Math 150: Intermediate Algebra Spring 2012 Fall 2005 : Mock Exam 4 (z z

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Philomena Marsh
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1 Math 150: Intermediate Algebra Spring 01 Fall 005 : Mock Eam 4 (z 9. - z NAME 10.6) TICKET # [ 13 problems: 10 points each ] Answer problems and epress your answers appropriately, that is ; simply state answers to simplification/evaluation problems as epressions, and epress solutions to equations in solution set notation. ALL WORK MUST BE SHOWN! 1. How many and of what type (comple, rational, or irrational) are the solutions to the quadratic equation: [Careful: The equation must be of the form a b c 0, before the discriminant can be used.] 3 5 Solve the given rational equation. Remember to check your solutions by insuring that they yield true statements. Another way to check the solutions is to compare them to the domain restricted value(s). Don t forget to use solution set notation m m 9 4

2 3. Use substitution to solve the following equation, which is quadratic in form. Don t forget to use solution set notation. 4 4k 13k Francis has a backyard that is of dimensions 0 meters by 30 meters. He wants to leave an even strip of grass of uniform width around the perimeter of the garden. What will the dimensions of the garden be if he has enough grass seed for an area of 184 square meters, and intends on using all of it? 0m Garden 30m

3 5. On the graph paper provided, accurately graph (including at least the verte and the two pairs of symmetrical points discussed in class) the following (vertical) parabola. y y ( 3) 5 6. If f ( ) 16 5 (A) Complete the square to find the verte and (B) Verify using the formula (when a b c 0, the verte can be found (C) (D) (E) b b a a by the point V (, f ( )). State whether the graph opens upward, downward, to the left, or to the right. (Hint: It can only be one of these four possibilities.) Also state whether the graph is wider, narrower, or the same shape as the graph of ( the mother of all quadratics ) y Lastly, if the quadratic yields a vertical parabola, use the discriminant to determine the number of and type (comple, rational, or irrational) of the -intercepts.

4 7. The function h( t) 16t 4t models the height (in feet) of a vertically (straight upwardly) thrown projectile, which is acted upon by gravity and was initially projected upwards at a velocity of 4 ft. sec By whichever means you wish, find the time at which the projectile reaches its maimum height, and what that maimum height is. Your answer may be epressed in ordered pair notation, but units need to included in the ordered pair. May I suggest that you find the verte and not make this harder than it is. 8. If it eists (that is, if the original function is one-to-one ), find the inverse function to the following function and then simultaneously graph (on the graph paper provided) them both on the same set of aes. Also graph the line y = to show the symmetry. [If it does not eist, give at least one pair of points at which the original function violates the horizontal line test.] g( ) 3, 3 y

5 9. Simultaneously (on the same set of aes), graph (on the graph paper provided) the following functions, f() and g(): Use the following T-tables to help you with the plotting of points. Note any symmetry, and from these observations, can you conclude anything about the relationship between these functions? Note this in the CLAIM section. f ( ) 3 and g( ) log 3 f() g() y CLAIM: 10. Substantiate your claim in problem # 9, by using both the following facts about inverse functions: f ( f 1 1 ( )) and f ( f ( ))

6 11. Evaluate/Simplify the following ( points for each sub-problem): a) 11 log (11) b) log 6( ) c) log 1 (64) d) log 3( ) e) log 49(7) Use logarithms and the change of base formula to solve the following eponential equations (5 points for each sub-problem). Don t forget to use solution set notation. a) 3 8 b) (round your answer to the nearest thousandth) 0.09 t 1000 e 6000 (round your answer to the nearest tenth)

7 13. Solve the following logarithmic equation that involves a base other than 10. Don t forget to use solution set notation. log 3(( 1) ) 4 Etra Credit (6 points): Use substitution to solve for all the solutions to the following equation, which is quadratic in form. Don t forget to use solution set notation

Math 155 Intermediate Algebra Practice Exam on Chapters 6 & 8 Name

Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 Name Find the function value, provided it eists. 1) f() = 7-8 8 ; f(-3) Simplify by removing a factor equal to 1. ) 5 + 0 + 3) m - m - m Find