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HONORS ALGEBRA 2 PRACTICE FINAL EXAMINATION ­ PART I (MULTIPLE CHOICE)

Directions: Use this practice assessment to help prepare for the actual Final Examination. You are able to use a calculator. Use a timer to practice working under time constraints (Time limit for this portion is 45 minutes).

x ? x+2

1. Which statement is true about the rational function f ( x) = A B C D E

There is a vertical asymptote at x = 2. There is point discontinuity at x = 2. The domain is all real numbers from (-2) to 2. There is a vertical asymptote at x = (-2). The function is continuous.

2. Solve: x 2 - 12x = 28

A B C D E

14 (-2) 14 and (-2) 6 ± 2 2 none of the above

3. The imaginary number i 51 is equivalent to

A B C D E

(-1) 1 (- - 1 ) -1 none of these 3 6 - 2i

4. Simplify:

A B C D E

9 - 3i 5 9 + 3i 16 9 + 3i 20 9+i 20 3i 5

5. If g ( x) = x + 3 and h( x) = x 2 + x - 1 , find the value for g[h(-20)] .

A B C D E

(-7123) 422 551 277 382

6. Given A (7, -3) and B (-11, 13), find the length of AB .

A B C D E

4.47 units 8.25 units 10.77 units 15.23 units 24.08 units

7. Simplify:

3m 2 - 12 4 m 2 + 8m 6m - 12 8m 2 + 16m

A B C D E

9( m - 2) 16m 2 (m + 2) m ( m 2 - 4) m-2

m+2 3(m - 2) 4( m + 2) 3

8. (8 - 2i )(5 + i )

A B C D E

38 - 18i 38 40 + 2i 42 - 2i 42

9. Simplify:

x -1 2 + 2 x - 1 5x + 5

A B C D E

7x - 6 5( x + 1)( x - 1) 7 5( x + 1) 3 x +1 7 x2 - 3 ( x 2 - 1)(5 x + 5) 7 5( x - 1)

2

10. A graphing program draws a line segment on a computer screen so its endpoints are at (5, 2) and (7, 8). What are the coordinates of the midpoint?

A B C D E

(0.5, 3) (3.5, 7.5) (6, 5) (6.5, 4.5) (12, 10)

11. Solve for x: log2 x + log2 (x - 2) = log2 3

A B C D E

(-1) 3 {- 1,3} 9 None of these

12. The center of a circle is (5, -4) and the radius, r, is 4 cm. Identify the equation of the circle.

A B C D E

( x - 5) 2 + ( y + 4) 2 = 4 ( x - 5) 2 + ( y + 4) 2 = 8 ( x + 5) 2 + ( y - 4) 2 = 8 ( x - 5) 2 + ( y - 4) 2 = 16 ( x - 5) 2 + ( y + 4) 2 = 16

13. There are 3 bacteria in a jar. After 1 minute, there are 9 bacteria. After 2 minutes, there are 27 bacteria. Which equation could you use to find the number of bacteria in the jar after t minutes? Let b represent the number of bacteria.

A B C D E

b = 3(t +1) b = t3 b = t +3 t = b3 b = 3t x-2 x-4 = x x-6 (-3) (-2) 1 2 3 1 256

14. Solve:

A B C D E

15. Solve: 4 3 p -1 =

A B C D E

(-1) 5 3 (-2) (-4) 1 6 (-3) 5 (-1)

16. Evaluate:

A B C D E

(-21) (-9) 8 9 None of these

3 2

17. Solve: 4

=x

A B C D E

16 10 8 12 64

18. Solve: x 2 + 64 = 0

A B C D E

± 8i 2 ± 2i 64i 2 ± 8i 8, (-8)

19. Simplify: 2a 3 5

3

- 8a12 125

A B C D E

- 2a 4 5 - 2a 3 125 a4 10 2 a -4 15 x - 15 = 3 - x 0 16 9 No real number solution None of the above

20. Solve:

A B C D E

21. Solve: n 2 - 3n - 1 = 0 1 A 0, 3 3± 7 B 2 3±i 5 C 2 3 ± 13 D 2 E 3± 5

22. Find g(x) · h(x) if g ( x) = x 2 - 7 and h( x) = 3 x + 2 .

A B C D E

3x 3 +2x 2 - 21x - 14 5x 3 - 21x - 14 5x 5 - 21x - 14 3x 2 -19x - 14 none of the above

23. Find the inverse of the function g ( x) = 5 - 2 x .

A B C D E

g ( -1) (x) = g ( -1) (x) = g ( -1) (x) = g ( -1) (x) =

x-2 5 x-5 2 2- x 5 5- x 2 x 5

g ( -1) (x) = 2 -

3x 2 24. 4y

-3

= 27 y 3 64 x 6 3y3 4 x6

- 27 x 64 y 6

A B C D E

64 y 3 27 x 6 64 y 3 9 x8

25. Simplify: 3 12 + 2 300 .

A B C D E

5 312 15 104 26 3 44 3 212 3

26. If possible, perform the matrix operation to find the value of x. 2 (-3) (-5) 14 2 4 = x 6 5 · y 3 ( - 2) 1 4 14 (-4)

A B C D E

(-5) (-4) 14 27 not possible

27. The table shows values for the equation y = 2x 3 - 3x 2 - 2 for the interval (-2) x 3. x y (-2) (-30) (-1) (-7) 0 (-2) 1 (-3) 2 2 3 27

Between which values of x in the interval will the graph of the function cross the x-axis?

