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MTH-5111 Pretest

MTH-5111 Pretest. Determine the following given: a) f ◦ g b) g ◦ f c) f ◦ g(-2). f(x). g(x). Observe the graphs for f and g below and choose the operation that corresponds to the graph for function h. x. x. hx). TRUE. FALSE. x.

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MTH-5111 Pretest

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  1. MTH-5111 Pretest • Determine the following given: • a) f ◦ g • b) g ◦ f • c) f ◦ g(-2)

  2. f(x) g(x) • Observe the graphs for f and g below and choose the operation that corresponds to the graph for function h. x x hx) TRUE FALSE x • Given functions f and g below, determine whether the following statements are TRUE or FALSE.

  3. Given functions f and g below, determine whether the following statements are TRUE or FALSE. TRUE FALSE • The zero of f ◦ g is the same as that of g. • Functions f ◦ g and g are negative over [-2,1]. • Functions f ◦ g is increasing over its domain like f. • Functions f ◦ g and f have the same range. • Functions f ◦ g and f both have only one zero.

  4. Resolve the following inequalities algebraically:

  5. Volume (mm3) time (s) • Joelle is intrigued by a an hour-glass (4-minute) timer that she received as a gift. She notices that when she starts the timer, the top section has more sand but as the sand trickles through, the bottom section will have more. The function provided determines the relationship between the volume of sand (in the section with the lesser amount) in cubic millimeters and time in seconds: • At what time is the volume of sand greater than 75 mm3 in both sections?

  6. B 12.8 cm 5 cm C D A H E C B D E 2 G O F A • Solve the following problems:

  7. B G F O C A D E TRUE FALSE • In a circle with centre O, A is a point of tangency of segment AB and both BE and BC are secants and BE is an angle bisector of ABC. Determine whether the following statements are TRUE or FALSE.

  8. C C E E B B O O D D STATEMENT JUSTIFICATION 1. Draw a segment from E to D. By Construction A A 2. mBED = mBAD = 90° Theorem 60 4. mEBD = mBDA 5. mBDC = ___________ Theorem 73 6. ΔBCD ~ ΔBDA 7. mABD = mBCD Theorem 50b • Complete the following proof: Hypothesis: Conclusion: mABD = mBCD

  9. B C D STATEMENT JUSTIFICATION A E Hypothesis: _________________________ __________________________ Conclusion: __________________________

  10. Solve the following problems and show the steps to your solutions. • a) The given figure represents a poster advertising ice cream cones where the circle represents the scoop of ice cream and has the equation: (x – 5)2 + (y – 2)2 = 13. The cone for the ice cream can be represented by an absolute value function: y O A B x The circle and the absolute value function intersect at their zeros. Determine the area of the cone (the shaded area).

  11. b) Two lines meet at point C. Line AC is represented by the equation: • It is a secant to a circle having the equation: (x – 5)2 + (y – 7)2 = 18. Line CD is tangent to this circle at point D (8,4) and y C B O A D x Calculate the measure of angle C to the nearest degree.

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