Algebra 4 [PRACTICE] Final Exam Part 1 1. Which function is shown in the graph?

A. y = −(x − 2)(x − 8)

B. y = − x − 4( )2+ 16

C. y = x2 − 8x + 16

D. y = (−x − 4)2 + 16

2. The graph of a rational function has asymptotes that intersect at the point 6, 4( ). Choose the correct

equation of the function.

A. y = 4x + 66x − 4

B. y = 6x + 44x − 6

C. y = 6x + 64x + 4

D. y = 8x2x − 12

3. The tables below give the balances A (in dollars) owed on two different loans over time t (in years). Determine the type of function represented by the data in each table.

A. Loan #1 and Loan #2 are both represented by a linear function.

B. Loan #1 and Loan #2 are both represented by an exponential function.

C. Loan #1 is represented by an exponential function and Loan #2 is represented by a linear function.

D. Loan #1 is represented by a linear function and Loan #2 is represented by an exponential function.

4. Find the expression with the smallest value.

A. 32 B. 256 3/4 C. 16( )3

D. They are all equal.

5. Evaluate the logarithm using and log325

A. 2.321 B. 0.430 C. -0.834 D. 0.9244

3log 2 0.631≈ 3log 5 1.465,≈

Loan #1

Time, t 1 2 3 4

Balance, A 16,000 15,620 15,240 14,860

Loan #2

Time, t 1 2 3 4

Balance, A 16,000 14,400 12,960 11,664

6.State the domain of the following function: f (x) = x + 5x − 6

A. All Real Numbers except -5.

B. All Real Numbers except x =6.

C. All Real Numbers except x = 5.

D. All Real Numbers except x = -6.

7. You have bowled 5 games and your average score is 140 points. You think you can score 160 points on each remaining game. How many more games do you need to bowl to raise your average game score to 150 points?

A. 5 games

B. 7 games

C. 9 games

D. 12 games

8. Multiply: x2 + x − 62x + 6

•x −1

x2 − 4x +3

A. 12

B. x − 22x − 6

C. x −1x −3

D. x − 62x

9. You invest $8000 with an interest rate of 4.75% for 8 years. How much do you have at the end of 8 years if it is compounded continuously?

A. $10856.07

B. $357609.47

C. $30400

D. $11698.27

10. Find the sum (k2 +1)k=3

6

∑

A. 10 B. 82 C. 90 D. 47

11. The table shows that the average number of people (N) who go to “Wild Water Park” during the day

depends on the number of degrees (D) above one hundred on that day. Write an equation that relates D to F.

A. N = 3166.0877(0.15)D B. N = 1368.7875(1.15)D

C. N = D(1.15)D D. N = 900(1.15)D

12. Find the complement of the probability given: P(A) = .42

A. .42 B. .68 C. .84 D. .58

13. Classify the solution(s) of the equation. 3x2 − 10 = 8

A. two pure imaginary solutions B. one real number solution

C. one imaginary solution D. two real number solutions

14. Which sinusoid has the longest period?

A. 2sin(9x) + 11 B. 11sin(2x) + 9

C. 3sin( 12 x) + 4 D. 10sin( 14 x) − 2

15. Which rational expression represents the ratio of the perimeter to the area of the given shape?

A. 17x22

B. 21x17

C. 2217x

D. 2221x

D 3 5 7 9

N 1368.7875 1810.2215 2394.0179 3166.0887

16. Determine which event is dependent.

A. You play a game that involves spinning a wheel. The wheel is divided into 4 sections, red, blue, green and yellow. Each section of the wheel has a different area. Event A: You spin blue. Event B: You spin green. B. You are playing a trivia game asks multiple choice questions. You randomly guess the answers to

the game questions. Event A: You guess question 1 correctly. Event B: You guess question 2 incorrectly.

C. You roll a six sided die and flip a coin. Event A: You get a 2 when rolling the die. Event B: You get heads when flipping the coin.

D. You randomly pick two prizes out of the prize bag. Event A: You pick a gift card. Event B: You pick a pair of headphones.

17. Evaluate the logarithm using and log310 • log35

A. 3.07 B. 2.096 C. 0.924 D. 4.92

18. Which function is not represented by the graph?

A. y = −π2

+ 4 sin x + π2

!

"#

$

%& +

π2

B. y = −π2

+ 4 sin x − π2

!

"#

$

%& −

π2

C. 4 sin2

y x π⎛ ⎞= −⎜ ⎟⎝ ⎠

D. y = 4 sin x + π2

!

"#

$

%&

19. Find the number of ways to arrange the letters of the word FLOWING.

A. 49

B. 5040

C. 20160

D. 823543

20. Use the Rational Root Theorem and the graph to find all the real zeros of the function ( ) 3 23 7 2 8.f x x x x= − − +

