Right Answers For Mathematics

Presented here are the questions from the FAA test. Read each question and click on the 'Answer' link to determine if your choice is correct or not.

## Mathematics Section A

1A-1
When using scientific notation, you can quickly determine the power of ten by counting the number of zeros. In the problem, 1,000,000 has six zeros which is equal to 10 to the sixth power.

1A-2
The square root of a number is the root f that number multiplied by itself. In this case the number is a complex number where you must follow the order of operation, where the times (x) and divide (/) operations precede the add (+) and subtraction (-) process. First divide -1776 by -2. The result 888. Now subtract 632. The answer is 256. The square root of 256 is 16.

1A-3
The square root of a number is te root of the umber multiplied by itself. You can calculate the square root of 3,722.1835 by using a calculator with a square root function, of by multiplying each selection by itself to see which one equals 3,7222.1835. The answer is 61.0097.

1A-4
Begin solving this problem by converting 1/81 into a decimal. The decimal equivalent of 1/81 is .021. Next, multiply 8,019.0514 by .012. The product of these two numbers is 99.0006. Now square 99.0006 to find the answer 9,802.1. 9,081 is the closest answer.

1A-5
The cube of a number is that number multiplied by itself three times. The answer is 262,144.

1A-6
When working with powers of 10, view the equation as (1 * 10^x). A negative exponent indicates you must move the decimal to the left. In (1 * 10^-6) move the decimal of 1 to the left six places. The answer is equal to .000001

1A-7
The square root of four is two. Two multiplied by itself five times equals 32.

1A-8
When working with powers of 10, a negative exponent indicates you must move the decimal to he left. The number of places the decimal should be moves i equivalent to the exponent's value. The answer is .000347

1A-9
When working with powers of 10 a positive exponent indicates you must move the decimal to the right. The number of places the decimal should be moved is equivalent to the exponent's value. The answer is equal to 1.63*10^4

1A-10
Here you must find the square root expressed in scientific notation. The square root of 124.9924 = 11.18. When working with scientific notation, a negative exponent indicates you must move the decimal to the left; whereas, a positive exponent indicates you should move the decimal to the right. The number of places the decimal is moved is equivalent to the exponent's value. The answer is equal to 1,118*10^-2

1A-11
The square root of 16 is four. Multiply four by itself four times to get an answer of 256.

1A-12
7^3 is equal to 343. The square root of 39 equals 6.24. the sum of these two values is 349.24.

1A-13
In this problem you must find the square root expressed in scientific notation. The square root of 1,824 is 42.078. When working with powers of 10, a negative exponent indicates you must move the decimal to the left; whereas, a positive exponent indicates you should move the decimal to the right. The number of places the decimal is moved is equivalent to the exponent's value. Using scientific notation, the answer is .42708*10^2.

1A-14
When using scientific notation, you can quickly determined the power of ten by counting the number of zeros. In this problem, 1,000,000,000 has nine zeros, which is equal 10 to the ninth power.

1A-15
The square root of 16 is four. Multiply four by itself four times to get an answer of 256.

1A-16
Begin by calculating the square roots in the numerator and squaring the denominator. Next, add the two values in the numerator and divide the sum the denominator. The answer is .0419.

1A-17
The decimal value .025 also can be written as 25/1000 and can be reduced to 1/40.

1A-18
To begin, convert the decimal value to a fraction. The fractional equivalent of 1.21875 is 1 and 21,875/100,000 and can be reduced to 7/32

1A-19
Compression ratio is the ratio of the cylinder volume with the piston at the bottom of the stroke to the cylinder volume with the piston at the top of the stroke. In this example, the volume with the piston at he bottom of the stroke is 84 cubic inches. To determine the volume with the piston at the top of the stroke you must subtract the piston displacement from84 cubic inches. This results in a volume of 14 cubic inches. The compression is 84:14 or 6:1 when simplified.

1A-20
When converting a fraction to a percentage, divide the numerator by the denominator and multiply the result by 100. The equivalent percentage value of 7/8 is 87.5 percent.

