Algebra II Semester Exam II Study Guide

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Simplify using the imaginary number i.

a. b. c. d.

Simplify the expression.

____ 2.

a. c. b. d.

____ 3.

a. c. b. d.

____ 4. Find the missing value to complete the square.

a. 2 b. 1 c. 4 d. 8

Solve the quadratic equation by completing the square.

____ 5.

a.

c.

b.

d.

Rewrite the equation in vertex form.

____ 6.

a.

c.

b. d.

Use the Quadratic Formula to solve the equation.

____ 7.

a.

c.

7

6

7

3

7

3

7

6

1

4

1

2

b.

d.

____ 8.

a.

c.

b.

d.

____ 9.

a. ,

b. ,

c. ,

d. ,

____ 10. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to

be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She

wants the area to be 155 square yards. The situation is modeled by the equation .

Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest

hundredth of a yard.

a. 12.7 yards c. 10.2 yards

b. 20.4 yards d. 320 yards

____ 11. Zach wrote the formula w(w – 1)(5w + 4) for the volume of a rectangular prism he is designing,

with width w, which is always has a positive value greater than 1. Find the product and then classify

this polynomial by degree and by number of terms.

a. ; quintic trinomial

b. ; quadratic monomial

c. ; cubic trinomial

d. ; quartic trinomial

____ 12. Write the polynomial in standard form.

a. c. b. d.

____ 13. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of

. If necessary, round to the nearest hundredth.

a. relative minimum: (–62.24, 0.36), relative maximum: (37.79, –3.69),

zeros: x = 5, –2, 2

b. relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79),

zeros: x = –5, –2, 2

c. relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79),

zeros: x = 5, –2

d. relative minimum: (–62.24, 0.36), relative maximum: (37.79, –3.69),

zeros: x = –5, –2

41

4

1

8

1

8

81

4

2

54

1

52

56

513 2

1

5

Divide using synthetic division.

____ 14.

a. , R 70 c. , R 46

b. , R –62 d. , R –38

____ 15. Over two summers, Ray saved $1000 and $600. The polynomial represents her

savings after three years, where x is the growth factor. (The interest rate r is x – 1.) What is the

interest rate she needs to save $1850 after three years?

a. 9.3% b. 1.1% c. –269.3% d. 0.1%

Factor the expression.

____ 16.

a. c.

b. d. no solution

For the equation, find the number of complex roots, the possible number of real roots, and the

possible rational roots.

____ 17.

a. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5

b. 7 complex roots; 2, 4, or 6 real roots; possible rational roots: ±1, ±5

c. 5 complex roots; 1, 3, or 5 real roots; possible rational roots: , ±1, ±5

d. 5 complex roots; 1, 3, or 5 real roots; possible rational roots: ±1, ±5

Evaluate the expression.

____ 18.

a. 604,800 b. 720 c. 120 d.

Use Pascal’s Triangle to expand the binomial.

____ 19.

a. b. c. d.

____ 20. A manufacturer of shipping boxes has a box shaped like a cube. The side length is

5a + 4b. What is the volume of the box in terms of a and b?

a. c. b. d.

Simplify the radical expression. Use absolute value symbols if needed.

____ 21.

a. b. c. d.

____ 22. The formula for the volume of a sphere is . Find the radius, to the nearest hundredth, of a

sphere with a volume of 15 in.3.

a. 3.58 in. b. 258.01 in. c. 1.53 in. d. 1.85 in.

Multiply and simplify if possible.

____ 23.

a. –3 b. 3 c. d. not possible

____ 24. Multiply and simplify . Assume that all variables are positive.

a. c.

b. d. none of these

____ 25.

a. b. c. d.

____ 26.

a. c.

b. d. none of these

Rationalize the denominator of the expression. Assume that all variables are positive.

____ 27.

a.

c.

b.

d. none of these

____ 28.

a.

c.

b.

d.

Subtract if possible.

____ 29.

a. c. b. d. not possible to simplify

Simplify.

____ 30.

a.

b. –22.5 c. –3.6 d.

____ 31. A rope is units long. The rope is cut into two pieces, so that the lengths of the pieces are in

the ratio 2 : 3. What is the length of the longer piece expressed in simplest radical form?

a. units c. units

b. units d. units

____ 32. Write the exponential expression in radical form.

a. b. c. d.

Solve the equation.

