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Math 1030 Practice Exam 2 March 9, 2012 Answer all questions below. Every question is worth the same number of points. You may use the available space for work, but must write ALL answers on the answer sheet. No cell phones, calculators, or notes are allowed during the exam. These rules will be strictly enforced. Name: _____________________________________________ Number: _______________ ‘lime or False: For #1-8 decide whether the statement is true or false. Write the entire word “flue” or the entire word word “False.” Tcac F&~Sc 1. a(b+c)=ab+ac 2. 3. (z+y)?~=z72±yhl m=~/~y~J 4. ~&±y=~€+~/~ 5. (xy)’~ 6. (. t = \,~y) if’ çy-=7 $~ ~ ± x3 W-a\s-c + Tcu~c 3z2 — 41 has S roots. Alegbra 9. Find x where (7— ±4 = 12 10. If g(x) is an invertible function, and g(2) = 7, then what is g~’(7)? 11. Find the inverse of f(x) = -~/2z ± 4. (You can check your answer by seeing if f’o f (z) 12. What is the implied domain of g(x) interval.) 5 = 2-~5z ± 1 C Page 2 — = 23? (Your answer should be an x) 13. Find the quotient 4x2 6x3 + 2 2x2—1 — ~-s,c 2. Z)( 42~ -\ 9, 4’,3 —~3% 4-7. -> ~~‘.S)( i-9 14. Find the quotient Lj 4x3 5x + 6 z—2 — a -5 (0 B 15. \‘Vhat is the slope of the straight line in 1R2 that passes through the points (2,4) and (5,10)? ‘5-a Page 3 :3— 16. Complete the square: Write 2z2 — 4z + 5 in the form afr + fl)2 + 25 It 17. How many roots does 2x2 — 6z + 10 have? 7-. b -~-)-aC~ 3(~- qQz)(~o) 40 .4> Lnb 13. Find the roots of —2x2 + 6x + 2 ‘94 -a Page 4 1~a_~g) ~, where a, fi, 7 E lit 20. (2 points) Completely factor —2z3 + 6z2 2z+ 6. (Hint: 3 is a root) (Your answer should be a product of a constant and maybe some linear and quadratic polynomials that have leading coefficients equal to 1, and such that any of the quadratics in the product have no roots.) — -2 C -ç -~ C 0 ~ 0 (%~_l~ ~ Page 5 Graphs 21. List all the monic linear factors of p(x) that you know from the graph below. .1 22. Graph —2~x 23. Graph ~/1~ — — 1 and label its x-intercept 1 and label the y-intercept. 24. Graph —3(x + 2)2 25. Graph 2x — — I and label its vertex. 3 and label its z- and y- intercepts. 26. Graph the polynomial p(x) —2(x — 2)Qv + 3)(z Page 6 — 4). Label the x- and y-intercepts. Number: Name: 12. 1. -3x F~dsc 2. Tcv~.e. 3. \tct\ce 4. Tciie~ 5. Tcuj’. 6. 8. Tcu...e ~se 9. ‘>(t~~F:~ •f. . ~ 10. + 13. 14. q~41x4l\ 4 17. as a 15. 16. i-q ~(~-O2~3 no ice 4-s ~~~i-JjZ~ 18. — / 19. 20. 2L 1L Page 7 -~ 4’~2~ (x-~) ( Cfl) ~x~\\ (~-~(X-3)~ (x-~) 23. 22. -2- 25. 24. -t I a) -3 q -3 26. Page 8 (0~-