1A-21
To begin, determine the ration of the two gears. The ratio is 42:14, or 3:1 when simplified. However, since the drive gear is smaller than the gear i's turning, the speed of the driven gear (spur gear) is less than the drive gear (pinion gear). To determine the speed of the spur ear divide the pinion gear RPM by 3. The speed of the spur gear is 140 RPM.

1A-22
You can solve this problem by calculating the amount of horsepower generated by 1 percent of power and then multiplying that number by 65. To determine the horsepower generated by 1 percent power, divide 108 HP by 87 percent. Approximately 1.24 HP is generated by each 1 percent of power. Therefore, 65 percent power generates 80.69 HP.

1A-23
A bolt's shank length goes from the bottom of the head to the end of the shank. On the other hand, grip length of the bolt goes from the bottom of the head to the beginning of the threads. To determine the grip length of the bolt described in the question, you must convert the bolt's shank length to an improper fraction (1 and 3/16 = 19/16).

1A-24
To convert a decimal to a common fraction, write the decimal as a fraction and reduce it to its lowest terms. For example, .0625 is equivalent to 625 ten thousandths or 625/10,000.

1A-25
To convert a fraction to a percent, divide the numerator by the denominator and multiply the product by 100. The equivalent percent value of 5/8 is 62.5 percent.

1A-26
The ratio of the two gears is 36:20. This can be reduced to 9:5.

1A-27
To begin, determine the ratio of the two gears. The ratio is 14:42, or 1:3 when simplified. This means that for every one turn of the driven gear (spur gear), the drive gear (pinion gear) turns thee times. Therefore if the driven gear turns at 140 RPM, the drive gear turns at 420 RPM.

1A-28
If an engine has a maximum horsepower of 98 HP and the engine is run at 75 percent power, then the amount of horsepower developed equals 75 percent times 98 HP. The amount of horsepower developed is 73.5 HP.

1A-29
If the price includes a 12 percent profit, then \$145.60 is equal to 112 percent of the cost. To determine the magneto's cost, divide \$145.60 by 112 percent to find what 1 percent is worth. In this cast, 1 percent of the price is \$1.30. Now, multiply the 1 percent price by 100 percent to get the magneto's cost of \$130.00. \$128.12 is incorrect because it represents the price of 12 percent of the selling price deducted from the selling price.

1A-30
To convert 0.17187 to a common fraction. rewrite it as a faction and reduce it to its simplest terms: 17,187/100,000 = 11/64

1A-31
To determine the maximum RPM, you must divide the known RPM by the decimal equivalent of the percentage. Based on this, the engine turns a maximum of 3,023 RPM.

1A-32
TO convert a fraction to a decimal, divide the numerator by the denominator. The decimal equivalent of 31/64 is .484375. 0.4844 is the closest.

1A-33
This problem asks what percentage of 65 is of 80. To calculate this, divide 65 by 80 and multiply the answer by 100. The answer is 81.25 percent. 81 percent is the closest answer.

1A-34
TO convert a fraction to a decimal, divide the numerator by the denominator. The decimal equivalent of the 7/32 is .21875. To determine the diameter, multiply the radius by two. The diameter is 0.4375.

1A-35
The question asks what percent 835.3 is of 1100. To calculate this, divide 835.3 by 1100 and multiply the answer by 100. The answer is 75.9.

1A-36
TO get a ratio, both the measurements must be in inches. Ten feet is equal to 120 inches. The ratio is 120:30 which reduces to 4:1.

1A-37
To determine a percentage, divide the number which for which percentage is desired by the maximum or total number and multiply by 100%.

1A-38
In a ratio, both numbers must be in like terms. Because of this, you must convert gallons to pounds. One gallon of gasoline weighs 6 lbs., so 200 gallons weighs 1,200 lbs. The ratio now becomes 1,200:1,680. This simplifies to 5:7.

1A-39
This problem involves the multiplication and division of signed numbers. Remember, division or multiplication of unlike signs always results in a negative number, whereas division or multiplication of like signs results in a positive number. The answer is -5.20.

