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Study Guide for the Navy/Marine Corps ASTB exam. Also of help for any other military flight exam. Contains worked math problems, mechanical comprehension, aeronautical and military knowledge

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Math Problems 1. A basketball player averages 21 points per game for the first 8 games of the season. If he is held scoreless in the next two games, how many average points per game must he score in his final 6 games in order to complete the season with an overall average of 21 points per game? 2. Assume the probability of having a boy is 50% and a girl is 50%. If a family has four children, what is the probability the family has at least two girls? (answer in fractions) 3. If you flip a coin three times, what is the probability of getting three tails in a row? (answer in decimal form) 4. If the tax rate is 3.5% and the amount to be raised is $6440, what is the base? 5. How much pure acid must be added to 12 ounces of 40% acid solution in order to produce a 60% acid solution? 6. x varies directly as y^2 and if x=9 when y=2, what is the value of x when y=8? 7. The hour hand of a clock is 3 ft long. How many feet does the tip of the hand move between 1:00 pm and 5:00pm? 8. An island is defended by a battery of coastal guns placed at the easternmost pt of the island, having a max range of 10 miles. A ship, sailing due north at 24 mph along a course that will bring it within 8 miles of these guns, is approaching the position where it will be 10 miles from these guns. Assuming that the ship will maintain a straight course and the same speed, for approximately how long will the ship be within range of the coastal guns? 9. If the entrance requirements of a certain college is 82, what mark must a student have in Geometry (weight 2) to be able to enter if his other marks are English 88 (weight 3), Spanish 78 (weight 2) and History 80 (weight 2)? 10. Two planes started at the same time from the same airport and flew in opposite directions. One flew 80 mph faster than the other. In four hours they were 2600 miles apart. What was the speed of the lower plane? 11. One recruit can complete a certain assignment in 40 minutes; another recruit can complete the same assignment in one hour. How long would it take to complete the assignment if the two recruits worked together? 12. A naval detachment has enough rations to feed sixteen people for 10 days. If four more people join the detachment, for how many fewer days will the rations last? 13. A field can be plowed by 9 machines in 5 hours. If 3 machines are broken and cannot be used, how many hours will it take to plow to field? 14. In a 3-hr examination of 320 questions, there are 40 mathematics problems. If twice as much time should be allowed for each mathematics problems as for each of the other questions, how many minutes should be spent on mathematics problems? 15. A cashbox contains a certain number of coins, of which 63 are dimes and 36 are nickels. The rest of the coins are quarters. If the probability of selecting a quarter from this bank is 1/5, how many quarters does the bank contain? 16. A closed rectangular box with a square base is 3 inches high. If the volume of the box is 48 square inches, what is the boxs surface area in square inches?

17. A tank holds that holds 500 gallons of water can be filled by 1 pipe in 25 minute and emptied by another in 50 minutes. How long would it take to fill the tank if both pipes are open? 18. If a driver completes a trip of 240 miles at a rate of 30 mph, at what rate would the driver have to return to average 40 mph for the round trip? 19. Batman can clean up all of the crime in Gotham city in 8hr working alone. Robin can do the same job alone in 12 hr. If Robin starts crime fighting at 8am and Batman joins him at 10 AM, at what time will they have all the crime cleaned up? 20. If each brick is 3 inches wide and 5 inches long, how many bricks would u need to build a wall that will measure 10 ft by 16 ft? 21. If it takes 6 people 10 hours to stack a certain amount of blocks and they start at 11am, but at 5pm one person is added every hour, how long will it take to complete the job?

