### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Math 1111 exam 1 study guide Math1111

GPA 4.0

### View Full Document

## 16

## 0

## Popular in College algebra

## Popular in Math

This 14 page Study Guide was uploaded by rachel Notetaker on Tuesday September 6, 2016. The Study Guide belongs to Math1111 at University of North Georgia taught by Dr. Serkan in Fall 2016. Since its upload, it has received 16 views. For similar materials see College algebra in Math at University of North Georgia.

## Popular in Math

## Reviews for Math 1111 exam 1 study guide

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/06/16

Math Study Guide – exam 1 Section 2.4 - Graph linear equations in 2 variables - Graph the equation and identify X & Y intercepts 1. -3x + 4y= 12 2. 2y= -5x + 2 X-intercept: X-intercept: Y-intercept: Y-intercept: 2. x= -6 4. 5y + 1= 11 X-intercept: X-intercept: Y-intercept: Y-intercept: - Determine the slope of a line - Given Word Problems 1. Find the average slope of a hill. - Determine the slope of a line passing through given points. 1. (4, -7) (2, -1)slope: 2. (2.6, 4.1) (9.5, -3.7) slope: 3. (3/4, 6) (5/2, 1slope: 4. (36, 25) (6, 5) slope: - Determine the slope of a line given the graph 1. 2. 3. slope: slope: slope: - Questions to know 1. What is the slope of a line perpendicular to the X-axis? 2. What is the slope of a line parallel to the X-axis? 3. What is the slope of a line defined by y = -7? 4. What is the slope of a line defined by x = 2? 5. If the slope of a line is 4/5, how much vertical change will be present for a horizontal change of 52 ft? 6. Suppose that y = P(t) represents the population of a city at time(t). What does P over t represent? - Apply the slope-intercept form - Write the equation in slope-intercept form and determine the slope and Y-intercept. - Graph the equation using the slope and Y- intercept. 1. 2x – 4y = 8 2. 3x = 2y - 4 slope-intercept form: slope-intercept form: slope: slope: y-intercept: y-intercept: 3. 3x = 4y 4. 2y – 6 = 8 slope-intercept form: slope-intercept form: slope: slope: y-intercept: y-intercept: 5. 0.02x + 0.06y = 0.06 6. x/4 + y/7 = 1 slope-intercept form: slope-intercept form: slope: slope: y-intercept: y-intercept: - Determine if the function is linear, constant, or neither. 1. f(x) = -3/4x 2. g(x) = -3/4x – 3 3. k(x) = -3/4 4. f(x) = 5x + 1 5. p(x) = 5 6. f(x) = 5x - Answer each part of the word problem. 1. The function given by y = f(x) shows the value of $5,000 invested at 5% interest compounded continuously, x years after the money was originally invested. th A) Findthhe average amount earned per year between the 5 and the 10 year. th B) Findthhe average amount earned per year between the 20 and the 25 year. C) Based on the answers from part A and part B, does it appear that the rate at which annual income increases is increasing or decreasing with time? 2. The population of the united states since the year 1960 can be approximated by f(x) = 0.009r^2 + 2.10t + 182, where f(x) is the population in millions and (t) represents the number of years since 1960. A) Find the average rate of change in US population between 1960 and 1970. B) Find the average rate of change in US population between 2000 and 2010. C) Based on the answers from part A and part B, does it appear that the rate at which US population increases is increasing or decreasing with time? - Use the graph to solve the equation and inequalities. - Write the solutions in interval notation. 1. 2x + 4 = -x + 1 2. -3x + 1 = -x - 3 2x + 4 -x + 1 -3x + 1 -x - 3 2x + 4 -x + 1 -3x + 1 -x - 3 Interval notation: Interval notation: 3. -3(x + 2) + 1 = -x + 5 4. 4 – 2(x + 1) + 12 + x = 0 -3(x + 2) + 1 -x + 5 4 – 2(x + 1) + 12 + x 0 -3(x + 2) + 1 -x + 5 4 – 2(x + 1) + 12 + x 0 Interval notation: Interval notation: Section 2.5 - Use the point-slope formula to write an equation of the line with what is given. - Write the answer in slope-intercept form. 1. passes through (-3, 5) m = -2 2. Passes through (-1, 0) m = 2/3 3. passes through (3.4, 2.6) m = 1.2 4. Passes through (6, 2) and (-3, 1) 5. passes through (2.3, 5.1) and (1.9, 3.7) 6. Passes through (3, -4) m = 0 7. passes through (2/3, 1/5) and slope is undefined. 