Nonlinear Equations in One Variable and Systems of Equations Practice

Sample questions

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1. Sample 1difficulty 2/5

   Simplify: $\sqrt{72}$.

   • A

     $3\sqrt{8}$

   • B

     $6\sqrt{2}$

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   • C

     $8\sqrt{3}$

   • D

     $2\sqrt{6}$

   Why

   $\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}$.

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2. Sample 2difficulty 2/5

   Simplify: $\sqrt{50}$.

   • A

     $2\sqrt{5}$

   • B

     $25\sqrt{2}$

   • C

     $10\sqrt{5}$

   • D

     $5\sqrt{2}$

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   Why

   $\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$.

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3. Sample 3difficulty 2/5

   Solve: $\sqrt{x} = 7$.

   • A

     $\sqrt{7}$

   • B

     $\dfrac{1}{7}$

   • C

     $49$

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   • D

     $14$

   Why

   Square both sides: $x = 49$.

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4. Sample 4difficulty 2/5

   Solve $x^2 + 7x + 12 = 0$.

   • A

     $x = 3, 4$

   • B

     $x = -3, -4$

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   • C

     $x = 2, 6$

   • D

     $x = -2, -6$

   Why

   Factor: $(x+3)(x+4) = 0$, so $x = -3$ or $x = -4$.

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5. Sample 5difficulty 2/5

   Solve $2x^2 - 8 = 0$.

   • A

     $x = 2$ only

   • B

     $x = \pm 4$

   • C

     $x = 4$ only

   • D

     $x = \pm 2$

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   Why

   $2(x^2 - 4) = 0$, so $x^2 = 4$, giving $x = \pm 2$.

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