math

Directions: Print this exam out, show all work on the paper.

Read the directions for each question carefully!
1) Simplify. Your answer must be a mixed number, with the fraction part in lowest terms.
22 7∙2 −1
32−15 ÷5

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2) A band estimates that 3 of people on its mailing list has seen the band play exactly once, and 10
that 9 of people on its mailing list have seen the band play more than once. What fraction of 20
people on the band’s mailing list have seen the band play at least once? Your answer must be a fraction on lowest terms.

3) Simplify: your answer must be a fraction in its lowest terms:
(2 +3)÷10 953

4) Which of the following frequencies will sound good (= little to no dissonance) with played simultaneously with 275 Hertz (a frequency often associated with C# Half credit if you miss one;
no credit if you miss more than one.
a) 165 Hz b) 235 Hz c) 495 Hz d) 360 Hz
4

5) A song has a time signature of 12/8. Which measure and beat correspond with the following beats in the song?
a) The song’s 48th beat b) The song’s 99th beat.

6) A song has a time signature of 12/8. The 6th beat of the 19th measure corresponds with which beat of the song?

7) Convert 26,489 to a mixed number. 61

8) Round 3,494,997.2984 to…
a) the nearest 1,000 b) the nearest 10,000 c) the nearest .01 d) the nearest 10

9) 16 ounces = 1 pound. A kick drum weighs 6 pounds, 3 ounces. Express this weight in terms of
a) pounds b) ounces

10) A marathon runner finishes her race in exactly 4.5 hours. She decides to train so that she can reduce her time to run the race by at least 6%. What time is she hoping to come in at (or under)? Your answer should be in terms of hours, minutes, and seconds.

11) 2,300 people attend a show. However, the band gets lost on the way to the venue. By the time they start playing, the audience has shrunk to 78% of what it had been. How many people are still there when the band starts playing?

12) A band performs on stage for 1 hour, 50 minutes. Their one opening act performs on stage for 40% as long as the band. When you combine the band and their opening act, how many minutes does the audience get to (hopefully) enjoy music at that show? Answer in terms of hours and minutes.

13) A band gets into someone’s old van in order to go play at a festival. There is a 6% chance that the van will break down at some point during the trip, and an 12% chance that the band will have some other sort of equipment break at the festival. What is the probability that neither the van nor any equipment breaks? Do not round your answer; your answer must be a %.

14) A band estimated that when a random ticket holder is invited on stage, there is a 1 chance 4
that the person will be over 30 years old. The band also estimates that half of its fans at any age are men and the other half are women. If they band invites a random ticket holder onstage, what is the probability that this person is a woman over 30 years old?

15) Solve for b: 6b + 4 = −2b − 16

16) A solo artist performing as one of several acts has exactly one hour to be on stage. It takes him an average of 5 minutes, 10 seconds per song played, as well as a total of 10 minutes to do other things such as finishing setting up, taking things down, and introducing himself to the audience. How many songs should he plan on playing? Round your answer down to the nearest integer.

17) A Boston-based band plays some gigs throughout New England, and is trying to decide whether it makes more sense to rent a van for a day each time it gets a gig outside the Boston Area, or if it should rent a van for the entire year. Renting a van to travel to a gig costs $130 for the rental, which includes insurance. Renting a van for the year costs $4000 for the van, and another $900 for insurance. What is the minimum number of trips that the band needs to make during the upcoming year in order for it to save money by renting a van for the entire year? Your answer should be an integer. [Hint: find the “break even point” – where both rental plans cost the same.]

18) Use iteration to solve for k: 4𝑘 = 57.10066935 … log (2𝑘)

19) When a band plays at the main stage of a 1100-person festival, they sell 21 T-shirts. Their next festival gig involves playing on the main stage at a 2,900-person festival. How many T- shirts do they expect to sell? Round your answer to the nearest integer.

20) A song takes 4 minutes, 27 seconds to play at 109 beats per minute. If the song is sped up to 132 beats per minute, how long will it take to play? Answer in terms of minutes and seconds, rounding your answer to the nearest second.

21) A 4-string bass guitar has a string length of 34 inches, and an open E-string vibrates at 41.2 Hz (E1) If the seventh fret is pressed down, the string vibrates at 61.8 Hz (B1). What is the distance from the bass guitar’s bridge to the seventh fret? Round your answer to the nearest 0.01 inch.

22) At the first 8 venues of a tour the average ticket price is $39, and at the other 4 venues on the same tour the average ticket price is $59. Assuming a band plays one show at each venue, what is the average ticket price for the entire tour?

23) Calculate the slope of the line below. The coordinates of the two dots on the line are all integers.

24) Solve for both variables: 5c + 2d = 13 2c + 4d = −6

25) A music school gives both private lessons and group lessons. Private lessons all are one price, and group lessons all are a different price. Four private lessons and three group lessons cost $395. Two private lessons and eight group lessons cost $360. What will be the price of three private lessons and seven group lessons? Hint: first write two equations, then solve them to get values for your variables “p” and “g”.

26) Indicate the number of significant digits in each of the following numbers: a) 142,000 b) −0.006070 c) 2 × 10−4 d) 200.0

27a) Convert −3.25 × 10−5 into a regular (decimal) number.

27b) Write 630,000 in Scientific Notation with four significant digits.

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