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Algebraic Expressions and Equations: Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Algebraic Expressions and Equations." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions.

Proficiency Exam

For problems 1 and 2 specify each term.

Exercise 1

((Reference)) 5 x+6y+3 z 5 x+6y+3 z size 12{5x+6y+3z} {}

Solution

5 x5 x size 12{5x} {}, 6y6y size 12{6y} {}, 3z3z size 12{3z} {}

Exercise 2

((Reference)) 8 m−2 n−48 m−2 n−4 size 12{8m - 2n - 4} {}

Solution

8 m8 m size 12{8m} {}, −2 n−2 n size 12{ - 2n} {}, -4

Exercise 3

((Reference)) In the expression −9 a−9 a size 12{ - 9a} {}, how many aa size 12{a} {}’s are indicated?

Solution

-9

For problems 4-9, find the value of each expression.

Exercise 4

((Reference)) 6 a−3 b6 a−3 b size 12{6a - 3b} {}, if a=−2a=−2 size 12{a= - 2} {}, and b=−1b=−1 size 12{b= - 1} {}.

Solution

-9

Exercise 5

((Reference)) −5 m+2 n−6−5 m+2 n−6 size 12{ - 5m+2n - 6} {}, if m=−1m=−1 size 12{m= - 1} {} and n=4n=4 size 12{n=4} {}.

Solution

7

Exercise 6

((Reference)) −x2+3x−5−x2+3x−5 size 12{ - x rSup { size 8{2} } +3x - 5} {}, if x=−2x=−2 size 12{x= - 2} {}.

Solution

-15

Exercise 7

((Reference)) y2+9 y+1y2+9 y+1 size 12{y rSup { size 8{2} } +9y+1} {}, if y=0y=0 size 12{y=0} {}.

Solution

1

Exercise 8

((Reference)) −a2+3 a+4−a2+3 a+4 size 12{ - a rSup { size 8{2} } +3a+4} {}, if a=4a=4 size 12{a=4} {}.

Solution

0

Exercise 9

((Reference)) −(5−x)2+7(m−x)+x−2 m−(5−x)2+7(m−x)+x−2 m size 12{ - \( 5 - x \) rSup { size 8{2} } +7 \( m - x \) +x - 2m} {}, if x=5x=5 size 12{x=5} {} and m=5m=5 size 12{m=5} {}.

Solution

-5

For problems 10-12, simplify each expression by combining like terms.

Exercise 10

((Reference)) 6 y+5−2 y+16 y+5−2 y+1 size 12{6y+5 - 2y+1} {}

Solution

4 y+64 y+6 size 12{4y+6} {}

Exercise 11

((Reference)) 14a−3 b+5 b−6 a−b14a−3 b+5 b−6 a−b size 12{"14"a - 3b+5b - 6a - b} {}

Solution

8 a+b8 a+b size 12{8a+b} {}

Exercise 12

((Reference)) 9 x+ 5 y−7+4 x−6 y+3(−2)9 x+ 5 y−7+4 x−6 y+3(−2) size 12{9x+5y - 7+4x - 6y+3 \( - 2 \) } {}

Solution

13x−y−1313x−y−13 size 12{"13"x - y - "13"} {}

For problems 13-22, solve each equation.

Exercise 13

((Reference)) x+7=15x+7=15 size 12{x+7="15"} {}

Solution

x=8x=8 size 12{x=8} {}

Exercise 14

((Reference)) y−6=2y−6=2 size 12{y - 6=2} {}

Solution

y=8y=8 size 12{y=8} {}

Exercise 15

((Reference)) m+8=−1m+8=−1 size 12{m+8= - 1} {}

Solution

m=−9m=−9 size 12{m= - 9} {}

Exercise 16

((Reference)) −5+a=−4−5+a=−4 size 12{ - 5+a= - 4} {}

Solution

a=1a=1 size 12{a=1} {}

Exercise 17

((Reference)) 4 x=1044 x=104 size 12{4x="104"} {}

Solution

x=26x=26 size 12{x="26"} {}

Exercise 18

((Reference)) 6y+3=−216y+3=−21 size 12{6y+3= - "21"} {}

Solution

y=−4y=−4 size 12{y= - 4} {}

Exercise 19

((Reference)) 5 m6=1035 m6=103 size 12{ { {5m} over {6} } = { {"10"} over {3} } } {}

Solution

m=4m=4 size 12{m=4} {}

Exercise 20

((Reference)) 7 y8+14=−1347 y8+14=−134 size 12{ { {7y} over {8} } + { {1} over {4} } = { { - "13"} over {4} } } {}

Solution

y=−4y=−4 size 12{y= - 4} {}

Exercise 21

((Reference)) 6 x+5=4 x−116 x+5=4 x−11 size 12{6x+5=4x - "11"} {}

Solution

x=−8x=−8 size 12{x= - 8} {}

Exercise 22

((Reference)) 4 y−8−6 y=3 y+14 y−8−6 y=3 y+1 size 12{4y - 8 - 6y=3y+1} {}

Solution

y=−95y=−95 size 12{y= { { - 9} over {5} } } {}

Exercise 23

((Reference) and (Reference)) Three consecutive even integers add to -36. What are they?

Solution

-14, -12, -10

Exercise 24

((Reference) and (Reference)) The perimeter of a rectangle is 38 feet. Find the length and width of the rectangle if the length is 5 feet less than three times the width.

Solution

l=13, w=6l=13, w=6 size 12{l="13", w=6} {}

Exercise 25

((Reference) and (Reference)) Four numbers add to -2. The second number is three more than twice the negative of the first number. The third number is six less than the first number. The fourth number is eleven less than twice the first number. Find the numbers.

Solution

6, -9, 0, 1

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