GRE Review  Algebra
Objectives • Students will be able to use the multiplication and addition principles together to solve linear equations Solve for x : 3x – 2 = 10 

Example 3w + 4 = 5w − 6 

Example 2(a − 3) = −5(2a +1) 

Solving a system of linear equations


Solving Quadratics  
Example Students will be able to • Solve equations by factoring


Example • If the quadratic does not factor, we will use the quadratic formula : 

Inequalities  
Example Students should be able to • solve linear inequalities 

Double Inequalities • They will sometimes stipulate some constraints on a variable . 0 < y < 1


Applications • It would be impossible to cover the myriad of applications that could be on the test. I will go through the thought process on just one here. 

Example • Lex is twice as far from the finish line as he is from the start of 18 mile race. How far has he run? 

Methodology • Step 1. Read the problem. If you don’t understand it, read it again. If you still don’t understand it, read it a 3rd time. • Step 2. Identify the given information • Step 3. Identify what you are trying to find. • Step 4. Draw a picture if necessary to help you visualize the problem. • Step 5. Start labeling the drawing or setting up a formula to solve . • Step 6. Solve the problem. • Step 7. Make sure your answer makes sense. 

Example • Lex is twice as far from the finish line as he is from the start of 18 mile race. How far has he run?


Coordinate Geometry  
Example ( Plotting Points ) • Plot the following pairs of points A (1, 3), B (2, 3), C (1, 2), D (0, 2).


Example Students should be able to • find the slope when given a line or points on the line


Derivation of the slope formula


Example • Find the slope of the line containing the points (0,1), (5, 3)

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