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Math 1111 exam 1 study guide

by: rachel Notetaker

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Math 1111 exam 1 study guide Math1111

Marketplace > University of North Georgia > Math > Math1111 > Math 1111 exam 1 study guide
rachel Notetaker

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This is a study guide for all the problems that will be on exam 1.
COURSE
College algebra
PROF.
Dr. Serkan
TYPE
Study Guide
PAGES
14
WORDS
CONCEPTS
Math
KARMA
50 ?

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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.

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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. (36, 25) (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?

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