Math Problems with answers 1. A basketball player averages 21 points per game for the first 8 games of the season. If he is held scoreless in the next two games, how many average points per game must he score in his final 6 games in order to complete the season with an overall average of 21 points per game? (28) a. Avg=21 b. # points needed to avg 21 for 8 games: 21*8=168 c. Total number of games: 8+2+6=16 games d. Overall score needed to avg 21 for 16 games: 21*16=336 e. Number of points left to score: overall score-8 game score= 336-168=168 f. Number of points to score per a game for 6 games: 168/6=28 points 2. Assume the probability of having a boy is 50% and a girl is 50%. If a family has four children, what is the probability the family has at least two girls? (answer in fractions) a. ( ) ( b. ( ) ( )( ) ( ) ( ) ( )

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3. If you flip a coin three times, what is the probability of getting three tails in a row? (answer in decimal form) a.( )

4. If the tax rate is 3.5% and the amount to be raised is $6440, what is the base? a. 0.035x=6440 b. c. d. 5. How much pure acid must be added to 12 ounces of 40% acid solution in order to produce a 60% acid solution? a. Pure Acid- x number of ounces, 100% pure acid=100x no of ounces of pure acid b. 40% Acid solution- 12 ounces, 40% pure acid= 480 ounces of pure acid c. 60% Acid solution- 12+x ounces, 60% pure acid=60(12+x) d. 60(12+x)=100x+480 e. 720+60x=100x+480 f. 40x=240 g. X=6 6. x varies directly as y^2 and if x=9 when y=2, what is the value of x when y=8? a. b. ; x=16*9 c. X=144

7. The hour hand of a clock is 3 ft long. How many feet does the tip of the hand move between 1:00 pm and 5:00pm? a. R=3 b. Multiple times by 2 c. 8. An island is defended by a battery of coastal guns placed at the easternmost pt of the island, having a max range of 10 miles. A ship, sailing due north at 24 mph along a course that will bring it within 8 miles of these guns, is approaching the position where it will be 10 miles from these guns. Assuming that the ship will maintain a straight course and the same speed, for approximately how long will the ship be within range of the coastal guns? a. The distance traveled is the distance from A to C. b. AB = c. d. 9. If the entrance requirements of a certain college is 82, what mark must a student have in Geometry (weight 2) to be able to enter if his other marks are English 88 (weight 3), Spanish 78 (weight 2) and History 80 (weight 2)? a. Multiply by weights and solve for remaining. b. Geometry: 2*x. English 88*3. Spanish 78*2. History 80*2. c. d. 738-580=158, e. X=158/2=79 10. Two planes started at the same time from the same airport and flew in opposite directions. One flew 80 mph faster than the other. In four hours they were 2600 miles apart. What was the speed of the lower plane? a. 4(x+x+80)=2600 b. 8x+320=2600 c. 8x=2280 d. X=280 11. One recruit can complete a certain assignment in 40 minutes; another recruit can complete the same assignment in one hour. How long would it take to complete the assignment if the two recruits worked together? a. Recruit 1: x/40 b. Recruit 2: x/60 c. =1 ; 12. A naval detachment has enough rations to feed sixteen people for 10 days. If four more people join the detachment, for how many fewer days will the rations last? a. Set original values equal to new values and solve for unknown. b. 16*10=20x 10 8 A B C

c. 20x=160; x=8 ration days per 20 persons. d. 10 ration days-8 ration days= 2 days less. 13. A field can be plowed by 9 machines in 5 hours. If 3 machines are broken and cannot be used, how many hours will it take to plow to field? a. Set two equations up as # machines x hours =1. Set equivalent to each other and solve for unknown. b. 9*5=1, 6*x=1. c. 14. In a 3-hr examination of 320 questions, there are 40 mathematics problems. If twice as much time should be allowed for each mathematics problems as for each of the other questions, how many minutes should be spent on mathematics problems? a. X= number of minutes to be spent on each math problem. b. c. d. e. . 15. A cashbox contains a certain number of coins, of which 63 are dimes and 36 are nickels. The rest of the coins are quarters. If the probability of selecting a quarter from this bank is 1/5, how many quarters does the bank contain? a. b. c. 16. A closed rectangular box with a square base is 3 inches high. If the volume of the box is 48 square inches, what is the boxs surface area in square inches? a. , ( ) ( ) ( ) b. ( ) ( ) ( ) c. 17. A tank holds that holds 500 gallons of water can be filled by 1 pipe in 25 minute and emptied by another in 50 minutes. How long would it take to fill the tank if both pipes are open? a. b.18. If a driver completes a trip of 240 miles at a rate of 30 mph, at what rate would the driver have

to return to average 40 mph for the round trip? a. 240/30=8 hrs b. 240/40=6 hrs c. Need speed to get 4 hours? 240/4=60mph

