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Lesson 5-6: Use Properties of Operations to Add, Subtract, Multiply, and Divide — Practice Questions

  1. 1. Simplify the expression: $3(-7)^2 = \_\_\_$.

  2. 2. Evaluate the expression $3 - x^2$ for $x = -4$. The value is ___.

  3. 3. Evaluate $\frac{3b^3}{6} - \frac{4 - a^2}{8}$ for $a = 6$ and $b = -2$. The result is ___.

  4. 4. Solve the formula $A = \frac{h}{2}(b + c)$ for the variable $c$.

    • A. $c = \frac{2A}{h} - b$
    • B. $c = \frac{2A}{h} + b$
    • C. $c = \frac{A}{2h} - b$
    • D. $c = \frac{2(A - b)}{h}$
  5. 5. Simplify the expression: $\sqrt{13^2 - 5^2} = \_\_\_$.

  6. 6. Evaluate the expression $m^3 + n^3$ for $m = 3$ and $n = 2$. The value is ___.

  7. 7. Evaluate the expression $(m + n)(m^2 - mn + n^2)$ for $m = 3$ and $n = 2$. The value is ___.

  8. 8. Evaluate $\sqrt{x^3 + y^3 + z^3}$ for $x=3, y=4, z=5$. Round to three decimal places. The value is ___.

  9. 9. Solve the formula $S = \frac{n}{2}(a + f)$ for the variable $a$.

    • A. $a = \frac{2S}{n} - f$
    • B. $a = \frac{S}{2n} - f$
    • C. $a = 2Sn - f$
    • D. $a = \frac{2(S-f)}{n}$