TABLE OF CONTENTS

## Baruch College MTH 2003 Final Overview

MTH 2003 is a precalculus course in Baruch College. MTH 2003 is a preliminary mathematics course students must take prior to starting the calculus as well as in quantitative courses in allied disciplines track. This course is a prerequisite for MTH 2205. Baruch College MTH 2003 Final Test has a calculator section. Therefore, the students are required to master TI 89 or TI 92 graphical calculator for this course.

To view the syllabus for Baruch College MTH 2003 __CLICK HERE__

To get your hands on Baruch College MTH 2003 Last Minute Cram Course, __CLICK HERE__

To view sample questions for Baruch MTH 2003 Final __CLICK HERE__.

## Baruch MTH 2003 Final Topic 1. The Line.

### Rule 1.

Slopes of parallel lines are equivalent.

### Rule 2.

Slopes of perpendicular lines are negative reciprocals of each other.

## MTH 2003, Sample Final SP17, Problem 1

We need to find the slope of a perpendicular line to the following linear function .

### Step 1.

Solve for :

### Step 2.

Slopes of perpendicular lines are negative reciprocals of each other.

The slope of the existing function is .

The negative reciprocal of the line is .

The answer is .

## Baruch MTH 2003 Final Topic 2. Parabola.

Quadratic equations and parabolas are the same thing. A quadratic equation looks like a parabola and every parabola can be expressed as a quadratic equation.

The final test often includes problems on vertex for functions

### Step 1.

### Step 2.

## MTH 2003, Sample Final SP17, Problem 3

Letâ€™s solve a specific problem on vertex. In Problem 3 of the Sample Final SP17, we need to find the vertex for

### Step 1.

### Step 1.

The coordinate pair of the vertex is .

The answer is .

## Baruch MTH 2003 Final Topic 3. Circle.

Equation of a circle with radius and origin is . Complete the square for and to turn the equation into the form .

## MTH 2003, Sample Final SP17, Problem 4

In Problem 4 of the Final Test SP17 we need to find the radius of the circle for

### Step 1.

Rearrange the equation to move and terms together.

### Step 2.

Letâ€™s now complete the squares for and :

The answer is .

## Baruch MTH 2003 Final Topic 4. Horizontal Asymptote.

Horizontal asymptote problems are typically very straight-forward. Identify the highest exponent with the coefficient on the top and on the bottom.

### Step 1.

If the exponent on top is higher than the exponent on the bottom, there are no horizontal asymptotes.

### Step 2.

If the exponent on top is equal to the exponent on the bottom, the horizontal asymptote is equal to the fraction of coefficients.

### Step 3.

If the exponent on top is less than the exponent on the bottom, the horizontal asymptote is equal to .

Keep in mind that if the horizontal asymptote is, say, , the equation for the horizontal asymptote is .

## MTH 2003, Sample Final SP17, Problem 5

Letâ€™s find the horizontal asymptote for .

### Step 1.

Take a look at the highest exponent of the top and the bottom.

The highest exponent of the numerator is .

The highest exponent of the denominator is .

Since the exponent of denominator is higher, the horizontal asymptote is .

The answer is .

## Baruch MTH 2003 Final Topic 5. Limits.

Letâ€™s consider limit problems of the following type: . Plug in into right away:

### Step 1.

If you get simplify top against the bottom and plug in again

### Step 2.

If you get then the limit is equal to

### Step 3.

If you get then the limit is undefined

## MTH 2003, Sample Final SP17, Problem 11

We need to find the following limit .

### Step 1.

Letâ€™s plug in into the fraction right away:

### Step 2.

Since we got , we know that the fraction can be definitely simplified

Letâ€™s plug in again:

The answer is .

## Baruch MTH 2003 Final Topic 6. Continuity.

When it comes down to limits and continuity problems, it is important to check the boundaries. Typical steps include plugging in all the border values into function and making sure these values are either matching or not. Matching values indicate that there is no discontinuity. Non-matching values indicate that there is a discontinuity.

Letâ€™s take a look at the specific problem below.

## MTH 2003, Sample Final SP17, Problem 12

In the Baruch MTH 2207 final SP17 test the following piece-wise function needs to become continuous on the entire interval .

### Step 1.

The border takes place at , so all we need to do is to plug it in into both equations and solve for :

## Baruch MTH 2003 Final Topic 7. Economic Functions.

There are a couple of very useful formulas for economic function problems. If you know these formulas, you should be all set:

### Revenue

, where is demand and is the production level

### Cost

, where is the production level

### Profit

, where is revenue and is the cost

## MTH 2003, Sample Final SP17, Problem 6

Great example to show the proper use of aforementioned formulas. The demand and we need to find the number of items to be sold to maximize revenue.

### Step 1.

The revenue function is

### Step 2.

To find the number of items that will maximize revenue, take the first derivative

### Step 3.

Set the denominator to and solve for

The answer is .

## Baruch MTH 2003 Final Topic 8. Derivative.

Derivatives is a very extensive topic. But we will do the basic version of derivatives in this section of the article.

Basic Derivative

Product Rule

Quotient Rule

## MTH 2003, Sample Final SP17, Problem 8

We need to find the derivative of . We are dealing with a fraction so, clearly, we are looking for the **Quotient Rule**.

### Step 1.

Letâ€™s assign the values for and , respectively:

and

and

Plug values into the formula:

### Step 2.

Plug in to find

The answer is .

## Baruch MTH 2003 Final Topic 9. Chain Rule.

Chain Rule.

Chain Rule application is very simple to use as long as you do not forget to multiply the end result by the derivative of the inside (the u\prime).

## MTH 2003, Sample Final SP17, Problem 15

### Step 1.

Make the U-substitution for

Letâ€™s make proper substitutions for and :

The answer is .

## Baruch MTH 2003 Final Topic 10. Horizontal Tangent Line.

If you do not know what to do on the Baruch MTH 2003 final, take the first derivative ðŸ˜€. Horizontal tangent lines are not the exception to this rule of thumb.

In order to find the points at which the first derivative is equal to follow these simple steps:

### Step 1.

Take the first derivative

### Step 2.

Set the first derivative

## MTH 2003, Sample Final SP17, Problem 7

Letâ€™s find the points at which horizontal tangent lines for are equal to .

### Step 1.

### Step 2.

### Step 3.

Letâ€™s now find the y value by plugging into the original function:

The tangent line is horizontal at .

The answer is .