Midterm 2 Preparation

Midterm 2: Version E

Find the solution set of the system graphically.

  1. \left\{ \begin{array}{rrrrr} x&-&y&=&-3 \\ x&+&2y&=&3 \end{array}\right.

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

  1. \left\{ \begin{array}{rrrrr} 2x&-&5y&=&-2 \\ 3x&-&4y&=&4 \end{array}\right.
  2. \left\{ \begin{array}{rrrrr} 4x&+&3y&=&-29 \\ 3x&+&2y&=&-21 \end{array}\right.
  3. \left\{ \begin{array}{rrrrrrr} x&+&y&-&3z&=&0 \\ &&2y&-&2z&=&-12 \\ 2x&-&3y&&&=&16 \end{array}\right.

Reduce the following expressions in questions 5–7.

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

Divide using long division.

  1. (3x^3 + 18 + 7x^2) \div (x + 3)

For problems 9–12, factor each expression completely.

  1. x^2 + 4x - 21
  2. 4x^3 + 4x^2 - 9x - 9
  3. 8x^3 - 27y^3
  4. x^4 - 624x^2 - 625

Solve the following word problems.

  1. The sum of the ages of a boy and a girl is 20 years. Four years ago, the girl was two times the age of the boy. Find the present age of each child.
  2. How many ml of a 16% sulfuric acid solution must be added to 20 ml of a 6% solution to create a 12% solution?
  3. A 60 kg blend of cereals and raisins is sold for \$213. If the cereal sells for \$3.40 per kg and the raisins sells for \$3.90 per kg, how many kg of each grade were used?

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

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