11.9: Proficiency Exam

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Proficiency Exam

For problems 1 and 2 specify each term.

Exercise \(\PageIndex{1}\)

([link]) \(5x + 6y + 3z\).

Answer: \(5x, 6y, 3z\)

Exercise \(\PageIndex{2}\)

([link]) \(8m - 2n - 4\)

Answer: \(8m, -2n, -4\)

Exercise \(\PageIndex{3}\)

([link]) In the expression \(-9a\), how many \(a\)'s are indicated?

Answer: -9

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

Exercise \(\PageIndex{4}\)

([link]) \(6a - 3b\), if \(a = -2\), and \(b = -1\).

Answer: -9

Exercise \(\PageIndex{5}\)

([link]) \(-5m + 2n - 6\), if \(m = -1\) and \(n = 4\).

Answer: 7

Exercise \(\PageIndex{6}\)

([link]) \(-x^2 + 3x - 5\), if \(x = -2\).

Answer: -15

Exercise \(\PageIndex{7}\)

([link]) \(y^2 + 9y + 1\), if \(y = 0\)

Answer: 1

Exercise \(\PageIndex{8}\)

([link]) \(-a^3 + 3a + 4\), if \(a = 4\).

Answer: 0

Exercise \(\PageIndex{9}\)

([link]) \(-(5 - x)^2 + 7(m - x) + x - 2m\), if \(x = 5\) and \(m = 5\).

Answer: -5

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

Exercise \(\PageIndex{10}\)

([link]) \(6y + 5 - 2y + 1\)

Answer: \(4y + 6\)

Exercise \(\PageIndex{11}\)

([link]) \(14a - 3b + 5b - 6a - b\).

Answer: \(8a + b\)

Exercise \(\PageIndex{12}\)

([link]) \(8x + 5y - 7 + 4x - 6y + 3(-2)\).

Answer: \(13x - y - 13\)

For problems 13-22, solve each equation.

Exercise \(\PageIndex{13}\)

([link]) \(x + 7 = 15\).

Answer: \(x = 8\)

Exercise \(\PageIndex{14}\)

([link]) \(y - 6 = 2\)

Answer: \(y = 8\)

Exercise \(\PageIndex{15}\)

([link]) \(m + 8 = -1\).

Answer: \(m = -9\)

Exercise \(\PageIndex{16}\)

([link]) \(-5 + a = -4\).

Answer: \(a = 1\)

Exercise \(\PageIndex{17}\)

([link]) \(4x = 104\).

Answer: \(x = 26\)

Exercise \(\PageIndex{18}\)

([link]) \(6y + 3 = -21\).

Answer: \(y = -4\)

Exercise \(\PageIndex{19}\)

([link]) \(\dfrac{5m}{6} = \dfrac{10}{3}\).

Answer: \(m = 4\)

Exercise \(\PageIndex{20}\)

([link]) \(\dfrac{7y}{8} + \dfrac{1}{4} = \dfrac{-13}{4}\).

Answer: \(y = -4\)

Exercise \(\PageIndex{21}\)

([link]) \(6x + 5 = 4x - 11\).

Answer: \(x = -8\)

Exercise \(\PageIndex{22}\)

([link]) \(4y - 8 - 6y = 3y + 1\).

Answer: \(y = \dfrac{-9}{5}\)

Exercise \(\PageIndex{23}\)

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

Answer: -14, -12, -10

Exercise \(\PageIndex{24}\)

([link] and [link]) 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.

Answer: \(l = 13\), \(w = 6\)

Exercise \(\PageIndex{25}\)

([link] and [link]) 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.

Answer: 6, -9, 0, 1