Math Final Exam Practice Test December 2, 2013

Transcription

1 Math Final Exam Practice Test December 2, 2013 Note that this Practice Test is longer than the Final Exam will be. This way you have extra problems to help you practice, so don t let the length scare you. Try not to use your notes while you work on these problems. NO CALCULATORS You might find the following formulas helpful. The same formulas will be given to you on the actual exam. Make sure you know how to use them! ax 2 + bx + c = a(x + b 2a )2 + c b2 4a α 1,2 = b ± b 2 4ac 2a a n = a 1 + d(n 1) n a i = n(a 1 + a n )/2 i=1 a n = a 1 r n 1 i=1 a i = 1 1 r

2 Math Final Exam Practice Test Page 2 of 41. MULTIPLE CHOICE ANSWERS 1. 2.

3 Math Final Exam Practice Test Page 3 of Suppose f(x) is the piecewise dened function given below. Graph f(x). f(x) = { x + 1 if x (, 2) x + 3 if x [ 2, ) 4. Suppose f(x) is the piecewise dened function given below. Graph f(x). f(x) = { x 2 if x 5 1 if x = 5

4 Math Final Exam Practice Test Page 4 of Suppose f(x) is the piecewise dened function given below. Graph f(x). f(x) = { x 3 if x (, 1) 2 if x [1, ) 6. Suppose f(x) is the piecewise dened function given below. Graph f(x). f(x) = { 3x if x 2 x 2 if x = 2

5 Math Final Exam Practice Test Page 5 of Whats the slope of the line 30x 6y = 3? 8. Whats the slope of the line 10x + 5y = 4? 9. Whats the slope of the line 6x + 3y = 237?

6 Math Final Exam Practice Test Page 6 of 41 Each of the systems below has a unique solution. Find the solution. 10. { 8x + 4y = 12 x 7y = 21

7 Math Final Exam Practice Test Page 7 of { 10x 3y = 52 3x + y = 16

8 Math Final Exam Practice Test Page 8 of { 3x = 5 2x 3y = 12

9 Math Final Exam Practice Test Page 9 of { 2x + 8y = 8 3x + 6y = 12

10 Math ( ) ( ) Final Exam Practice Test Page 10 of Find Find ( ) ( ) Find 3 ( ) Find 11 ( ) 3 2

11 Math ( Final ) Exam ( Practice ) Test Page 11 of Find the product Find the product ( ) ( )

12 Math Final Exam Practice Test Page 12 of Find the product Find the product

13 Math Final Exam Practice Test Page 13 of Find the determinant ( ) 2 1 det Find the determinant det ( )

14 Math Final ( Exam ) Practice Test Page 14 of What is the inverse of? What is the inverse of ( ) 1 1? 2 5

15 Math Final Exam Practice Test Page 15 of Use that = to find a solution for 4x + 3y + 3z = 2 3x + y + 2z = 4 x y z = 22

16 Math Final Exam Practice Test Page 16 of Use that = to find a solution for 3x y z = 1 8x + 10y + 3z = 7 2x + 3y + z = 4

17 Math Final Exam Practice Test Page 17 of (2 pt) Which of the following is a true statement? (a) Z R Q N (b) N Z Q R (c) Z N Q R (d) N Q R Z 2. (2 pt) } +} (a) True (b) False 3. (2 pt) } +} (a) True (b) False

18 Math Final Exam Practice Test Page 18 of (2pt) Decide whether the given sequence is arithmetic, geometric, or neither. 2, 5, 10, 8,... (a) arithmetic (b) geometric (c) neither 5. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither. 2, 4, 8, 32,... (a) arithmetic (b) geometric (c) neither 6. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither. 3, 7, 24, 31,... (a) arithmetic (b) geometric (c) neither 7. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither. 6, 36, 66, 96,... (a) arithmetic (b) geometric (c) neither

19 Math Final Exam Practice Test Page 19 of (4pt) Find i=1 (a) 5 (b) 500 (c) 100 (d) (4pt) Find 40 i=1 i (a) 40 (b) 1 (c) 1640 (d) 820

20 Math Final Exam Practice Test Page 20 of (4pt) What is the sum of the first 41 terms of the sequence 0, 2, 4, 6,...? (a) 1640 (b) 2 (c) 80 (d) (4pt) What does the following series equal: ?

21 Math Final Exam Practice Test Page 21 of (4 pt) You have three pairs of shoes, five pairs of pants, six shirts, two jackets, and three hats to choose from. How many different outts can you put together that use one pair of shoes, one pair of pants, one shirt, one jacket, and one hat? Your answer should be a real number. 13. (4 pt) There are 9 people on a boat. One person needs to be the captain, one needs to be the first mate, and you need a person to swab the decks (no person can do more than one job). How many different ways can those three jobs be filled by the 9 people on board? Your answer should be a real number.

