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Algebra II / Mr. Hansen |
Name:
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Test on Chapters 3 and 4
Time limit: 26 minutes (39 minutes for extended
time). Calculator is allowed only on question #1. Do not spend too much time
on any single problem. Point values are shown on the board.
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Part I: Calculator Portion |
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1. |
Consider the following
system of equations:
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(a) |
Write the solution set. You
do not need to show work. |
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(b) |
Use determinant notation to write the numerator determinant for y. Please remember that determinants
are square (same numbers of rows and columns). |
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(c) |
I will tell you that the denominator
determinant for this system is –20. Compute the numerator determinant for y, i.e., the numeric value for the
grid pattern you wrote in part (b). You do not need to show work. |
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Part II: Non-Calculator Portion |
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2. |
Compute each of the
following determinants. Show your work.
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3. |
Prove that your solution
set to #1 satisfies the third and fourth equations. |
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4. |
How many equations do you
need to check in #1 if you were to be thorough? _________ |
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5. |
Find an equation of the line
through (3, –1) that is perpendicular to the line having x-intercept 3 and y-intercept
4. |
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6. |
Sketch each line and write
an equation. |
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(a) . . . vertical,
crossing the x-axis 3 units to the
right of the origin |
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(b) . . . having x-intercept and y-intercept both equal to –2 |
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(c) . . . passing through
(1, –p) with slope 2 |
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(d) . . . passing through
(2, 2.5) with undefined slope |
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7. |
(a) Graph the solution set
of the following system of inequalities. |
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(b) What do the letters rref stand for? |
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Write the solution set for each
of the following rref augmented matrices. |
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(c) |
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(d) |
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(e) |
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