Delta College Middle School Math Competition Practice Test A 2018

Transcription

1 Delta College Middle School Math Competition Practice Test A 208

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3 ) In the Noveo music group there are 4 times as many flutes as there are bassoons. The number of clarinets is 8 more than triple the number of bassoons. The sum of the number of flutes and the number of clarinets is 5. What is the total number of flutes, clarinets, and bassoons in the group? a) 6 b) 7 c) 8 d) 9 e) 20 2) Which number below can be written as a finite, non-repeating decimal? 7 a) b) c) d) e) ) The eighth positive even number is added to double the 96 th prime number. The resulting sum is halved. If the 96 th prime number is now subtracted from this quotient, the result is what number? a) b) 8 c) 9 d) 8 e) 96 4) For every 25 notes in a piece of music, Kiliniec makes an average of 3 errors. If she practices one hour each day for a week, she can eliminate 5 out of 6 of her errors. What is her new error rate? a) error/25 notes b) 2 errors/25 notes c) 3 errors/25 notes d) errors/9 notes e) error/50 notes 5) A composer has written four different categories of song. Twenty percent of her songs are love songs. One half of her songs are rock and 2/5 of her songs are new age. She has also composed 5 rap songs. How many songs has she written? a) 40 b) 30 c) 5 d) 30 e) none of these 6) What is the arithmetic mean of the set containing every multiple of 3 between 93 and 946? a) 928 b) c) 929 d) e) 930 7) The digits through 8 are separated into four groups of two digits and the product of each group is found. Let L be the largest of the four products. Find the smallest possible value of L. a) 6 b) 24 c) 8 d) 2 e) 20 8) $4,300 has been raised to fund the Harmonee Middle School international choral competition. This amount represents 2% of the total amount needed. What is this total amount? a) $7,50,000 b) $75,000 c) $286,000 d) $2,860,000 e) $4,586 9) Amadeus leaves home and travels at a rate of 30 mph toward Vienna. He forgot his viola so texted his brother for help! Two hours after Amadeus left, his brother, Ludwig, left the same home (WITH the viola) and took the same route but traveled at a rate of 50 mph. In how many hours will Ludwig reach Amadeus? a) 2 b) 3 c) 4 d) 5 e) 6 0) In a warehouse, boxes of sheet music 20 inches tall, 24 inches tall, and 45 inches tall are being stacked next to each other in 3 piles. What is the shortest height possible at which the three stacks will be the same height? a) 80 in. b) 90 in. c) 360 in. d) 450 in. e) 20 in. ) Ms. Woodwind purchased a new speaker system. The cost of the speaker system, including a 7.5% sales tax was $24,600. What was the cost of the speaker system before taxes? a) $32800 b) $4,057.4 c) $8,450 d) $22, e) none of these 2) Find the percent discount of a pair of ballet slippers if they were originally $05.00 and now cost $62.50? (rounded to the nearest tenth of a percent) a) 59.5% b) 68.9% c) 25.0% d) 40.5% e) 80.0%

4 3) A middle school band teacher took her 208 students to an opera at the Temple Theatre. The group was given a private performance for $ The students plus the teacher and plus one parent chaperone for every 3 students attended the opera. How much was the cost of attendance per person? a) $5.95 b) $6.50 c) $5.50 d) $6.25 e) $5.52 4) If a can of paint covers 52 square feet and rectangular sign is 45 feet long and 30 feet wide, how many cans of paint will someone need to paint the sign? (round your answer to the nearest can of paint) a) b) 2 c) 3 d) 4 e) 5 5) A digital player piano completes one cycle of programmed music in 32 hours. If the piano starts a cycle at 7:00 a.m. on Tuesday, when will it complete 0 cycles? a) Monday at 8:00 p.m. b) Monday at 2:00 p.m. c) Tuesday at 3:00 p.m. d) Tuesday at 3:00 p.m. e) Monday at 3:00 p.m. 6) Nhia is painting the walls of a room that is 6 m wide, m long, and 2.5 m high. The room has 3 windows, each 0.9 m by.3 m, and one door, m by 2.5 m. The ceiling will not be painted. If one gallon of paint covers 36 square meters, how many gallons of paint does he need to buy? a) 2 gallons b) 3 gallons c) 4 gallons d) 5 gallons e) 6 gallons 7) A label is wrapped around a soup can that has a diameter of 8 cm and a height of 2 cm. Which answer is closest to the area of the label? a) cm 2 b) cm 2 c) cm 2 d) cm 2 e) cm 2 8) What is the measure of angle x? x a) 24 b) 27 c) 34 d) 38 e) 43 9) A CD player was on sale for $58 at a department store. At the store, each new CD is on sale for $.99 each. If Myles purchases a player and some CDs for $265.9, how many CDs did he purchase? (assume: there is no sales tax) a) 6 b) 7 c) 8 d) 9 e) 0 20) An auditorium is shaped like a trapezoid. The front of the auditorium is 90 feet across and the back 25 feet across, and it is 80 feet from front to back. If each seat needs a space that is 2.5 feet wide by 3 feet deep, approximately how many seats will the auditorium hold? a) 2580 b) 2785 c) 2900 d) 305 e) 320 2) If A B = 7(A B) ½ - B 2, then evaluate 3 6. a) 27 b) 95 c) 26 d) -27 e) ) A HOT JAM!! jacket was purchased for $30 after a 20% discount along with a COLD BUTTER!! t-shirt purchased for $2 after a 30% discount. What was the single percentage discount received on the total purchase? a) 24.4% b) 25% c) 23.6% d) 26% e) none of these