22 Math Final Exam Practice Test Page 22 of (4 pt) A sports team is selling season ticket plans. They have 15 home games in a season, and they allow people to purchase tickets for any combination of 9 home games. How many ways are there to choose a collection of 9 home games? Your answer may have factorials in it. 15. (4 pt) What is ( ) 50? Simplify your answer all the way. 3

23 Math Final Exam Practice Test Page 23 of (2 pt) Draw the first 10 rows of Pascal s Triangle. 17. (4 pt) Use the Binomial Theorem and Pascal s Triangle above to expand (x 1) 8. Simplify each term as much as possible.

24 Math Final Exam Practice Test Page 24 of (1pt Extra Credit) What does the following series equal: ? 19. (2 pts) (True/False) 7x x 4 3x 3 7x 2 + 2x 1 has 8 roots. 20. (2 pts) (True/False) 3x 5 has 1 root.

25 Math Final Exam Practice Test Page 25 of (2 pts) What is the slope of p(x) = 13x + 2? 22. (2 pts) What is the slope of p(x) = πx + 97? 23. (3 pts) Graph p(x) = 3x (3 pts) Graph p(x) = 2x + 3

26 Math Final Exam Practice Test Page 26 of 41

27 Math Final Exam Practice Test Page 27 of (2 pts) What is the y intercept of p(x) = 5x ? 26. (2 pts) What is the x intercept of p(x) = 5x ?

28 Math Final Exam Practice Test Page 28 of 41 For the next 7 questions consider p(x) = 5x 2 15x (3 pts) Complete the square 28. (3 pts) What s the vertex of the corresponding parabola? 29. (2 pts) Is the parabola opening up or down? 30. (3 pts) What s its discriminant? 31. (2 pts) How many roots does it have?

29 Math Final Exam Practice Test Page 29 of (4 pts) What are its roots? 33. (5 pts) Use the previous 6 questions to graph p(x) labeling its vertex and any x and y intercepts.

30 Math Final Exam Practice Test Page 30 of 41 For the next 7 questions consider p(x) = 4x 2 x (3 pts) Complete the square 35. (3 pts) What s the vertex of the corresponding parabola? 36. (2 pts) Is the parabola opening up or down? 37. (3 pts) What s its discriminant? 38. (2 pts) How many roots does it have?

31 Math Final Exam Practice Test Page 31 of (4 pts) What are its roots? 40. (5 pts) Use the previous 6 to graph p(x) labeling its vertex and any x and y intercepts.

32 Math Final Exam Practice Test Page 32 of (8 pts) Fully factor 4x 3 20x x 3

33 Math Final Exam Practice Test Page 33 of (8 pts) Fully factor 5x 3 9x 2 + 8x 20

34 Math Final Exam Practice Test Page 34 of (4 pts) Graph (x 1)(x 2)(x 2)(x 3)(x 2 + x + 5) making sure to show all the x intercepts and behavior on the far right and left.

35 Math Final Exam Practice Test Page 35 of (4 pts) Graph 13x(x + 1)(x 2)(x + 2)(x 3)(2x 2 + 3x + 3) making sure to show all the x intercepts and behavior on the far right and left.

36 Math Final Exam Practice Test Page 36 of (3 pts) If a is a real nuimber, a 0 = (a) 0 (b) 1 (c) a (d) 46. (3 pts) If a is a real nuimber, a 1 = (a) 0 (b) 1 (c) a (d) 47. (3 pts) (a) 4 (b) 8 (c) 8 (d) 1 8 (e) 1 8 (f) 12 (g) Not Defined

37 Math Final Exam Practice Test Page 37 of (3 pts) If 8 x = 1 4, then x = (a) 2 (b) 2 (c) 1 2 (d) 1 2 (e) 3 2 (f) 2 3 (g) 3 2 (h) 2 3 (i) Not Defined 49. (3 pts) If a is a real nuimber, log a (1) = (a) 0 (b) 1 (c) a (d) (e) Not Defined 50. (3 pts) log 2 (4) = (a) 0 (b) 1 (c) 2 (d) 1 2 (e) 16

38 Math Final Exam Practice Test Page 38 of (3 pts) log 5 ( 1 25 ) = (a) 0 (b) 1 (c) 2 (d) 1 2 (e) 2 (f) 52. (5 pts) Solve for x: 5 3x 2 = 125

39 Math Final Exam Practice Test Page 39 of (5 pts) Solve for x: log 2 (x) log 2 (x + 4) = (5 pts) Solve for x: log 3 (15x) + log 3 (x + 1) = 4

40 Math Final Exam Practice Test Page 40 of (10 pts) Graph f(x), making sure to show VERTICAL ASYMPTOTES, X INTER- CEPTS, and BEHAVIOR AT FAR RIGHT AND FAR LEFT. f(x) = 2(x 3)(x + 1) x(x + 3)

41 Math Final Exam Practice Test Page 41 of (10 pts) Graph f(x), making sure to show VERTICAL ASYMPTOTES, X INTER- CEPTS, and BEHAVIOR AT FAR RIGHT AND FAR LEFT. f(x) = 5(x 3)(x + 1)(x 2) x(x + 3)(x 2 5x) The End.