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Math 1050 Section 1 Final Name: Read all directions carefully and show all your work for full credit. Each question is worth 5 points for a total of 100 points. Good Luck!!! 1. Solve the following system of equations using Gaussian Elimination, GaussJordan Elimination, or Crammer’s Rule. x − 3y + z = 4 2x − 7y + 2z = 7 −3x + 9y − 4z = −11 2. Find all solutions to the equation |x − 1| = 4. 4. Sketch the graph of the function f (x) = −(x − 3)2 + 2 below. 3. Find an equation for the line passing through the points (-2,3) and (5,6). 5. If h(x) = x3 − 4x + 1 and g(x) = x2 − 2 then find (h ◦ g)(x). 6. Find the coordinates of the vertex of the parabola −3x2 + 12x − 5. 8. Sketch the graph of the function (x+ 4)2 (x−2)(x+1)2 using the x-intercepts. 9. Perform the division 7. Factor the following polynomial completely 2x3 − 9x2 + 4x + 15. x3 − 4x2 + 2x − 1 x−2 10. Condense the following to a logarithm of a single quantity. 12. Sketch the graph of the function G(x) = log2 (x). 1 5log2 (x + 3) − log2 (2x − 1) + log2 5 3 2 11. Find all solutions to 34x 32x = 3−3x+6 . 13. Find the determinant 2 7 −1 3 0 −9 −4 1 0 14. Find g(2) where g(x) = 4x4 − 9x3 + 6x2 − 10x + 9 15. Perform the following matrix multiplication −4 1 2 −1 3 · 2 7 0 5 −7 −1 3 16. Write out the first 5 terms of the sequence an = (−1)n 2(n − 1). 17. Find P4 n=1 (2 + 3n−1 ). 18. Simplify (4 − 2i)2 . (IE write as a complex number of the form a + bi where a, b in R) 19. Expand (3x + 2)4 using Pascal’s triangle. 20. Jill has a job that pays $4 on the first day. Every subsequent day she gets paid 3 dollars more than she did the previous day. For example on day 2 she gets $7 and on day three she gets $10 and so on. How much does Jill make in 100 days? To answer this question you should use one of the formulas below. 1 − rn n Sn = (a1 +an ) or Sn = a1 2 1−r