Algebra 2 Honors Final Exam

Game show question (it is way too long to type out)

$3925

Simplify (10-x^2 - 3x/ x^2 +2x -8). Identify any x-values for which the expression is undefined.

(-x-5/x+4). The expression is undefined at x=2 and x=-4

Convert the point (15, 5pi/3) from polar coordinates to rectangular coordinates

(15/2, -15√3/2)

Factor (2x-1)^3 -27 as the difference of two cubes. Then, simplify each factor.

(2x-4)(4x^2 + 2x + 7)

Write the arithmetic series 5 +1 -3 -7 -11 -15 -19 in summation notation

(7 over E k=1)(9-4k)

Add (x+9)/(x-2) + (-8x -39)/(x^2 +x-6). Identify any x-values for which the expression is undefined.

(x+6/x+3) The expression is undefined at x=-3

Subtract (2x^2-48/ x^2 -16) - (x+6/x+4)

(x-6/x-4) The expression is undefined at x=4 and x=-4

Evaluate log4 (1/16) by using mental math

-2

An automobile insurance company claims that its rates for teenage drivers average $410 less per year than the same coverage from another company. In a random sample of 35 customers, the average savings was $390 per year, with a standard deviation of $55 per year. What is the z-value rounded to the nearest hundredth? Is there enough evidence to reject the claim?

-2.15; there is enough evidence to reject the claim

Solve the inequality -8xsquared - 14x + 4 > -11

-2.5 < x < 0.75

Find the first five terms of the sequence an=2^n-5

-3, 1, 3, 11, 27

A group of 3 students went to drink pearl tea and study at a local tea shop. The ship offers 12 different flavors of pearl tea. What is the probability that at least 2 students ordered the same flavor? Express your answer as a decimal, and round to the nearest ten thousandths.

0.4271

Samuel Pepys, whose diary provides an eyewitness account of the Great Fire in London in 1666, wrote to Sir Issac Newton about a game involving three players rolling dice. He asked which of the following was more likely: 1. Player A rolls six dice and rolls at least one six. 2. Player B roles twelve dice and roles at least two sixes. 3. Player C rolls eighteen dice and rolls at least three sixes. If the probability that Player A rolls at least one six is 0.6651, what is the probability that Player C rolls at least three sixes? Express your answer as a decimal, and round to the nearest ten thousandth.

0.5973

Find the probability of rolling a 5 or an odd number on a number cube. Express your answer as a fraction in simplest form.

1/2

An experiment consists of rolling a number cube. What is the probability of rolling a number greater than 4? Express your answer as a fraction in simplest form.

1/3

Solve √6x-2 < or = 3

1/3 <or= x <or= 11/6

Write the expression ^11√10^8 by using radical exponents

10^(8/11)

Use synthetic substitution to evaluate the polynomial P(x) = x^3 - 4x^2 + 4x - 5 for x=4

11

Given f(x) x^3 and g(x)= 4x + 3, find g(f(3)).

111

Find the sum for the arithmatic series (13 over E k=1)(15k-4)

1313

A building has a triangular floor with sides 150, 200, and 280 feet. To the nearest square foot, what is the area of the floor of the building?

14,464 ft^2

A marching band formation consists of 8 rows. The first row has 5 musicians, the second has 7, the third has 9, and so on. How many musicians are in the last row?

19 musicians

Find all the real fourth roots of 16

2 and -2

Find the missing terms in the arithmetic sequence 18, _ , _ , _ , 42.

24, 30, 36

Find the measure of the reference angle for theta= 142 degrees.

38 degrees

The distance d in meters traveled by a skateboard on a ramp is related to the time traveled t in seconds. This is modeled by the function: d(t) = 4.9t^2 - 2.3t + 5. What is the maximum distance the skateboard can travel, and at what time would it achieve this distance? Round you answers to the nearest hundreth.

4.73 meters at 0.23 seconds

Simplify the expression ^4√256z^16

4z^4

What expression is equivilent to (3-2i) ^2

5-12i

Find the product (5x-3)(x^3 - 5x +2)

5x^4 - 3x^3 - 25x^2 + 25x - 6

Identify the degree of the monomial -5r^3s^5

8

An oil company plans to add a chemical to its gasoline to make it burn more clearly, The company conducts and experiment to see whether adding the chemical affects the gasoline mileage of the cars using their gasoline. State the null hypothesis for the experiment.

Adding the chemical does nor affect gasoline mileage

Determine whether the sequence 12, 40, 68, 96 could be geometric or arithmetic. If possible, find the common ratio or difference.

It could be arithmetic with d=28

Identify the leading coefficient, degree, and end behavior of the function P(x) = -5x^4 - 6x^2 + 6

LC: -5, D:4, end behavior: positive to negative, negative to negative.

Writhe the simplest polynomial function with zeros 5, -4, and 1/2.

