**Unit 5: Algebra**
*One of the most important mathematical subtopics you need to master to
do well on the SAT is algebra. Understanding how to solve an equation
or rearrange it according to your needs to solve a more complex problem
is one of the most basic and widely-applicable skills in mathematics.
This unit will cover the basic algebraic rules and methods of solving
various types of equations, as well as graphing and solving functions.*

**Unit 5 Time Advisory**

This unit should take approximately 2 hours to complete.

☐ Subunit 5.1: 0.25 hours

☐ Subunit 5.2: 0.25 hours

☐ Subunit 5.3: 0.25 hours

☐ Subunit 5.4: 0.5 hours

☐ Subunit 5.6: 0.75 hours

**Unit5 Learning Outcomes**

Upon successful completion of this unit, the student will be able to:
- Translate word problems into algebraic equations and vice versa.
- Reorganize algebraic equations to find the value of an unknown
variable.
- Use algebra to solve word problems.
- Solve a system of equations.
- Use factoring to solve a quadratic equation.
- Explain the definition of a function.
- Graph and provide solutions to a function.
- Find the slope of an equation.

**5.1 Reorganizing/Solving an Equation**
- **Web Media: Khan Academy’s “Multi-Step Equations”**
Link: Khan Academy’s “Multi-Step
Equations” (YouTube)

```
Instructions: It is very important to be comfortable with basic
algebraic rules to do well on the SAT. If you need a quick review
of the methods for solving an algebraic equation, watch this
video.
Watching this video should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**5.2 Word Problems**
- **Web Media: Khan Academy’s “Basic Rate Problem”**
Link: Khan Academy’s “Basic Rate
Problem” (YouTube)

```
Instructions: Do not fear the rate problem. Watch this video for a
review of this topic and become prepared for these popular
questions! Write down the rate formula in your notes, so you can
easily refer to it when working on practice problems.
Watching this video and pausing to take notes should take
approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**5.3 Systems of Equations**
- **Web Media: Khan Academy’s “Systems of Equations”**
Link: Khan Academy’s “Systems of
Equations” (YouTube)

```
Instructions: Please click on the link above and watch this video,
which explains how to answer questions where you are given two or
three equations and need to determine the value of a common
variable.
Watching this video and pausing to take notes should take
approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**5.4 Functions**
- **Reading: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and
Formulas”**
Link: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and
Formulas” (PDF)

```
Instructions: Please click on the link above and select the link to
the “SAT Math Facts and Formulas” PDF. Read the sections entitled
“Factoring, Solving,” “Functions,” and “Lines (Linear Functions)”.
Make notes or flashcards of any concepts you need to review in order
to remember for the test. This resource will cover the topics
outlined in subunits 5.4 and 5.5.
Reading these sections and taking notes should take approximately
30 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**5.5 Slope**
*Note: This topic is covered by the “SAT Math Facts and Formulas”
reading assigned below subunit 5.4. In particular, review the formula
for slope, and the formulas for writing an equation in ‘point-slope’ and
‘slope-intercept’ form, as described under the “Lines (Linear
Functions)” heading. Understanding how slope describes a line in a
graph, how slope can be found within an equation, and how to write an
equation for a line in a graph will help you quickly understand
graphical transformations (where you are asked to find the formula for a
line that is similar to a line that you are given the formula for), as
well as other algebraic and graphical problems on the SAT.*

**5.6 Algebra Practice Problems**
- **Assignment: cK-12: Jason Shah’s “SAT Prep - Math Questions” and
“SAT Prep - Math Questions with Explanations”**
Link: cK-12: Jason Shah’s “SAT Prep - Math
Questions” (HTML) and
“SAT Prep - Math Questions with
Explanations” (HTML)

```
Instructions: Please click on the first link above for “Math
Questions” and complete questions 3-5 to apply your new knowledge
and to practice answering functions and algebra questions.
Once you have completed the questions, please click on the second
link above for “Math Questions with Explanations” and review the
correct answers for questions 3-5. For any questions you missed,
read and review the provided explanations until the correct answer
makes sense to you. You may want to look back at the previous
sections in this unit for help. Once you have studied the correct
answer, think about how you will approach a similar problem in the
future and will avoid making a similar mistake.
Completing this assignment should take less than 15 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Assignment: cK-12: Jason Shah’s “SAT Prep II - Math Questions” and “SAT Prep II - Math Questions with Explanations”**Link: cK-12: Jason Shah’s “SAT Prep II - Math Questions” (HTML) and “SAT Prep II - Math Questions with Explanations” (HTML)Instructions: Please click on the first link above for “Math Questions” and complete questions 3-5 to apply your new knowledge and to practice answering functions and algebra questions.

Once you have completed the questions, please click on the second link above for “Math Questions with Explanations” and review the correct answers for questions 3–5. For any questions you missed, read and review the provided explanations until the correct answer makes sense to you. You may want to look back at the previous sections in this unit for help. Once you have studied the correct answer, think about how you will approach a similar problem in the future and will avoid making a similar mistake.

Completing this assignment should take less than 15 minutes.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Assignment: cK-12: Jason Shah’s “SAT Prep III - Math Questions” and “SAT Prep III - Math Questions with Explanations”**Link: cK-12: Jason Shah’s “SAT Prep III - Math Questions” (HTML) and “SAT Prep III - Math Questions with Explanations” (HTML)Instructions: Please click on the first link above for “Math Questions” and complete questions 3-5 to apply your new knowledge and to practice answering functions and algebra questions.

Once you have completed the questions, please click on the second link above for “Math Questions with Explanations” and review the correct answers for questions 3–5. For any questions you missed, read and review the provided explanations until the correct answer makes sense to you. You may want to look back at the previous sections in this unit for help. Once you have studied the correct answer, think about how you will approach a similar problem in the future and will avoid making a similar mistake.

Completing this assignment should take less than 15 minutes.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.