19. Batman can clean up all of the crime in Gotham city in 8hr working alone. Robin can do the same job alone in 12 hr. If Robin starts crime fighting at 8am and Batman joins him at 10 AM, at what time will they have all the crime cleaned up? a. Robin =x+2/12, batman= x/8b. 20. If each brick is 3 inches wide and 5 inches long, how many bricks would u need to build a wall

that will measure 10 ft by 16 ft? a. 3 inches=1/4 foot, 1 row= 10x4=40 bricksb. c. 5 inches=~1/2 foot, 1 column= 2x16=32 bricks Whole wall= 40x32=~1280 bricks

21. If it takes 6 people 10 hours to stack a certain amount of blocks and they start at

11am, but at 5pm one person is added every hour, how long will it take to complete the job? a. 60=6(5)+7(x)+8(x-1)+9(x-2)+10(x-3) b. 60=30+7x+8x-8+9x-18+10x-30 c. 60+26=15x+19 d. 76=34x e. X=1.6 hrs less, 8.4hrs

Mechanical Knowledge 1. Amplitude of AC wave necessary to have same DC voltage is called effective amplitude. 2. Transformers take energy from more coils to less coils. 3. A ball hanging from a crane is an example of potential energy. 4. In an elbow pipe where two holes are drilled at opposite corners of the bend, the pressure is lowest inside the bend. 5. The mechanical advantage of a pulley system is defined as the ratio of torques between the output and input pulleys. 6. The mechanical advantage is 3, Pulley # 2 will turn at half the speed of pulley #1. (see picture on right) 7. For sprocket on right, the distance the chain will travel in 1 full revolution is equal to: a. Circumference= 2r=25=2x15.70=31.40=32 inches. 8. If a cam is diamond shaped, it will cause 2 contacts per a revolution. 9. Sam left his home at 11am traveling along Rt9 at 30 mph. At 1 pm, his sister Jenna left home and started after him on the same road at 45 mph. At what time did Jenna catch up with Sam? a. 30x=45x-90, 15x=90, x=30/5=6. 11am+6 hrs=5pm

Aeronautical 1. The first digital fly by wire was tested on the F-8 in 1992. 2. AQ Rating stands for Aviation Fire Control Technician. 3. A plane declaring emergency always has the right of way. 4. The first aviation vessels built solely for launching aircraft were built by the Swedish Navy. 5. Windlasses are used for lifting and lowering anchors. 6. Hand signal for stop is two hands, palm out, above head, waving back and forth. 7. A runway numbered 22 has an opposite runway numbered 4 (22-18). 8. A runway aligned 36-0 is N/S. 9. A rocket engine can operate outside the atmosphere. 10. A headwind will shorten takeoff run and increase angle of climb. (feel wind on your face) 11. 1 nautical mile is 6,076ft. 12. 25 degrees N by 90 degrees W is the gulf of Mexico. 13. A line drawn from a fix in the direction in which a ship is moving is called a course line. (plot the course line). 14. As the weight of the load carried by a ship increases, the freeboard (amt of boat above water) decreases and draft increases (amt of boat under water). 15. Fog forms when warm air moves over cold water. 16. LT and Ensign and Captain are company grade officer, Admiral and Commodore are flag grade officer. 17. In an F-14, an NFO is called a radar intercept officer (RIO) 18. Bonhomme Richard was an American warship commanded by John Paul Jones, the father of the Navy, I have not yet begun to fight! 19. Delta is NOT a US space vehicle. 20. A warm front is indicative of conditions of fog or a steady long period of rain. 21. Latitude is measured from the equator.

Spatial Apperception

1. B 2. Use the ABCs a. Attitude b. Bank c. Coast 3. In banked horizon lines should be opposite to a line drawn from tip to tip of the banking plane.