Quiz about Honors Algebra 2 Final Exam Review

Question 1

Find all numbers that must be excluded from the domain of the rational expression.

Accepted Answer

$$x e-5,\ x e-7$$

Answer

$$x e5\ ,\ x e7$$

Answer

$$x
e0$$

Answer

$$x
e5$$

Question 2

Simplify

Accepted Answer

$$\frac{x-2}{x+3}$$

Answer

$$\frac{x+2}{x+3}$$

Answer

$$\frac{x-3}{x+2}$$

Answer

$$\frac{x+2}{x-3}$$

Question 3

Simplify.

Accepted Answer

1

Answer

$$\frac{x^2-16x+64}{(x-8)^2}$$

Answer

$$\frac{(x-8)^2}{81}$$

Answer

$$x$$

Answer

99

Question 4

Add or subtract as indicated: $$\frac{9x-13}{x^2-9x+18}-\frac{8x-7}{x^2-9x+18}$$

Accepted Answer

$$\frac{1}{x-3}$$

Answer

$$\frac{1}{x^2-9x+18}$$

Answer

$$\frac{x+6}{x^2-9x+18}$$

Answer

$$\frac{1}{x-6}$$

Question 5

Solve the following linear equations.

3x + 4 + 2(x + 1) = -4x + 7

Accepted Answer

$$x\ =\ \frac{1}{9}$$

Answer

$$x=3$$

Answer

$$x=\frac{1}{3}$$

Answer

$$x\ =\ 9$$

Question 6

Solve the equation and check your solution.

$$\frac{1}{x+6}+\frac{2}{x+3}=\frac{-3}{x^2+9x+18}$$

Accepted Answer

No Solution

Answer

$$x\ =\ -6$$

Answer

$$x\ =\ 0$$

Answer

$$x\ =\ -3$$

Question 7

Perform the indicated operations and write the result in standard form. (5 + 6i)(4 - i) - (3 - i)(3 + i)

Accepted Answer

16 + 19i

Answer

36 + 19i

Answer

16 + 29i

Answer

18 + 19i

Question 8

Solve the equation by the square root property. $$(x-4)^2=25$$

Accepted Answer

{-1, 9}

Answer

{-5, 5}

Answer

{-9, -1}

Answer

{29}

Question 9

Solve the equation by factoring.

$$4x^2-27x=7$$

Accepted Answer

{-1/4, 7}

Answer

{-4, 7}

Answer

{1/27, -1/4}

Answer

{-4, 4}

Question 10

Solve the equation using the quadratic formula and find exact solutions:

$$16x^2+1=5x$$

Accepted Answer

$$\frac{5\pm i\sqrt{39}}{32}$$

Answer

$$\frac{-5\pm i\sqrt{39}}{32}$$

Answer

$$\frac{-5\pm\sqrt{39}}{32}$$

Answer

$$\frac{5\pm\sqrt{39}}{32}$$

Question 11

Solve the polynomial equation by factoring and then using the zero product principle.

$$3x^3+4x^2=48x+64$$

Accepted Answer

$$x\ =-4,-\frac{4}{3},\ 4$$

Answer

$$x\ =\ -4,\ 0$$

Answer

$$x\ =\ -4,\ \frac{4}{3},\ 4$$

Answer

$$x\ =\ -\frac{4}{3},\ 0,\ 4$$

Question 12

Solve the radical equation, and check all possible solutions.

$$\sqrt{20x+20}=x+6$$

Accepted Answer

{4}

Answer

{3}

Answer

{-4}

Answer

{-3}

Question 13

For the given functions f and g, find the indicated composition. $$f(x)=17x^2-3x,\ g(x)=14x-9\ \ \ \ \ Find\ (f∘g)(2)$$

Accepted Answer

6080

Answer

5221

Answer

859

Answer

1178

Question 14

Write the standard form of the equation of the circle with the given center and radius. center (9, -4) and radius is 11.

Accepted Answer

$$(x-9)^2+(y+4)^2=121$$

Answer

$$(x-4)^2+(y+9)^2=11$$

Answer

$$(x+4)^2+(y-9)^2=11$$

Answer

$$(x+9)^2+(y-4)^2=121$$

Question 15

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. The playground will use 216 feet of fencing. Find the dimensions of the playground that maximize the total enclosed area.