5 23) A cylindrical drum is 6 cm high and has a radius of 6 cm. There is both a cone and a circular disk inside the drum. The cone s volume is 30% of the volume of the drum. The ratio of the disk's circumference to its diameter is given be M. What do you get when the volume of the cone is divided by M? a) 4 cm 3 b) 36 cm 3 c) 64.8 cm 3 d) 203 cm 3 e) cm 3 24) A concert hall was full. There were 72 people in attendance. What was the capacity of the concert hall? a) 96 people b) 86 people c) 94 people d) 98 people e) none of these 25) What is a) b) ? [Leave the denominator factored.] c) d) e) ) If the length of a rectangle is increased by 30 percent while its width is decreased by 20 percent, what happens to the area? a) increases by 4% b) increases by 5% c) increases by 6% d) increases by 0% e) none of these 27) If eight horses are entered in a race and there can be no ties, how many different ways can they finish? a) b) 336 c) 720 d) 36 e) 20,60 28) An operation is defined as x y = x + 2(x + y). What is (3 5) 2? a) 30 b) 6 c) 88 d) 225 e) ) When Mike visited the United States from Canada, he exchanged $3.50 Canadian for $0 U.S. If he exchanges his remaining $600 Canadian for U.S. dollars, how much more in dollars will he receive? (round to the nearest cent) a) $20.00 b) $ c) $80.00 d) $ e) $ ) What is the cost of seeding a rectangular lawn 0 ft by 30 ft if pound of seed costs $5.85 and covers 50 sq ft? a) $28.70 b) $22.00 c) $564.0 d) $09.20 e) none of these 3) The Spring inventory of a music store showed that there were 28% more piano books on the shelves than the Fall inventory showed. If there were 60 piano books in the Spring inventory, how many were there in the Fall inventory? a) 95 b) 05 c) 5 d) 25 e) 35 32) Anne spends 8 hours a week practicing three aspects of playing the tuba. She practices articulation, 7 dynamics, and vibrato. She spends of her time practicing articulation and of her time practicing vibrato. 2 6 How much time does Anne spend practicing dynamics? a) 3.5 hours b) 3 hours c) 4.5 hours d) 6 hours e) 7 hours 33) A drummer in a marching band marches meter north, then meter west, then meter north, then meter west, etc., until he marches a total of 4 meters. How many meters is the drummer from the point at which he started? a) 29 b) c) 4 d) e) 46

6 34) On her first 2 tests, Minnie averaged 83%. On her next 3 tests she averaged 93%. If she wants to average 9% on 7 tests, what should she average on last 2 tests? a) 9% b) 92% c) 93% d) 94% e) 96% 35) A dart board is composed of three concentric circles with radii of 5 cm, 0 cm, and 20 cm. What is the probability that a dart that randomly hits the target will hit within the outer ring of the dart board? a) 0.45 b) 0.75 c) 0.8 d) 0.5 e) ) THE MIDDLE SCHOOL band spent $299 on a purchase of saxophones and trumpets. The number of saxophones purchased was 9 less than double the number of trumpets purchased. The cost of each trumpet was $50 and the cost of each saxophone was $549. How much more was spent on the trumpet purchase than on the saxophone purchase? a) $5 b) $20 c) $399 d) $35 e) $600 37) A marching band with 30 members is making the shape of a regular hexagon with a marcher at each vertex and other marchers spaced 2 feet apart along each six-foot edge. The remaining marchers are evenly arranged inside the hexagon. What is the average number of square feet per each of the inside marchers? a) b) c) d) e) ) Sam, Paul, and Judy were paid a total of $2520 to compose a piece of music. Sam worked 30 hours on the piece, Paul worked 66 2 % more hours than Sam worked, and Judy worked twice as many hours as Sam 3 worked. If the fee is shared among the three musicians based on their number of hours worked, how much money did Paul earn? a) $840 b) $080 c) $500 d) $900 e) $670 39) A package of 3 Rico clarinet reeds can be purchased for $ The Lavoz clarinet reeds, in packages of 5, can be purchased for $ Which is the better buy and how much is the savings? a) Rico, by 2 cents/reed b) Rico, by.8 cents/reed c) Lavoz, by 2 cents/reed d) Lavoz, by.8 cents/reed e) none of these 40) A Steinway grand piano has a ticket price of $50,000. The musician who wants to buy this piano is offered a $0,000 off coupon and a 5% discount. These deals can be used in any order the musician wants. If sales tax is 6% what is the cheapest price the musician could pay? a) $34,450 b) $36,040 c) $28,750 d) $42,500 e) 34,000