P(x) = x^3 - (3/2)x^2 - (39/2)x + 10

Determine whether the data set could represent a quadratic function. Explain

The 2nd differences between y-values are constant for equally spaced x-values, so it could represent a quadratic function

Rana is playing a board game. The players take turns rolling a pair of number cubes. On her next turn, Ransa must roll a 5 to win the game, but if she rolls doubles, she gets and extra turn. Explain why the evens "roll a 5: and "roll doubles" are mutually exclusive. If the probability of rolling a 5 is 1/9 and the probability of rolling doubles is 1/6, what is the probability that Randa rolls either a 5 or doubles on her next turn? Express your answer as a fraction in simplest form.

The events are mutually exclusive because the sum of a double roll can never equal 5. (5/18)

Identify the roots of -3x - 21x^2 + 72x +540 = 0. State the multiplicity of each root.

The root 5 has a multiplicity of 1, and the root -6 has a multiplicity of 2.

Solve the polynomial equation 3x^5 + 6x^4 - 72x^3 = 0 by factoring

The roots are 0, -6, and 4

What expression is equal to log50

ln50/ln10

Write the exponential equation 2^3 = 8 in logarithmic form

log2 8 = 3

Find the value of the sine, cosine, and tangent functions for theta where A=96, B=28, and c=100

sin theta= 7/25; cosine theta= 24/25; tangent theta= 7/24

Find the number and type of solutions for xsquared - 9x = -8

the equation has two real solutions

The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by the formula s= √30fd, where f is the coefficient of friction and d is the length of the skid marks in feet, On the highway near Lake Tahoe, a police officer finds a car on the shoulder, abandoned by a driver after a skid and crash, He is sure that the driver was driving faster than the speed limit of 20 mi/h because the skid marks measure 9 feet and the coefficient of friction under those conditions would be 0.7. At about what speed was the driver driving at the time of the skid? Round your answer to the nearest mi/h/

14 mi/h

Given f(x)= 2x^2 + 8x -4 and g(x)= -5x + 6, find (f-g)(x).

2x^2 + 13x -10

A 35-foot telephone pole casts a 46-foot shadow on the ground while the sun is shining. To the nearest degree, what is the angle of elevation of the sum from the end of the shadow?

37 degrees

Divide by using synthetic division (x^2 - 9x + 10) / (x-2)

x-7 + (-4/(x-2))

The area of a rectangle is equal to x^2 + 10x + 16 square units. If the length of the rectangle is equal to x+8 units, what expression represents its width?

(x+2)

Complete the square for the expression x^2 - 16x + ____. Write the resulting expression as a binomial squared.

(x-8)^2

Simplify [(-5/x-4) + (x+6/x+4)] / (x+3/x-4)

(x^2 -10x -26/10(x+3))

Find the geometric mean of (-1/48) and (-1/75)

+ or - (1/60)

Let g(x) be a vertical shift of f(x) = -x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x).

-3x + 12

let g(x) be the transformation, vertical translation 3 units down, of f(x)= -4x + 8. Write the rule for g(x).

-4x +5

For h(x) = 2x^2 + 6x - 9 and k(x) = 3x^2 - 8x + 8, find h(x)-2k(x)

-4x^2 + 22x - 25

Rewrite the polynomial 12xsquared + 6 - 7x^5 + 3x^3 + 7x^4 - 5x in standard form. Then, identifying the leading coefficient, degree, and number of terms. Name the polynomial.

-7x^5 + 7x^4 + 3x^3 + 12x^2 - 5x + 6; LC: -7; D: 5

At a small high school, there are 80 girls in the senior class. Some of them play basketball, some play soccer, some play both, and some play neither. The table shows the joint and marginal frequencies for the senior girls. If you know that a girl plays soccer, what is the probability that she will also play basketball? Express your answer as a decimal. If necessary, round your answer to the enarest hundredth.

0.23

The heights of adult males in the United States are approximately normally distributed, the mean height is 70 inches (5 feet 10 inches) and the standard deviation is 3 inches. Use the table to estimate the probability that a randomly-selected male is between 67 and 74.5 inches tall. Express your anser as a decimal.

0.77

What is the expected value of rolling the six-sided number cube represented by the net? Express your answer as a decimal rounded to the nearest hundredth.

2.83

There are 256 players competing in a national chess championship tournament. The players compete until there is 1 winner. How many matches must be scheduled in order to complete the tournament?

255 matches

Find the 7th term of the geometric sequence with a3= 16 and a5= 64

256

Simplify (2z^3-6z^2/z^2 -3z). Identify any z-values for which the expression is undefined

2z; z does not equal 3 or 0

Express log3 6 + log3 4.5 as a single logarithm. Simplify, if possible

3

Simplify the expression log4 64

3

Factor the expression 81x^6 + 24x^3y^3

3x^3(3x + 2y)(9x^2 -6xy +4y^2)

Find the complex conjugate of 3i + 4

4-3i

A surveyor whose eye level is 5 feet above the ground determines the andgle of elevation to the top of an office building to be 41.7 degrees. If the surveyor is standing 4- feet from the base of the building, what is the height of the building to the nearest foot?