A. x = 1, 2, ⅓

B. x = 1, -2, ⅜

C. x = -1, 2, 4/3

D. x = -1, -2, ⅓

3log 2 0.631≈ 3log 5 1.465,≈

21. Given x>1, find the expression with the greatest value.

A. x34 B. x4( )

4 C. x4 3 D. They are all equal.

22. Sin(θ)=6/10. Find the Cos(θ).

A. 5/3 B. 4/3

C. 5/4 D. 10/6

23. How many real solutions are there to the function f (x) = 9 + x2

A. one pure imaginary solutions B. one real number solution

C. two imaginary solution D. two real number solutions

24. Convert 5π/4 to degrees.

A. 54° B. 225°

C. 75° D. 0.068°

25. What is the solution of the logarithmic equation log2 x = −3

A. no solution B. x = 1/8

C. x= -6 D. x= -1

Algebra 4 Final Exam Part 2

26. Describe the transformation of ( ) 3logf x x= represented by the graph of g.

A. A translation 2 units up

B. A rotation 90° clockwise

C. A translation 2 units left

D. A reflection over the line y=x

27. Which function represents exponential decay?

A. y = 3e0.9x B. y = -3e-2x

C. y = .5e2x D. none of the above

28. Find the logarithm that represents 34 = 81 correctly.

A. log4 81 = 3 B. log3 81 = 4

C. log4 3 = 81 D. log3 4 = 81

29. You and your friends are ordering a pizza that is made with two cheeses and three toppings. The table below shows the possible choices. How many different pizzas are possible?

A. 32 B. 336 C. 2100 D. 967680

30. Which statements describe the transformations of the graph of f x( ) = x2 + 2 represented by

f x( ) = 7 − x2

A. a reflection over the y-axis and a vertical translation units up

B. a reflection over the x-axis and a vertical translation 7 units up

C. a reflection over the y-axis and a vertical translation 5 units up

D. a reflection over the x-axis and a vertical translation 9 units up

Cheese Mozzarella Romano Cheddar Goat

Toppings Pepperoni Sausage Ham Bacon

Pineapple Onion Basil Red Pepper

31. If you arrange the letters ZIRDYZ in a random order. What are the chances is spells DRIZZY?

A. 1720

B. 2360

C. 6 / 720 D. 1360

32. Use the sequence 13, −43, 163, −643,! to describe the pattern.

A. arithmetic B. geometric

C. parabolic D. There is no pattern

33. Use the sequence 12, −52, 252, −125

2,! to write the next term.

A. 250/2 B. -250/2 C. 625/2 D. -625/2

34. A survey asked people about whether they prefer to sleep or to party at night. The table shows the results of the survey. What is the probability that a randomly selected person is over 30 and prefers to party?

A. 17/36 B. 27/47 C. 19/36 D. 17/83

35. How many different ways can you arrange the letters STUDYBUDDY?

A. 100 B. 151200 C. 3628800 D. 2610

36. You flip 11 coins. What are the chances that exactly 5 of them are heads?

A. 555

B. 5

39,916,800

C. 511

D. 4622048

Preference

Sleep Party Total

Age

Under 30 20 19 39

Over 30 27 17 44

Total 47 36 83

37. Which equation has an inverse that is not a function.

A. y = 9x − .25 B. y = x2 + 300 C. y = 2x

D. y = 99 − x

38. Given the function 99sin(98x − C) + 97 As the constant “C” decreases what happens to the sinusoid wave?

A. It moves up. B. It moves to the right

C. It moves to the left. D. The period gets longer.

39. Which of the rational expressions cannot be simplified?

A. x3 − 27x2 − 6x + 9

B. 3 2

23 7 215 14

x x xx x+ − −

+ −

C. x + 7x2 − 49

D. 2

22 5 3

2 15x xx x

+ −− −

40. Choose the system of quadratic inequalities whose solution is represented in the graph.

A. y < -x2 – 2x + 3

y < x2 + 2x + 3

B. y < -x2 – 2x + 3

y ≥ x2 + 2x - 8

C. y > -x2 – 2x + 3

y < x2 + 2x - 8

D. y < -x2 – 2x - 8

y ≤ x2 + 2x + 3

41. When you factor x5 + 20x4 + 155x3 + 580x2 + 924x you get (x + 2)(x + 3)(x + 4)(x + 5)(x + 6) . What do you get when you multiple (x + 4) • (x + 2) • (x + 5) • (x + 3) • (x + 6)

A.155x5 + x4 + 680x3 + 20x2 + 924x B. x5 + 20x4 + 155x3 + 580x2 + 924x

C. x5 + 155x4 + 580x3 + 924x2 + 20x D. none of the above

42. Find 29P4 .

A. 116 B. 570024 C. 707281 D. none of the above

43. Solve for x: log6 x = 2

A. 6 2 B. 6

C. 64 D. 36

44. Condense the following expression 2log39 + 6log3x − 5log3 y

A. log381x6

y5 B.

2log39 + 6log3x5log3 y

C. log3(81 + x

6 − y5) D. log318 • 6x5y

45. Expand the following expression

A. ln9+ ln 4x + ln y − ln11 B. ln9+ 4ln x + ln y − ln11

C. ln9x4 + ln y − ln11 D. ln9+ 4ln x − ln y − ln11

46. Find 14C4

A. 56 B. 1001 C. 24024 D. 38416

47. State the domain and range of the function g(x) =

A. Domain: All real numbers except 0, Range: All real numbers except 9

B. Domain: All real numbers except 5, Range: All real numbers except 0

C. Domain: All real numbers except 9, Range: All real numbers except 5

D. Domain: All real numbers except 0, Range: All real numbers except 5

48. Find the product.

A. 5x4 B. 8x3y2

10x5y2

8x2 yi4xy

3

y4

9x+5

ln 9x4 y11

C. 8y4 D. 5x3y2

49. Find the difference.

A. 31/12x B. 8/24x

C. 18/12x D. 18/24x

50. Solve the equation.

A. 4 B. -4

C. 60 D. -2

65x

=2x − 4

154x

−76x