For the Final Exam, you should complete the exercises in the “MAT1275 FINAL EXAM” WebWork set, and submit the written solutions via Blackboard. **You will be graded on your written solutions!**

Here is an outline of the exercises and what you should include in your written solutions for each exercise:

**#1:** **Solving a quadratic equation** by factoring and using the ac-method (you may need to use the “ac-method”): write up your algebra

**#2: 2×2 linear system**: show all the algebra for solving the system algebraically; sketch the graphs of the lines and show they intersect at the solution you found algebraically

**#3: Equation of a circle: **show algebra for rewriting in standard form (hint: completing the square(s)); sketch a graph of the circle with the center and 4 points on the circle labelled with their (x,y) coordinates (as on Exam #2)

(hint: go straight up, down, left and right from the center to find the coordinates of 4 points!)

**#4: Solving a quadratic equation (using the quadratic formula):** show algebra for finding the solution(s) using the quadratic formula; simplify your solutions

**#5: Graph of a quadratic function:** show algebra for finding the intercepts and the vertex; sketch a graph of the parabola with the intercepts and vertex labelled with their (x,y) coordinates (as on Exam #2)

**#6: Complex number division or simplifying a fraction:** show all the algebra (hint: use the “complex conjugate” of the denominator or least common denominators, respectively)

**#7: Solving an exponential equation** (using logarithms): show the algebra to get the solution in “exact form” (i.e., in terms of logarithms) (hint: see the examples we did in class last week, and *Intermediate Algebra* Sec 10.5, Example 10.41)

**#8:** **Finding the trig ratios: **see the WebWork exercises in “TrigometryRatios” and examples we did in class:

- sketch the triangle
- show the algebra using the Pythagorean Theorem to solve for the missing sidelength
- write out all the trig ratios

**#9: Solving a right triangle (using trigonometry):** see the WebWork exercises in “SolvingRightTriangles”, examples we did in class and/or Example 5 in *Algebra and Trigonometry*, Sec 7.2

- sketch the right triangle
- solve for the missing angle (using the fact that the angles in the triangle add up to 180 degree)
- solve for the missing sidelengths using the basic trig ratios (sin, cos and/or tan) and some algebra

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