____ 33.

a. 1 b. –7 c. –1 d. –1

____ 34.

a. –5, 11 b. 5 c. 11 d. –11

____ 35.

a. i, i

c. i, i

b. i, i

d. ,

____ 36.

a. 14, 4 c. 14, –14

b. –4, –14 d. –4, 4

____ 37. Let and . Find 2f(x) – 3g(x).

a. c. b. d.

4

3

4

3

3

4

3

4

16

9

16

9

4

3

4

3

____ 38. Graph and its inverse.

a.

c.

b.

d.

____ 39. Police can estimate the speed of a vehicle before the brakes are applied using the formula

, where s is the speed in miles per hour and d is the length of the vehicle’s skid

marks. What was the approximate speed of a vehicle that left a skid mark measuring 100 feet?

a. about 29 miles per hour c. about 48 miles per hour

b. about 10 miles per hour d. about 43 miles per hour

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

Graph the function.

____ 40.

a.

c.

b.

d.

Graph the exponential function.

____ 41.

a.

c.

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4 6–2–4–6 x

4

–4

–8

–12

–16

–20

y

2 4 6–2–4–6 x

4

8

12

16

–4

y

b.

d.

____ 42.

a.

c.

b.

d.

2 4 6–2–4–6 x

4

8

12

16

–4

y

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

2 4 6–2–4–6 x

4

–4

–8

–12

–16

–20

y

____ 43. Graph .

a.

c.

b.

d.

Evaluate the logarithm.

____ 44.

a. –3 b. 5 c. –4 d. 4

____ 45.

a. 5 b. –5 c. 4 d. 3

____ 46. The pH of a juice drink is 2.6. Find the concentration of hydrogen ions in the drink.

a. 2.6 b. c. d.

4 8 12–4–8–12 x

4

8

12

–4

–8

–12

y

4 8 12–4–8–12 x

4

8

12

–4

–8

–12

y

4 8 12–4–8–12 x

4

8

12

–4

–8

–12

y

4 8 12–4–8–12 x

4

8

12

–4

–8

–12

y

2.5 103

2.5 103

Graph the logarithmic equation.

____ 47.

a.

c.

b.

d.

State the property or properties of logarithms used to rewrite the expression.

____ 48.

a. Quotient Property c. Difference Property

b. Product Property d. Power Property

____ 49.

a. Quotient Property c. Addition Property

b. Power Property d. Product Property

____ 50.

a. Power Property and Product Property

b. Quotient Property and Product Property

c. Quotient Property only

d. Power Property only

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

2 4 6 8 10–2–4–6–8–10 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

____ 51. A company with loud machinery needs to cut its sound intensity to 37% of its original level. By

how many decibels would the loudness be reduced? Use the formula . Round to the

nearest hundredth.

a. 2.01 decibels c. 1.37 decibels

b. 2.12 decibels d. 4.32 decibels

____ 52. Solve . Round to the nearest ten-thousandth.

a. 0.6616 b. 2.6466 c. 1.7509 d. 1.9091

____ 53. Solve .

a. 12.3308 b. 43.3013 c. 86.6025 d. 1875

____ 54. Simplify .

a. 3 b.

c. 3e d.

____ 55. The generation time G for a particular bacteria is the time it takes for the population to double. The

bacteria increase in population is shown by the formula , where t is the time period

of the population increase, a is the number of bacteria at the beginning of the time period, and P is

the number of bacteria at the end of the time period. If the generation time for the bacteria is 6

hours, how long will it take 8 of these bacteria to multiply into a colony of 7681 bacteria? Round to

the nearest hour.

a. 177 hours b. 76 hours c. 4 hours d. 85 hours

____ 56. Solve .

a. 50,000 b. 74.2 c. 10 d. 3

Use natural logarithms to solve the equation. Round to the nearest thousandth.

____ 57.

a. –0.448 b. 0.327 c. 0.067 d. –0.046

____ 58.

a. –0.288 b. –0.275 c. 0.275 d. 0.288

____ 59. The amount of money in an account with continuously compounded interest is given by the formula

, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate

to the nearest hundredth of a year how long it takes for an amount of money to double if interest is

compounded continuously at 6.2%. Round to the nearest tenth.

a. 1.1 yr b. 6.9 yr c. 11.2 yr d. 0.6 yr

Write the number in the form a + bi.

____ 60.

a. c. b. d.