8. given a line defined by x = 4, what is the slope? 9. given a line defined by y = -2 what is the slope? - Determine the slope of a line parallel to the given line. - Determine the slope of a line perpendicular to the given line. 1. m = 3/11 2. m = -6 3. m = 1 4. m is undefined - Determine if the line defined by the given equations are parallel, perpendicular, or neither. 1. y = 2x – 3 2. 8x – 5y = 3 3. 2x = 6 y = -1/2x + 7 2x = 5/4y + 1 5 = y - Write an equation of the line satisfying the given conditions. - Write the answer in slope-intercept form. 1. passes through (2, 5) and is parallel to the line defined by 2x + y = 6. 2. passes through (6, -4) and is perpendicular to the line defined by x – 5y = 1. 3. passes through (2.2, 6.4) and is perpendicular to the line defined by 2x = 4 – y. - Create linear functions to model data. 1. A sales person makes a base salary of $400 per week plus 12% commission on sales. A) write a linear function to model the sales person’s weekly salary S(x) for x dollars in sales. B) Evaluate S(8000) and interpret the meaning in the context of this problem. 2. Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a $60,000 taxable value in a municipality with a 19 mil tax rate would require (0.019)($60,000) = $1140 in property taxes. In one county, homeowners pay a flat tax of $172 plus a rate of 19 mil on the taxable value of the home. A) Write a linear function that represents the total property tax T(x) for a home with a taxable value of x dollars. B) evaluate T(80,000) and interpret the meaning in the context of this problem. - The fixed and variable costs to produce an item are given along with the price at which an item is sold. - Write a linear cost function that represents the cost C(x) to produce x items. - Write a linear revenue function that represents the revenue R(x) for selling x items. - Write a linear profit function that represents the profit P(x) for producing and selling x items. - Determine the break-even point. 1. Fixed cost: $2275 variable cost per item: $ 34.50 price at which item is sold: $80.00 Section 3.1 - Graph a quadratic function written in vertex form. 1. f(x) = -(x – 4)^2 + 1 parabola opens up or down: vertex: x-intercept(s): y-intercept: sketch the function: determine the axis of symmetry: minimum: maximum: domain: range: 2. f(x) = 2(x + 1)^2 – 8 parabola opens up or down: vertex: x-intercept(s): y-intercept: sketch the function: determine the axis of symmetry: minimum: maximum: domain: range: 3. f(x) = 3(x – 1)^2 parabola opens up or down: vertex: x-intercept(s): y-intercept: sketch the function: determine the axis of symmetry: minimum: maximum: domain: range: 4. -1/5(x + 4)^2 + 1 parabola opens up or down: vertex: x-intercept(s): y-intercept: sketch the function: determine the axis of symmetry: minimum: maximum: domain: range: - Write f(x) = ax^2 + bx + c into vertex form. 1. f(x) = x^2 + 6x + 5 vertex form: vertex: x-intercept(s): y-intercept: sketch the function: determine the axis of symmetry: minimum: maximum: domain: range: - Solve word problems involving quadratic functions. 1. The population P(t) of a culture of the bacterium is given by P(t) = -1718t^2 + 82,000t + 10,000, where t is the time in hours since the culture was started. A) determine the time at which the population is at a maximum. B) determine the maximum population. 2. suppose that a family wants to fence in an area of their yard for a garden. One side is already fenced. A) if the family has enough money to buy 160 ft of fencing, what dimensions would produce the maximum area for the garden? B) what is the maximum area? 3. A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 20 in long and 12 in wide. He makes a fold along the two long sides a distance of x inched from the edge. A) write a function to express the volume in terms of x. B) what value of x will maximize the volume of water that can be carried by the gutter? C) what is the maximum volume?

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.