About This Chapter
Illinois TAP Math: Algebra - Chapter Summary
The lessons in this chapter will help you gain the knowledge you'll need to solve the algebra questions on the mathematics portion of the Illinois TAP - Test of Academic Proficiency exam. You'll learn about graphs and how to create them, as well as inequalities and various types of equations. The video lessons cover:
- Parts of a graph
- Variables in algebra
- Expressing relationships as algebraic expressions
- Linear equations
- Intercepts, standard form and graphing linear equations
- Equations of a line using point-slope formula
- Abstract algebraic examples and going from a graph to a rule
- Writing a linear equations
- Understanding and using a system of equations
- Inequalities and graphing 1- and 2-variable inequalities
- Solving equations on a scientific calculator
- Solving word problems with 1 or 2 variables
These lessons will give you an understanding of concepts such as linear equations, systems of equations and graphs. You'll learn how to use this knowledge to express algebraic functions. Mastering skills such as finding the value of an unknown in an equation will prepare you for the test, and the video lessons and accompanying self-assessment quizzes make learning enjoyable.
Objectives of the Illinois TAP Math: Algebra Course
Passing the TAP test is required in order to obtain a license to teach in Illinois. The TAP consists of three parts with a total of 170 questions, plus a writing section. Each of these sections is scored separately, and licensing candidates must pass each one. The algebra questions are part of the mathematics portion of the test, which contains 50 multiple choice questions.
1. What Are the Different Parts of a Graph?
Being able to read a graph isn't just vital for an algebra class. Graphs and charts are used everywhere! We'll take a crash course on the basic x/y plane used in algebra and the fundamental vocab you need.
2. What is a Variable in Algebra?
Did you ever encounter something like a + b = c and wonder how all these letters snuck into a math problem? In this lesson, we'll learn about variables, as well as other parts of equations, constants and coefficients.
3. Expressing Relationships as Algebraic Expressions
What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.
4. Evaluating Simple Algebraic Expressions
In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.
5. What is a Linear Equation?
Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.
6. Linear Equations: Intercepts, Standard Form and Graphing
Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.
7. Equation of a Line Using Point-Slope Formula
It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.
8. Abstract Algebraic Examples and Going from a Graph to a Rule
Just because you now know what a linear equation is doesn't mean that you are a master! This video will help you learn how to apply your knowledge of linear equations in more abstract algebraic ways.
9. Graphing Undefined Slope, Zero Slope and More
There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!
10. How to Write a Linear Equation
Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.
11. What is a System of Equations?
So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.
12. How Do I Use a System of Equations?
There are a few classic algebra word problems, such as the one about two trains traveling at different speeds. In this lesson, you'll learn how to take a word problem and convert it into the system of equations that will allow you to find the answer using either substitution or elimination.
13. What is an Inequality?
Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!
14. How to Graph 1- and 2-Variable Inequalities
So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!
15. Graphing Inequalities: Practice Problems
If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.
16. Solving Equations on the CLEP Scientific Calculator
In this lesson, learn how to use the Solver function of the CLEP calculator. With calculators, you can solve equations numerically (find a number answer) even when you cannot solve the problem explicitly.
17. How to Solve Equations by Graphing on the CLEP Scientific Calculator
In this lesson, review how to graph equations with the CLEP calculator. Given a function, find the maximum and minimum values over a range and the roots of the equation. Learn how you can use this to solve a system of equations by graphically finding intersects.
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Other chapters within the ILTS TAP - Test of Academic Proficiency (400): Practice & Study Guide course
- About the Illinois TAP Test
- Illinois TAP Reading Comprehension: Vocabulary & Language
- Illinois TAP Reading Comprehension: Find the Main Idea & Supporting Details
- Illinois TAP Reading Comprehension: Inference & Interpretation
- Illinois TAP Reading Comprehension: Critical Reasoning
- Illinois TAP Reading: Summarizing & Interpreting Information
- Illinois TAP Language Arts: Grammar
- Illinois TAP Language Arts: Writing Mechanics
- Illinois TAP Writing: Understanding Audience
- Illinois TAP Writing: Development & Organization
- Illinois TAP Writing: Editing & Revision
- Illinois TAP Writing: Clarity
- Illinois TAP Writing: Practice
- Illinois TAP Math: Integers
- Illinois TAP Math: Fractions, Decimals & Percents
- Illinois TAP Math: Estimation & Measurement
- Illinois TAP Math: Reasoning Skills
- Illinois TAP Math: Geometry
- Illinois TAP Math: Data & Statistics
- ILTS TAP - Test of Academic Proficiency Flashcards