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# Math 115 Test 1 Study Guide MATH 115

Towson

GPA 3.2

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## About this Document

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## Popular in Basic Math for the sciences

## Popular in Mathematics (M)

This 8 page Study Guide was uploaded by Katlyn Burkitt on Monday September 28, 2015. The Study Guide belongs to MATH 115 at Towson University taught by Dr. David Buchoff in Summer 2015. Since its upload, it has received 48 views. For similar materials see Basic Math for the sciences in Mathematics (M) at Towson University.

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Date Created: 09/28/15

Math 115 Study Guide Test 1 How to solve an equation Example 12x 5x 4 25 2x5x425 7x425 7x25 4 7x221 52E 7 7 x3 What is the 5 step strategy for solving word problems 0 Familiarize yourself with the problem 0 Translate the written information into math 0 Solve 0 Check your answer 0 State the answer in written form Example When two times a number is decreased by 5 and the result is 45 what is the number 2x 5 45 2x 45 5 2x250 x50 2 x 25 Find the intersection of two equations Examples Club A offers membership for a fee of 24 plus a monthly fee of 15 Club B offers membership for a fee of 14 plus a monthly fee of 20 After how many months with the total cost be equivalent And what will be the total cost 0 Write and equation for both Clubs Club A 24 15m 6 Club B 14 20m c 0 Set the equations equal to each other 24 15m 14 20m o Solve form 24 14 15m 2 20m 10 15m 2 20m 10 2 20m 15m 105m 2 s m m 2 At two months the cost is the same 0 To find the cost substitute 2 in for m 24152c 2430c 54c 14202c 1440c 54 c The total cost at 2 months for both clubs is 54 You must have an understanding of the formulas for perimeter and area 1 2l w Example A rectangular field is twice as long as it is wide if the perimeter is 12 what are the dimensions 122w22w 122w42w 124w4 a 1 w For quadrilaterals The area of a rectangle is unknown the width is 7 less than the length Length 9 a 99 7a 92a 18a Solve Formulas without numbers T Z af Solve or a ax2bxc0 A You must know how to factor x2 4x 12 0 To factor you must find two numbers that when Multiplied together equal c but when added equal b x 6 x 2 0 Then to find the solution set or xintercepts Set each expression equal to 0 x60 x 20 Andsolveforx Solve an equation using the square root property x 32 36 1X 32 Em a 3 6 Solution set is 9 3 Solve an equation by completing the square x2 2x 80 0 Divide b by two 0 Square that number 0 Add to both sides 0 Factor left 0 Simplify right 0 Solve using square root property x22x1801 2x181 x12 81 1X12 x x1 9 x19 x1 9 00 R H H O x bi b2 4ac Solve using the quadratic formula x 2a 2x2 3x 10 T x 3 3 42 1 22 3i9 8 1 x 22 WW x 3 4 How to find the hypotenuse or sides of a triangle using the Pythagorean Theorem and the Square root property A rectangular park is 10miles long and 2miles wide how long is the route that cuts diagonally across the park a2b2c2 10m 22 102 C2 4100C2 104C2 lo 42 WM12C 102c 20c How do you know if a relation or graph is a function If X repeats it is not a function The vertical line test if you can draw a vertical line anywhere on a graph and it passes through only one point then the graph represents a function Solve functions at different values fx x2 3x 3 Evaluateat2fx 3 If you see this then you replace x in the original equation with what is in the parenthesis f 2 22 3 2 3 Then you solve as you would regularly f 2 4 6 3 f 2 1 Subsitute fx 3 x 32 3x 3 3 X 3 Multiply X x2 3 9 Combine like terms fx 3 x2 6x 9 3x 9 3 fx 3 x2 9x 21 Domain The total of all x values Range The total of all y values Xlntercepts Where the Graph crosses the xaxis Yintercepts Where the graph Crosses the yaxis Domain 00 00 Range 00 O Xlntercept 0 Yintercept 0 When a function is increasing The values of x that the functions y is increasing When a function is decreasing The values of x that the y values are decreasing What is a maxima The value of x where y is the greatest What is a minima The value of x where y is the least gx x 5 ifx 2 5 gx x 5 ifx lt 5 For a problem such as this if you are given a value of x and told to evaluate the function at that value you must substitute it in for the appropriate part For example if you are given x2 you would substitute it into gx x 5 because 2 is greater than 5 if you were given a number less than 5 you would substitute it into x 5 Find the slop of a line when given two points Slope y2 y X2 X1 Find the slope of a line that crosses through the points 88 and 4 4 4 8 Slope 48 4 Slope E 1 Slope 5 Put the equation into point slope form y 311 mx x1 Given the slope m 3 and the point 39 y 9 3x 3 Then take that and solve for y to put the equation in slope intercept form ymxb y93x9 y3x After completing the problems on this study guide make up your own It really helps to keep the ideas fresh in your mind

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