Midterm 2 Preparation

Midterm 2: Version C

Find the solution set of the system graphically.

  1. \left\{ \begin{array}{rrrrrrr} 2x&-&y&-&2&=&0 \\ 2x&+&3y&+&6&=&0 \end{array}\right.

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

  1. \left\{ \begin{array}{rrrrr} 3x&-&4y&=&13 \\ x&+&y&=&2 \end{array}\right.
  2. \left\{ \begin{array}{rrrrr} 4x&-&3y&=&6 \\ 3y&+&4x&=&2 \end{array}\right.
  3. \left\{ \begin{array}{rrrrrrr} x&+&y&+&z&=&6 \\ &&2y&+&4z&=&10 \\ -2x&&&+&z&=&-3 \\ \end{array}\right.

Reduce the following expressions in questions 5–7.

  1. 36 + \{-2x - \left[6x - 3(5 - 2x)\right]\}^0 + 6x^3
  2. 6a^2b(a - 3)(a + 3)
  3. (x^2 + 3x + 5)^2

Divide using long division.

  1. (2x^4 + x^3 + 4x^2 - 4x - 5) \div (2x + 1)

For problems 9–12, factor each expression completely.

  1. x^2 + 17x - 18
  2. 2a^2 - 4ab - 30b^2
  3. 8x^3 - y^3
  4. 16y^4 - x^4

Solve the following word problems.

  1. The sum of a brother’s and sister’s ages is 30. Ten years ago, the brother was four times his sister’s age. How old are they now?
  2. Kyra gave her brother Mark a logic question to solve: If she has 18 coins in her pocket worth \$1.20, and if the coins are only dimes and nickels, how many of each type of coin does she have?
  3. Tanya needs to make 10 litres of a 25% alcohol solution for the University Green College Founders Social by mixing a 30% alcohol solution with a 5% alcohol solution. How many litres each of the 30% and the 5% alcohol solutions should be used?

<a class=”internal” href=”/intermediatealgebraberg/back-matter/midterm-two-version-c-answer-key/”>Midterm 2: Version C 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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