Brooklyn Technical High School
Exam #2
Summer 2016
Discovery Math
Name ____________________________
Instructor: Mr. Rodriguez Period ______
1) Factor completely: 12 x2  16 x  3
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2) Factor completely: 2bx  4by  cx  2cy
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3) Simplify completely.
5x  x2
x 2  25
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4) Express the product of the algebraic fractions in simplest form:
 2 x  y  x  3 y   y 2  2 x  y 
xy  2 x  y 
xy  x  3 y 
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5) Express the quotient in simplest form
a 3  b3 a 2  b 2

b2  ab a  b
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6) Combine and express in simplest form
y
y 3

y  2y y  2
2
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7) Simplify completely:
y x

x y
x y
xy
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8) Solve for all values of x that satisfy the equation:
4.3  x  5  5  2.7 x  9
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9) Arthur weighs 54 lbs. more than Lily. Their combined weight is 280 lbs. less than 6 times Lily’s weight. How
much does Arthur weigh?
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10) Mike has 60 coins in his pocket all quarters and nickels. The total is $5.60. How many nickels does Mike have
in his pocket?
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11) One third of the sum of the two smallest of 3 consecutive odd integers is 91 less than the largest of the 3
consecutive odd integers. Find the value of the largest consecutive odd integer.
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12) Two planes leave the same point at 8 AM. Plane 1 heads East at 600 mph and Plane 2 heads West at 450 mph.
How long will they be 1400 miles apart? At what time will they be 1400 miles apart? How far has each plane
traveled?
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13) In a candy shop, chocolate which sells for $4 a pound is mixed with nuts which are sold for $2.50 a pound are mixed to
form a chocolate-nut candy which sells for $3.50 a pound. How many pounds of nuts are used to make 30 pounds of the
mixture?
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14) Concrete can be made by mixing cement, sand, and gravel in the ratio 3:6:8. How much cement is needed to make
1700 m3 of concrete?
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