Algebra 2 by Richard Wright

Previous LessonTable of Contents Next Lesson

Are you not my student and
has this helped you?

1-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers.

    1-01

    Graph the system and estimate the solution.

  1. \(\left\{ \begin{align} y&=\frac{2}{3}x+1 \\ y&=-\frac{1}{2}x-\frac{5}{2} \end{align}\right.\)
  2. \(\left\{ \begin{alignat}{3} 2x&+&y&=&3 \\ x&-&y&=&0 \end{alignat} \right.\)

    3. Graph the system of inequalities.

  3. \(\left\{ \begin{align} y& < 2x+1 \\ y& ≥ -x-2 \end{align} \right.\)

    4. 1-02

    Solve the system algebraically.

  4. \(\left\{ \begin{align} y=x+2 \\ 2x-2y=3 \end{align} \right.\)
  5. \(\left\{ \begin{alignat}{3} 3x&-&2y&=&-7 \\ x&+&2y&=&11 \end{alignat} \right.\)
  6. Jim has two jobs. The first week he works 2 hours at job A and 3 hours at job B and earns $57.50. The second week he works 5 hours at job A and 2 hours at job B and earns $75. What is his pay rate at job A?
  7. How do you know if there are many solutions when you are solving algebraically?

    8. 1-03

    Is the given point a solution to the system?

  8. \(\left\{ \begin{alignat}{4} x&-&y&+&2z&=&-7 \\ &&y&-&3z&=&11 \\ x&&&+&z&=&-2 \end{alignat}\right.\) point (1, 2, −3)

    9. Solve the system algebraically.

  9. \(\left\{ \begin{alignat}{4} x&+&y&+&z&=&4 \\ -x&+&y&-&2z&=&-4 \\ &-&2y&-&z&=&-4 \end{alignat}\right.\)
  10. What does the graph of a linear equation in three variables look like?

    11. 1-04

    Simplify.

  11. \(\left[\begin{matrix}1&8\\-3&5\\\end{matrix}\right]-\left[\begin{matrix}-2&0\\-9&-4\\\end{matrix}\right]\)
  12. \(3\left[\begin{matrix}2&8\\\end{matrix}\right]\)
  13. \(2\left[\begin{matrix}3\\-4\\\end{matrix}\right]+\left[\begin{matrix}1\\5\\\end{matrix}\right]\)

    14. 1-05

    Simplify.

  14. \(\left[\begin{matrix}1&2\\\end{matrix}\right]\left[\begin{matrix}-2&3\\-1&4\\\end{matrix}\right]\)
  15. \(\left[\begin{matrix}1&2\\-2&-1\\\end{matrix}\right]\left[\begin{matrix}3&-3\\1&-1\\\end{matrix}\right]\)
  16. How do you know if two matrices can be multiplied?

    17. 1-06

    Evaluate the determinant.

  17. \(\left|\begin{matrix}3&-1\\2&7\\\end{matrix}\right|\)
  18. \(\left|\begin{matrix}1&3&0\\-2&-1&2\\4&0&-1\\\end{matrix}\right|\)
  19. Find the area of the triangle with vertices (1, 2), (0, −2), (3, 1).

    20. 1-07

  20. What is the product of a matrix with its inverse?
  21. Find inverse of \(\left[\begin{matrix}2&1\\1&-3\\\end{matrix}\right]\).
  22. Use an inverse to solve \(\left\{ \begin{alignat}{3} 2x&+&y&=&8 \\ x&-&3y&=&-3 \end{alignat} \right.\).

Answers

  1. (−3, −1)
  2. (1, 1)
  4. No solution
  5. (1, 5)
  6. $10 per hour
  7. All variables are eliminated and the result is a true statement.
  8. Yes
  9. (1, 1, 2)
  10. A plane
  11. \(\left[\begin{matrix}3&8\\6&9\\\end{matrix}\right]\)
  12. \(\left[\begin{matrix}6&24\\\end{matrix}\right]\)
  13. \(\left[\begin{matrix}7\\-3\\\end{matrix}\right]\)
  14. [−4 11]
  15. \(\left[\begin{matrix}5&-5\\-7&7\\\end{matrix}\right]\)
  16. The number of columns in the 1st matrix = number of rows in the 2nd matrix
  17. 23
  18. 19
  19. \(\frac{9}{2}\)
  20. Identity matrix
  21. \(\left[\begin{matrix}\frac{3}{7}&\frac{1}{7}\\\frac{1}{7}&-\frac{2}{7}\\\end{matrix}\right]\)
  22. (3, 2)