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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