algebra ii semester exam ii study...
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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.