Midterm 2 Preparation

Midterm 2: Version B

Find the solution set of the system graphically.

  1. \left\{ \begin{array}{rrrrr} x&+&y&=&5 \\ 2x&-&y&=&1 \end{array}\right.

For problems 2–4, find the solution set of each system by any convenient method.

  1. \left\{ \begin{array}{rrrrrrr} 4x&+&3y&=&8&& \\ &&x&=&4y&+&2 \\ \end{array}\right.
  2. \left\{ \begin{array}{rrrrr} 5x&-&3y&=&2 \\ 3x&+&y&=&4 \end{array}\right.
  3. \left\{ \begin{array}{rrrrrrr} x&+&y&+&z&=&3 \\ x&&&-&2z&=&-7 \\ &&-2y&+&4z&=&20 \end{array}\right.

Reduce the following expressions in questions 5–8.

  1. 5 - 3\left[4x - 2(6x - 5)^0 - (7 - 2x)\right]
  2. 3a^2(a + 3)^2
  3. (x^2 + x  + 5)(x^2 + x  - 5)
  4. \left(\dfrac{x^{4n}x^{-6}}{x^{3n}}\right)^{-1}

For problems 9–12, factor each expression completely.

  1. 14axy - 6az - 7xy + 3z
  2. a^2 + 2ab - 15b^2
  3. 2x^3 + 8x^2 - x - 4
  4. 27x^3 + 8y^3

Solve the following word problems.

  1. The sum of the ages of a father and his daughter is 38. Six years from now, the father will be four times as old as his daughter. Find the present age of each.
  2. A 90 kg mixture of two different types of nuts costs \$370. If type A costs \$3 per kg and type B costs \$5 per kg, how many kg of each type were used?
  3. A student lab technician is combining a 10% sulfuric acid solution to 40 ml solution at 25% to dilute it to 15%.  How much of the 10% solution does the student need to add?

<a class=”internal” href=”/intermediatealgebraberg/back-matter/midterm-two-version-b-answer-key/”>Midterm 2: Version B Answer Key

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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