ELEMENTARY ALGEBRA WITH GEOMETRY FINAL EXAM REVIEW. 4. 3a + 5 = 5a x 7 = 4 2(3x + 4) 8. Solve for a: 5a + 3b = Solve for y: x + 2y = 4

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1 Updated Spring MTH 098 ELEMENTARY ALGEBRA WITH GEOMETRY FINAL EXAM REVIEW Evaluate. 1. ab a ac when a =, b =, and c =. ac (a + b) when a = 1, b =, and c =. a ac ( b) when a = 6, b =, and c = Solve the equations for the variable.. a + 5 = 5a = ( + ) 6. ( ) + = ( ) = 8. Solve for a: 5a + b = Solve for y: + y = Simplify, leaving positive eponents in the answer. 10. ( y ) 11. (a 1 b ) 1. ( ) ( y 1 ) 1. 6ab 1a b ab 7ab ab 16a b Simplify

2 Updated Spring 009 Perform the indicated operation, leaving answers in simplest form. 19. (b + 5) (b ) 0. (5 + ) ( + 7) 1. ( 6) ( 1). ( + 7) ( 7). ( 1) ( + 1). (y + ) 5. ( ) 6. ( + 6) + ( + 8 9) 7. (a a + 9) ( a + 5a + 1) 8. ( 7y + y + ) (y 5y + 8) 9. ( y ) ( y ) 0. (5a b) ( a b ) 1. ( + ) a 15a + 0a 5a. 1a 16a + 8a a ab 6. a b 8 0 y y a b 18 y 16ab 8. 9 y y y 9. y y y b + b b Factor completely.. 5a 5a y y 7. 8a b + 1a b a b

3 Updated Spring y 50. b 81c 51. (a b) + (a b) 5. + a 1a 5. 8y + y + 6y + 5. a a p + 5p a + 17a + 5a y + y 6. a a + 17a Solve the equations = = ( 5) = = = = 9 Solve the inequalities and graph on a number line y < ( 5) > 1 + Simplify. Leave your answer in simplest radical form, if necessary y y y

4 Updated Spring 009 Find the midpoint of the line segment joining the given points and the distance between the given points. 81. (, 9) and (5, ) 8. (0, ) and (, ) 8. (7, 9) and (1, 1) Find the slope of the line containing the given points. 8. (0, 5) and (, ) 85. (, 1) and ( 6, 5) 86. Find the slope of a line parallel to a line with slope. 87. Find the slope of a line perpendicular to a line with slope Find the slope of a line parallel to the line y = Find the slope of a line perpendicular to the line y = +. For the following linear equations, write each equation in the form y = m + b, find the slope and the - and y-intercepts, and graph y = y = 9. 5 y = 5 Graph the equations and find the slope of each line. 9. y = 5 9. = Find the length of the missing side of the right triangle cm 17 cm 15 cm cm

5 Updated Spring If l 1 and l are parallel, find angles, y and z. l 1 y z 110 l 98. If l 1 and l are parallel, find angles a, b and c. l a b c l 80 Solve the system of linear equations algebraically (use either substitution or addition). 99. y = y = 5 + 5y = 18 y = y = y = 1 + y = 1 6y = 8 For the following word problems, identify the variable used, set up an equation and solve algebraically. 10. Find the length of a rectangle whose perimeter is 10 meters and whose width is 17 meters. 10. Find two complementary angles such that the larger angle is 10 degrees more than three times the smaller angle The larger of two supplementary angles is 5 times the smaller angle. Find the larger angle.

6 Updated Spring A birdseed miture is made by combining sunflower seeds with cracked corn. If the sunflower seeds sell for $0.70 per pound and the cracked corn costs $0.5 per pound, how much of each should be used for 10 pounds of a birdseed miture that sells for $0.65 per pound? 107. The height of a triangle is 10 feet and the base is 1 feet. Find the area of the triangle One number is eight less than another number. The sum of the two numbers is 50. Find the smaller number The sum of three consecutive odd integers is 117. Find the three integers A company invested $10,000 in two money market accounts for one year, one earning 9% simple interest, the other 7.5% simple interest. How much did they invest in each account if the total interest earned was $855? 111. Calvin traveled 160 miles from Rochester to Binghamton in hours. Find his rate, to the nearest tenth. 11. In an isosceles triangle, two sides are equal. The third side is 8 inches less than one of the equal sides. The perimeter is 6 inches. Find the length of one of the equal sides. 11. A man 6 feet tall casts a shadow feet long at the same time a nearby building casts a shadow 8 feet long. Find the height of the building. 11. Denny takes hours to rake the leaves from his lawn. His son Jordan takes 5 hours. How long does it take if they work together?