Math 150 – Fall 2015
Final Exam Review
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Final Exam Examples
This is not a comprehensive review; just a few extra examples.
Example 1. Fully simplify cos sin−1 −4
+ tan−1 56 .
7
Example 2. Write functions of the fom f (x) = a sin k(x−a)+b and f (x) = a cos k(x−
a) + b, where a, k, and b are positive and as small as possible.
Example 3. Find the points that solve the system of equations below. Give your
answer as the SUM of the x-values of the solutions.
4y + (x − 2)2 = 9
(x − 2)2 + y 2 = 5
Math 150 – Fall 2015
Final Exam Review
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Example 4. Determine the center and radius of the circle 2x2 + 2y 2 − 6x + 12y − 7 = 0.
Example 5. Algebraically calculate and simplify the inverse of the function f (x) =
5(1 − 3x)2 + 4, where x ∈ (−∞, 31 ].
Example 6. For the number z = 2i + 3, calculate |z| · (5 − 3i) · z.
Math 150 – Fall 2015
Final Exam Review
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Example 7. Solve the inequality and express your answer in interval notation.
x2 +10
x+5 ≤ 2
Example 8. In the real numbers, fully simplify the expression
p
6
128x2 y 1 8z 7 .
Example 9. Find the difference quotient of f (x) = −3x2 + x and fully simplify your
answer.
Example 10. Solve the equation 4x2 − 5x − 2 = 0 over the complex numbers.