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Name __________________________________ Math 1302 – Exam II – March 6, 2006 Show Work on all problems. If you give me the answer only, I will count it wrong. Make sure to begin with #1. You should complete every problem that appears easy to you – This test is written so that you can complete about 60- 70 % within the first 15 minutes and the remaining 30 % in about 40 minutes. Do not spend time trying to remember how to do a problem at the very beginning – save those for the end of class. 1. Number of absences up to today. ___________ Give me a close approximation if not sure of exact number. A blank answer will result in points counted off. 2. State the quadratic formula that is used to solve equations of the form ax2 + bx + c = 0 3. Assuming that a) ( 2 – 3x ) ( 2 + 3x ) represents a difference of squares, what is the product in simplest form? _____________________ b) ( 3 + 4y)( 9 – 12y + 16y2 ) represents a sum of cubes, what is the product in simplest form ? ______________________ 4. Factor each of the following polynomials (completely). If polynomial does not factor, then indicate by writing prime. a) 4x3 - 9y2x = ____________________ b) 5 + 40x3 = _____________________ c) ( x + 2)2 - 9 = ___________________ 5. Simplify the following algebraic fractions. Perform the given operation and simplify. a) b) x 1 3x 3 = 3 8 7x 2 x 6 = 3x 4 3x 4 c) ( (2 d) e) 1 4x 2 1 = ) 2 x 4x 2x 3 x 2 x = 4x x 4 1 1 x 1 1 x = 6. George starts at 8:00 AM and works for three hours. Al starts helping at that point and usually Al can complete the job by himself in 9 hours. At what time will they finish ? Define your variable(s) and set up an equation in one variable. I want the equation – not the solution. Assume that George can do the job in 12 hours if he works by himself. 7. What quadrant is the point in ? a) A (-2, 12 ) → ______________________ b) B( - 2, - 2 ) → ___________________ 8. Write the four basic forms of in in their simplest form ____________ ______________ _____________ _______ 9. Write in one of the simplest forms of i n . a) i19 = _______ c) ( i3257)4 = ________ d) i – 15 = _________ 10. Simplify. Do not use your calculator on this – not even for checking purposes. 16 + 3 - 64 + 2 4 - 3 8 = _____________ 11. Simplify – write your final answer in the form a + bi. ( 2 – 3i) + ( 3 + 5i) = _______________ 3i = ____________ 3i 2i ( 1 – 3i) = ________________ i _________ 1 3i 12. Plot the following complex number; - 4 + 3i . Find its modulus. _____________ 13. Find the conjugate of -4 – 2i → ____________ 14. 6i → ________________ What is the imaginary part of the complex numbers -1-2i →_____ 15. Find the solution of each of the following. a) 2x2 = 7x c) 3x3 = 12x b) 180 – 5x2 = 0 d) 4x2 - 3x - 7 = 0 16. More equations. a) x4 - 3x2 - 4 = 0 → x = ________________________ b) x ( x + 3 ) ( 2x – 1 ) ( x2 + 4 ) = 0 → x = _________________ 17. Find the value of the discriminant that corresponds to the equation 5x2 – 4x + 2 = 0 → ________________ 18. Find the solution by using the quadratic formula. x2 + 4 = 0 19. Solve by completing the square – no other method will do. 2x2 - x - 8 = 0