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.
Let’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.
Let’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 let’s factor it using the quadratic formula:
Step 3.
Let’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.
Let’s refresh our memory:
, where:
CSTM 0120, Sample Final F022A, Problem 2
We need to completely factor and
Step 1.
Let’s factor
Step 2.
Let’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.
Let’s factor the two constants first:
Step 2.
Let’s identify the greatest common factor for the constants:
and
would represent the greatest common factor of the constant.
Step 3.
Let’s now find the greatest common factor for the
Step 4.
Finally, let’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 .
Let’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.
Let’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 let’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. Let’s solve for y from the second equation:
Step 2.
Let’s plug the y-term into the first equation:
Step 3.
Let’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 let’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.
Let’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
Let’s simplify the following expression:
Step 1.
Let’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 .