Accepted Answer

36 ft by 54 ft

Answer

27 ft by 54 ft

Answer

36 ft by 45 ft

Answer

54 ft by 54 ft

Question 16

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. $$f(x)=x^3+11x^2+39x+45$$

Accepted Answer

-3, touches the x-axis and turns around; -5, crosses the x-axis

Answer

3, crosses the x-axis; -3, touches the x-axis and turns around; -5, crosses the x-axis

Answer

-3, crosses the x-axis; -5, touches the x-axis and turns around

Answer

3, crosses the x-axis; -3, crosses the x-axis; -5, crosses the x-axis

Question 17

Solve the equation $$3x^3-19x^2+30x-8=0$$ given that 2 is a zero.

Accepted Answer

{2, 4, 1/3}

Answer

{2, 1, 4/3}

Answer

{2, -1, -4/3}

Answer

{2, -4, -1/3}

Question 18

Find an nth degree polynomial function with real coefficients satisfying the given conditions. degree: n = 3; and -4 and i are zeros where f(-3) = 60.

Accepted Answer

$$f(x)=6x^3+24x^2+6x+24$$

Answer

$$f(x)=6x^3+24x^2-6x-24$$

Answer

$$f(x)=-6x^3-24x^2-6x-24$$

Answer

$$f(x)=-6x^3-24x^2+6x+24$$

Question 19

Find the vertical asymptotes, if any, of the graph of the rational function.

$$\frac{x-9}{x^2-8x+15}$$

Accepted Answer

x = 3

Accepted Answer

x = 5

Answer

x = -9

Answer

x = -3

Answer

x = -5

Question 20

Find the horizontal asymptote, if any, of the graph of the rational function. $$g(x)=\frac{8x^2-2x-8}{3x^2-6x\ +\ 4}$$

Accepted Answer

y = 8/3

Answer

y = 1/3

Answer

y = 0

Answer

no horizontal asymptote

Question 21

Find the slant asymptote, if any, of the graph of the rational function.

$$f(x)=\frac{x^2-7x+2}{x+6}$$

Accepted Answer

y = x - 13

Answer

x = y + 7

Answer

y = x + 9

Answer

no slant asymptote

Question 22

Determine the constant of variation for the stated condition. t varies directly as r and inversely as s, and t = 5 when r = 84 and s = 35.

Accepted Answer

k = 25/12

Answer

k = 7

Answer

k = 35

Answer

k = 12/25

Question 23

Use the compound interest formula $$A=P(1+\frac{r}{n})^{nt}$$ or $$A=Pe^{rt}$$ . Round to the nearest cent.

Find the accumulated value of an investment of $9000 at 7% compounded continuously for 3 years.

Accepted Answer

A) $11,103.10

Answer

B) $10,890.00

Answer

C) $11,025.39

Answer

D) $11,203.10

Question 24

Evaluate the expression. $$\log_28$$

Accepted Answer

3

Answer

2

Answer

6

Answer

8

Question 25

Evaluate the expression. $$\log_{64}4$$

Accepted Answer

1/3

Answer

3

Answer

12

Answer

1

Question 26

Evaluate the expression.

$$\ln\frac{1}{e^{10}}$$

Accepted Answer

-10

Answer

$$\frac{1}{10}$$

Answer

10

Answer

$$-\frac{1}{10}$$

Question 27

Solve the equation by expressing each side as a power of the same base and then equating exponents.

$$4^{x+5}=8^{x-1}$$

Accepted Answer

x = 13

Answer

x = 1

Answer

x = 6

Answer

x = 8

Question 28

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

$$e^{x+3}=7$$

Accepted Answer

-1.05

Answer

2.30

Answer

-0.99

Answer

-0.70

Question 29

log 3x = log 4 + log (x - 1)

Accepted Answer

4

Answer

-4

Answer

-4/7

Answer

3/2

Question 30

Find out how long it takes a $2900 investment to double if it is invested at 8% compounded quarterly. Round to the nearest tenth of a year. Use the formula. $$A=P\left(1+\frac{r}{n}\right)^{nt}$$

Accepted Answer

8.8 years

Answer

9 years

Answer

8.6 years

Answer

9.2 years

Question 31

The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. $$\left(\frac{3\sqrt{7}}{4},\ \frac{\sqrt{7}}{4}\right)$$ . Find sin t.

Accepted Answer

$$\frac{\sqrt{7}}{4}$$

Answer

$$\frac{3\sqrt{7}}{7}$$

Answer

$$\frac{\sqrt{7}}{3}$$

Answer

$$\frac{3}{4}$$

Question 32

Determine the phase shift of the function. $$y=3\sin(x-\frac{\pi}{2})$$

Accepted Answer

$$\frac{\pi}{2}$$ units to the right

Answer

3 units down

Answer

$$\frac{\pi}{2}$$ units to the left

Answer

3 units up

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