A B C D E

(-2) and 1 (-1) and 0 0 and 1 1 and 2 2 and 3

28. Which binomial is a factor of 6x 2 - 19x ­ 36?

A B C D E

3x - 4 2x + 9 x-9 3x + 4 x-6

29. What is the solution set for 3x + 6 = 12

A B C D E

{2} {- 2,2} {- 6,2} {- 2}

Ø

30. Write ln 16 = x in exponential form.

A B C D E

10 x = 16 e 16 = x e x = 16 10 16 = x log16 log(e)

HONORS ALGEBRA 2 PRACTICE FINAL EXAMINATION ­ PART I (MULTIPLE CHOICE) ANSWER KEY

1. D 2. C 3. C

4.

C

5.

E

6.

E

7.

C

8.

D

9.

B

10.

C

11.

B

12.

E

13.

A

14.

E

15.

A

16.

D

17.

C

18.

A

19.

B

20.

D

21.

D

22.

A

23.

D

24.

D

25.

C

26.

D

27.

D

28.

D

29.

C

30.

C

HONORS ALGEBRA 2 PRACTICE FINAL EXAMINATION ­ PART II (FREE RESPONSE)

Directions:

Use this practice assessment to help prepare for the actual Final Examination. You are able to use a calculator. Use a timer to practice working under time constraints (Time limit for this portion is 45 minutes). Practice writing your solutions in a neat and organized manner for this portion of the assessment.

1.

Complete the following table.

Value of the Discriminant

b2 ­ 4ac > 0

Type and Number of Solutions for ax2 + bx + c = 0

______ real number solutions ______ imaginary solutions

Examples of Graphs of Related Functions f(x) = ax2 + bx + c

f(x)

x b2 ­ 4ac = 0 f(x) ______ real number solutions ______ imaginary solutions x b2 ­ 4ac < 0 f(x) ______ real number solutions ______ imaginary solutions x

2.

If x varies directly as y and x = 6 when y = 12, then find x when y = 100.

3.

If

1 x 4 3

= (-5), then what is the value of x?

4.

What is the sum of the zeros of the function f(x) = 5x 2 ­ 3x ­ 2?

5.

The estimated budget for a new zoo honoring Dr. Seuss is $50 million. The planning budget contains three categories: acquisition of animals, a, facilities construction, c, and surplus, s. The amount allocated to the construction of facilities was equal to the total of the acquisition of the animals and the surplus combined. The budget committee estimated that 15% of the total budget would be surplus. The following linear system represents this information. a + c + s = 50 (in millions) a+s=c 0.15(a+ c + s) = s a. Solve the linear system to find the amount budgeted for each category.

b. A corporate sponsor donated $10 million to the Seuss Fund for advertising and for the ceremonies to celebrate the opening of the zoo. The gift was deposited into a three-year certificate of deposit at a rate of 6% compounded quarterly. What is the total amount of money available at the end of three years?

Use the formula for compound interest: A = P 1 +

r n

nt

6.

Sketch a graph that meets the given requirements. a. An exponential function that illustrates growth.

b. A quadratic function with one real solution.

c. A cubic function with two real solutions.

7.

In 1990, a developing country had a population of about 12,000. A study conducted between 1970 and 1990 produced the following population model for future planning: P = 6.4t 2 + 135t + 6750, where t = 0 corresponds to 1970.

a. In what year will the population reach 14,125?

b. Explain how you determined your answer. Use words, symbols, or both in your explanation.

8.

On the day Chris was born, his grandparents opened a savings account for him and deposited $100 into the account. Neither Chris nor his parents deposited or withdrew any money from the account. The table below shows the balance in the savings account over the first 10 years.

Time (in years) 0 2 4 6 8 10

Balance $100.00 $106.99 $119.14 $132.49 $149.52 $168.25

Use the ExpReg (y = ab x ) function to determine the exponential equation that best fits the data.

a. Write the equation of the curve of best fit.

b. Chris checks the balance on his sixteenth birthday. Does he have enough money to buy a stereo system on sale for $209.99? Use mathematics to justify your answer.

HONORS ALGEBRA 2 PRACTICE FINAL EXAMINATION ­ PART II (FREE RESPONSE) ANSWER KEY

1. 2 real number solutions 0 imaginary solutions

x f(x)

f(x)

1 real number solution 0 imaginary solutions

x

0 real number solutions 2 imaginary solutions

f(x)

x

2.

x = 50

3.

x=2

4.

(-0.4) + 1 = (0.6)

[Graph the function and locate the zeros ­ x-intercepts ­ using 2nd TRACE.]

5.

Part A ­

a = 17.5 million

c = 25 million

s = 7.5 million

Part B ­

P = $10,000,000

r = 0.06

n = 4 payments/year

t = 3 years

Thus (or ), A $11,956,181.71

6.

a.

b.

c.

7.

a.

When x = 25, so in 1995 the population will be 14,125.

b.

I used my calculator to graph P = 6.4t 2 + 135t + 6750. Then, I used 2nd GRAPH to use the Table function. I searched until I found where y = 14,125 and located the x-coordinate.

8.

a.

y = $97.63(1.054) x

b.

Yes, Chris has enough money to purchase the stereo system. I substituted 16 in for x (this represents Chris' age). When I solved the equation, I was able to see that y = $226.48, which is more than $209.99. Thus (or ), Chris has more than enough money to purchase the stereo system.

Be sure you have attempted all the problems on the practice Final Exam. Additionally, use your Math Reference, online resources, and text in order to fully prepare.

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