Midterm 3 Preparation and Sample Questions

Midterm 3: Version B

For problems 1–4, perform the indicated operations and simplify.

  1. \dfrac{5m^3}{4n^2}\div \dfrac{3m^3}{13n^3} \cdot \dfrac{12m^4}{26n^2}
  2. \dfrac{3x^2+9x}{3x+9}\div \dfrac{x^2+3x-18}{6x^2+18x}
  3. \dfrac{5x}{x+3}-\dfrac{5x}{x-3}+\dfrac{90}{x^2-9}
  4. \dfrac{\dfrac{9a^2}{b^2}-25}{\dfrac{3a}{b}+5}

Reduce the expressions in questions 5–7.

  1. \sqrt{72d^3}+4\sqrt{18d^3}-2\sqrt{49d^4}
  2. \dfrac{\sqrt{a^6b^3}}{\sqrt{5a}}
  3. \dfrac{\sqrt{5}}{3+\sqrt{5}}

Solve for x.

  1. \sqrt{4x+12}=x

For problems 9–12, find the solution set by any convenient method.

  1. \phantom{1}
    1. 2x^2=98
    2. 4x^2=12x
  2. \phantom{1}
    1. x^2-x-20=0
    2. x^2=2x+35
  3. \dfrac{x-3}{x+2}+\dfrac{6}{x+3}=1
  4. x^4-5x^2+4=0
  5. The length of a rectangle is 3 m longer than its width. If it has a perimeter that is 46 m long, then find the length and width of this rectangle.
  6. Find three consecutive even integers such that the product of the first two is 16 more than the third.
  7. A boat cruises upriver for 4 hours and returns to its starting point in 2 hours. If the speed of the river is 5 km/h, find the speed of this boat in still water.

<a class=”internal” href=”/intermediatealgebraberg/back-matter/midterm-3-version-b/”>Midterm 3: Version B Answer Key

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