Final Exam - Math

[Pages:10]Discrete math

Final Exam

1.) Find

-- 1)

2.) Find 3.) What is the 101st term of the sequence 11, 16, 21,26, ...? 4.) What's the 98th term of --5 --10. --20, --40,...?

5.) Suppose a set A contains 512 objects. How many 78 object subsets of A are there?

6.) How many ways are there to choose and order 57 objects from a collec tion of 367 objects?

7.) How many different ways are there to order 83 different objects?

8.) You're decorating a room by choosing a color to paint the walls with and a color of carpet to use for the floor. If you have 5 different colors of paint to choose from for the walls and 6 different colors of carpet to choose from for the floor, then how many different wall and floor color combinations could you create?

9. Write (7) as an integer in standard form.

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Algebra

10.) Write (%~) ~ as a rational number in standard form.

11. Write Y~ M 26 2 as an integer in standard form.

12.) `Write a? as an integer in standard form. (Notice that this is asking for the y-intercept ol tile graph of ax.)

13.) Write log~(1) as an integer in standard form. (The answer has some thing to do with the x-intercept of log~(x).)

14.) Write 1og2(~) as an integer in standard form.

15.) Find x where x3(x +

16.) Find z where 3ex(___~) 5 = 8.

17.) Find x where 5 logjx) + log6(x2) + 4 = 10.

18.) Find the inverse of g(x) = e2X + 3. (You can check you answer by seeing if g~' o g(x) = x.)

19.) What is the implied domain of f(x)

-- 2x + .~3 -- 5x. (Your

answer should be an interval. Does it make sense to put numbers from your

interval into f(x)? It should. Does it make sense to put numbers that aren't

in your interval into f x . It shouldn't.)

20.) Find Xd--2

11. 3

x2 Ic 2

21.) Complete the square: 2 -- 4x -- 7. (You can check your answer by using basic algebra rules to turn your answer into something that looks like ax2 + bx + c. That something should equal --x2 -- 4x -- 7.)

22.) Find a root of x3 2x2 x + 2

23.) Completel3 factor ~ -- 6x2 + 2x -- 6. (Hint: 3 is a root.) (Is your answer a product of only a ~onstant and maybe some linear and quadratic polynomials that have leading co fflcients equal to 1, and such that any of the quadratics in the product hay no roots? It should be.)

Linear algebra 24.) Find the product

(2 i"~f'i 3

ci i,1\~~o 1

25.) Write the following system of three linear equations in three variables as a matrix equation

x 6y-- z=9 3y-- 4z=5

--4x 3y-- 8z=O

26.) Solve for x. y, and z ii

/4 3 3\/xN fiN

/4 ~ 3\' /i ~

(31 2)(y)=(O) and (3121=11--11

--1 --1) \zJ \--2 ,J

\--1 --1 --1)

\--2 1 --s

Graphs 27.) Graph e~2 -- 1 and label its x-intercept.

28.) Graph 4(x + 1)2 + 2 and label its vertex.

29.) Graph -- log~(--x) and label its x-intercept.

30.) Graph p(x). (Label all x-iutercepts.) p(x) = --5x5 + 20x4 + lOx3 -- 70x2 + 15x -- 90 = --5@ + 2)(x -- 3)(x -- 3)(x2 + 1)

31.) Graph f(x) (Label all x-intercepts and all vertical asymptotes.)

f(x)

2x--2 --3x3--6x2--3z--6

2(x--1) --3(x+2)(z2+1)

32.) Graph

Ii ifz ................
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