41 ft

After takeoff from an airport, an airplane's angle of ascent is 10 degrees. The airplane climbs to an altitude of 10.000 feet. At that point what is the land distance between the airport and the airplane? Round your answer to the nearest foot.

56,713 ft

Expand the series: (6 over E k=2)(-1)^k(7-k)k and evaluate.

6

Find the first 5 terms of the sequence with a1= 6 and an= 2a-1 for n>or=2

6, 11, 21, 41, 81

Divide by using long division (5x + 6x^3 - 8) / (x-2)

6x^2 + 12x + 29 + (50/(x-2)

Multiply (8x^4y^2/3z^3) x (9xy^2z^6/4y^4). Assume that all expressions are defined

6x^5z^3

A person is selected at random. What is the probability that the person was not born on a Monday? Express your answer as a percent. If necessary, round your answer to the nearest tenth of a percent.

85.7%

Solve x^4 - 3x^3 - x^2 - 27x- 90 = 0 by factoring

Solutions: 5, -2, 3i, and -3i

Decide whether the sampling method could result in a biased sample. Explain your reasoning. A TV station wants to get the opinions of viewers on the look of a new game-show set. The station's staff e-mails a survey to all viewers who have subscribed to their online program guide.

The sample could be biased. Some people who watch the show do not subscribe to the program guide.

Decide whether the sampling method could result in a biased sample. Explain your reasoning. The Candlelit-Dinner Candle Store surveys its Monday customers to find out their opinion on a new scented candle.

The sample could be biased. The sample does not include the customers who shop there on days other than monday

Solve (x^2 +x -30)/(x-5) = 11. Check your answer

There is no solution because the original equation is undefined at x=5

The volume V of a cylinder varies jointly with the height h and the radius squared r^2, and V= 157.00cm^3 when h=2 and r^2= 25cm^2. Find V when h= 3 cm and r^2 = 36cm^2. Round your answer to the nearest hundredth.

V=339.12cm^3

Determine whether the sequence -1, 7, 15, 23, 31,... could be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

Yes; common difference 8; next 3 terms are 39, 47, 55

Write a possible explicit rule for nth term of the sequence 23.1, 20.2, 17.3, 14.4, 11.5, 8.6...

an= 26-2.9n

Evaluate the piece wise function f(x)= { 11 if x is < or = to 5; -14 if 5<x<or=6; 1 if 6<x} for x=-1 and x=9

f(-1)= 11; f(9)=1

Write a quadratic function that fits the points (0,6), (2,4), and (3,6)

f(x) x^2 -3x + 6

Use inverse operations to write the invers of f(x) = (x/4) - 5

f^-1(x)= 4(x+5)

The daily profit of a bicycle store can be modeled by f(x)= x^3 - 5x^2 +2x + 2 where x is the number of bicycles sold. Let g(x) = f(x+4). Find the rule for g, and explain the meaning of the transformation in terms of daily profit.

g(x) = x^3 + 7x^2 + 10x - 6; the shop makes the same profit after selling 4 fewer bikes.

The function g is a translation 3 units left and 2 units up of f(x)= √x+9. Write the function g(x)

g(x)= √x+12+2

Constellations are made up of more than one star. The table shows the number of stars that make up various constellations. Find the mean, median, and mode of the data set.

mean: 32.3; mode: 23; median: 30

Find the end behavior of the function P(x) =-8^x

negative to 0, positive to negative

Solve the equation (6x/x-3) = (4x+6/x-3)

no solution

Find the absolute value |-7-9i|

square root of 130

Solve the equation sintheta= 0,3 to the nearest tenth. Use the restrictions 90< x < 180.

theta = 162.5 degrees

The price of dance lessons depends upon the number of lessons that you select. If x is the number of lessons then the fee for the lessons (in dollars) can be found using the piecewise function f(x)= {40x if 0<x< or= 4; 30x if 4<x<or= 8; 25x if x>8}. The lessons are increasing by 10% per lesson with a $5 processing fee for each student. What is the new function for the cost of lessons?

this is a long answer and i'm too lazy to type it

Solve the inequality (5/x+3) <6 algebraically.

x<-3 or x>(-13/6)

Solve the equation 2x^2+ 18 = 0

x= + or - 3i

Use a trigonometric function to find the value of x

x= 25√2

Solve the equation (2x/x^2 - 7x -18) = (6x/x^2 +x-2)

x=0 or x=13

Solve 8^(x+8) = 32^x

x=12

Find the roots of the equation 30x - 45 = 5x^2 by factoring

x=3

Solve the equation x-9= (-18/x)

x=3 or x=6

Solve log5 x^10 - log5 x^6 = 21

x=5^21/4

Solve √11x = 3√x+2.

x=9

Write an expression that represents the width of a rectangle with length x + 5 and area x^3 + 12x^2 + 47x + 60.

x^2 + 7x +12

Determine by composition whether f(x) = 1/5x +4 and g(x)= 5x-20 are inverses

yes, they both equal x