝑖𝑖) + 7𝑖𝑖

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