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# MATH 95 - Midterm 1 Study Guide MATH 95

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This 4 page Study Guide was uploaded by Alex Tucker on Tuesday October 18, 2016. The Study Guide belongs to MATH 95 at University of Oregon taught by Craig Tingey in Fall 2016. Since its upload, it has received 28 views. For similar materials see Math 95 in Math at University of Oregon.

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Date Created: 10/18/16

MATH 95 Midterm 1 Study Guide ____________________________________________________________________________ Lines The points on a line satisfy an equation of the form: Ax+By+C=0 Slope= rise Slope = change(y) m = (y 1y2)/(1 -2 ) run change(x) Equations: 1. Standard Form Ax+By+C=0 2. Slope-Intercept y=mx+b 3. Point-Slope y-y1=m(x-x 1 Parallel = lines have same slope ex. 2 Perpendicular = lines have negative reciprocal slopes ex. -½ Example: Find an equation of the line through (-1,2) & (3,1) 2−1 = −1 −1−3 4 m= -¼ −1 y= 4 x+b −1 2= 4 (−1)+b 1 2= 4b b= 1¾ Systems of Linear Equations Substitution Method Addition Method 1) Solve one of equations for 1 1) Multiply both equations to get variable LCM and FOIL 2) Substitute into other sign 3) Use formula from one to find remaining variable Substitution Method Solve 2x+y=1 & 3x+2y=0 X Y y=-2x+1 2(2)+y= 1 3x+2(- 2x+1)=0 4+y=1 -4 -4 3x-4x+2=0 y=-3 -x+2=0 -2 -2 −x=−2 −1 x = 2 (2,-3) Addition Method Solve 3x-4y=-2 5x+3y=1 X Y 3 (3x-4y=- 5 (3x-4y=-2) 2) -3 (5x+3y=1) 4 (5x+3y=1) 15x-20y=-10 -15x-9y=-3 9x-12y=-6 20x+12y=4 −29 y=−13 −29 29 x=−2 29 13 −2 y= 29 x= 29 −2 13 ( , ) 29 29 Factoring To factor something is to write it as a product (multiply) of 2 or more things Greatest Common Factor (GCF): largest # that divides into 2 numbers GCF of 18 & 12 18: 1,2,3,6,9,18 12: 1,2,3,4,6,12 GCF = 6 Least Common Multiple (LCM): smallest # that multiplies both GCF of 18 & 12 18: 18,36,54,72 12: 12,24,36,48 LCM = 36 2 3 3 2 48a c & 18a b 6a Factor GCF = 6a (8c +3ab) AC Method 1) Compute AC 2) Find numbers that multiply to ac & add to b 3) Fill in boxes 4) Factor out GCF of each row / column 5) Answer on edges! 2x +x-6 ac=(2)(-6) = -12 x +4 2 2x 4 x -3x - 6 2x-3 (2x-3)(x+4) Multiplication & Division of Rational Expressions Rational = RATIO Multiplying Dividing a c ac a c a d ad × = ÷ = × = b d bd b d b c bc Multiply 2 2 (x −2x−8) × (x +3x+2) x −4 x +x−20 (x−4)(x+2)(x+1)(x+2) (x+2)(x−2)(x+5)(x−4) (x+1)(x+2) (x−2)(x+5) Divide (x+2) (x−3) ÷ (x+1) (x+2) (x+2) (x−3) (x+1)× (x+2) (x−3) (x+1)

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