TABLE OF CONTENTS

## Baruch College CSTM 0120 Final Overview

CSTM 0120 is an prealgebra course in Baruch College. This is a non-credit course containing those topics from intermediate algebra that are needed prior to taking MTH 1030, College Algebra.

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## Baruch CSTM 0120 Final Topic 1. Factoring Binomials.

Many binomial problems from the CSTM 0120 final can be solved with the application of the difference of squares formula.

## CSTM 0120, Sample Final F019A, Problem 1

### Step 1.

Letâ€™s first factor by using the formula above:

### Step 2.

by taking the greatest common factor:

We have different factors including:

The answer is , since is not included the list of the factors above.

## Baruch CSTM 0120 Final Topic 2. Factoring .

If you know quadratic equation by heart, you should be able to get a large part of CSTM 0120 final test problems correct.

Letâ€™s refresh our memory:

, where:

## CSTM 0120, Sample Final F019A, Problem 2

We need to completely factor

### Step 1.

Quickly realize that it is a trinomial and chances are we need to turn that into a quadratic equation:

We can also see that every term in the trinomial is a factor of .

### Step 2.

Only pay attention to the trinomial now and letâ€™s factor it using the quadratic formula:

### Step 3.

Letâ€™s combine the first two steps together:

From the multiple choices presented, is one of the factors.

The answer is .

## Baruch CSTM 0120 Final Topic 3. Factoring .

Factoring is similar to factoring from the previous problem.

Letâ€™s refresh our memory:

, where:

## CSTM 0120, Sample Final F022A, Problem 2

We need to completely factor and

### Step 1.

Letâ€™s factor

### Step 2.

Letâ€™s factor

We have the following factors:

Thus, the answer is .

## Baruch CSTM 0120 Final Topic 4. Greatest Common Factor.

The trick behind greatest common factor problems is to find the greatest common factor for every term individually.

### Step 1.

Factor the constant

### Step 2.

Find the greatest common factor of the constants

### Step 3.

Find the greatest common factor for the first variable

### Step 4.

Find the greatest common factor for the second variable

## CSTM 0120, Sample Final F022A, Problem 3

In this problem we need to find the greatest common factor for the expression

### Step 1.

Letâ€™s factor the two constants first:

### Step 2.

Letâ€™s identify the greatest common factor for the constants:

and

would represent the greatest common factor of the constant.

### Step 3.

Letâ€™s now find the greatest common factor for the

### Step 4.

Finally, letâ€™s find the greatest common factor for the

### Step 5.

Combining greatest common factors of the constant, -term and -term we get:

The answer is .

## Baruch CSTM 0120 Final Topic 5. Line Equations.

Given a point and a slope the following formula can be used to find the line equation:

## CSTM 0120, Sample Final F019, Problem 19

Problem 19 of the Sample Final F019 is a great example of a linear equation problem. We are given a point and a slope .

### Step 1.

Plug in the values into the formula:

### Step 2.

Multiply everything out and move x-term and y-term to one side and everything else to the other side:

The answer is .

## Baruch CSTM 0120 Final Topic 6. Slope.

A linear equation is defined as: . In such equations, the slope is .

## CSTM 0120, Sample Final F019, Problem 18

In problem 18 of the Sample Final F019, we need to find the slope of the function .

Letâ€™s reorganize the equation .

It is very clear and apparent that the slope of such function is .

The answer is .

## Baruch CSTM 0120 Final Topic 7. Adding Rational Expressions.

Rational expressions problems typically include the following steps:

### Step 1.

Identify lowest common denominator

### Step 2.

Turn every fraction to the lowest common denominator

### Step 3.

Combine both fractions

### Step 4.

Simplify

## CSTM 0120, Sample Final F019, Problem 14

We need to simplify

### Step 1.

Lowest common denominator for :

Thus, the lowest common denominator is:

### Step 2.

Letâ€™s convert denominators of both terms of the expression to :

### Step 3.

Combine both fractions:

### Step 4.

The fraction cannot be simplified further.

The answer is .

## Baruch CSTM 0120 Final Topic 8. Systems of Linear Equations: Solving by Substitution.

### Step 1.

Solve for in terms of or solve for in terms of

### Step 2.

Plug the found expression into the second equation and solve for the other term.

Sounds pretty confusing, but letâ€™s see how we can apply such method on the existing system of linear equations.

## CSTM 0120, Sample Final F039, Problem 26

We need to solve the following system of equations by substitution

### Step 1.

Second equation is much better for substitution purposes. Letâ€™s solve for y from the second equation:

### Step 2.

Letâ€™s plug the y-term into the first equation:

### Step 3.

Letâ€™s now plug into

The answer is .

## Baruch CSTM 0120 Final Topic 9. Systems of Linear Equations: Solving by Addition.

### Step 1.

Multiply both equations by respective multiplier to be able to cancel out -term or -term

### Step 2.

Solve for the remaining term

### Step 3.

Plug back the remaining term to solve for the eliminated term

Again, sounds pretty confusing, but letâ€™s see how we can apply such method on the existing system of linear equations.

## CSTM 0120, Sample Final F039, Problem 25

We need to solve the following system of equations by addition:

### Step 1.

Letâ€™s cancel the y-term. We can do so by multiplying the top equation by and the bottom equation by .

### Step 2.

After adding both equations we get:

### Step 3.

Plug in into the top equation to solve for

The answer is .

## Baruch CSTM 0120 Final Topic 10. Simplifying Complex Fractions.

### Step 1.

Factor every fraction

### Step 2.

Combine fractions together

### Step 3.

Simplify

## CSTM 0120, Sample Final F019, Problem 12

Letâ€™s simplify the following expression:

### Step 1.

Letâ€™s factor every single term of the expression:

### Step 2 & Step 3.

Combining and simplifying the fraction can be done in one action here:

The answer is .