1A-40
When expressing a number in scientific notation, the base number is multiplied by ten raised to a given power (exponent). In conventional form the base number is expressed with the firs significant digit as a single digit whole number, followed by the second and third significant digits rounded to the nearest 100th. The base number is then multiplied by the power of ten raised to a positive or negative integer.

## Mathematics Section B

1B-1
When solving this equation, begin by solving the square roots first. Once this is done you can perform addition and subtraction.

1B-2
To solve this problem, begin by solving everything in parentheses. remember, any number raised to the zero power is 1. Next, multiply where appropriate and then add. The answer is 5

1B-3
Complex problems such as this require the operations to be done in a particular order. Begin by doing everything in parentheses. This simplifies the equation to [-12 + -18] / 2. Now, solve what is in the brackets and divide the result by 2. The answer is -15.

1B-4
To begin, convert the fractions in the equation to decimal numbers by dividing the numerator by the denominator. The decimal equivalent of 3/8 is .375 and 3/4 is .75. When solving any equation, you must do what is in parentheses first. once this is done, you can divide by .75. The answer is 32.

1B-5
To begin, convert the fractions in the equation to decimal numbers by dividing the numerator by the denominator. The decimal equivalent of 3/8 is .375 and to 1/6 is .167. When solving any equation, you must do what is in parentheses first. Once this is done, you can divide by .167. The answer is 71.86.

1B-6
To begin, convert the fractions in the equation to decimal numbers by dividing the numerator by the denominator. The decimal equivalent of 1/2 is .5. When solving any equation, you must do what is in parentheses first. Once this is done, you can multiply from left to right. The answer is 10.

1B-7
When solving any equation, you must do what is in parentheses first, and then brackets. This is followed by the operation of multiplication and then addition. The answer is 82.

1B-8
When solving any equation, you must do what is in parentheses first, then brackets. This is followed by the operation of multiplication and then addition. The answer is -96.

1B-9
When solving any equation, you must do what is in parentheses first. This is followed by the operation of multiplication and then addition. The answer is 22.

1B-10
When solving complex equations, begin by solving everything in parentheses first. Once this is done you can perform multiplication and division followed by addition and subtraction.

1B-11
When solving complex equations, begin by solving everything in parentheses first. Once this is done, you can perform multiplication, followed by addition. The answer is 14.00 the closest.

1B-12
When solving complex equations, begin by solving everything in parentheses first. Once this is done, you can perform multiplication and division, followed by addition. The answer is 11.9.

1B-13
Reserved

1B-14
When solving any equation, you must do what is in parentheses first. This is followed by the operation of multiplication, division, and then addition. The answer below rounds the solutions to the nearest 100th. However, when the equation is solved with a calculator that does not round the answer is still 5.59.

1B-15
To solve this problem, you must first calculate how many miles the airplane can fly on the one gallon gas. To do this, divide the miles flown (750) by the number of gallons used (60). The airplane can fly 12.5 miles on one gallon of gas. To determine the amount of gas required to fly 2,500 miles, divide 2,500 by 12.5. A total of 200 gallons are required to fly 2,500 miles.

1B-16
See explanation for 1B-15. In this case, 875 miles divided by 70 gallons equals 12.5 miles per gallon. 3,000 miles / 12.5 miles per gallon = 240 gallons.

## Mathematics Section C

1C-1
The height of the cylinder is 20 inches. Therefore, the height of the sheet of metal must be 20 inches. To determine the length required, you must calculate the circumference of the cylinder using the formula given. The circumference is 25.132 which is slightly smaller than 25 and 9/64. Therefore, a 20 inch x 25 and 9/64 inch sheet of metal is required to fabricate the cylinder.

1C-2
To determine the volume of a rectangle, multiply the length (L) times the width (W) times the depth (D). However, the question asks for cubic feet and the dimensions are given in inches. Therefore, you must convert the inches into feet and then compute the volume. The answer is 12.5 cubic feet.

1C-3
Using the given relationship of 7.5 gal = 1 cu. ft., you can determine the number of cubic feet required to hold 60 gallons by dividing 60 by 7.5. The answer is 8 cu. ft.

1C-4
When asked to compute the piston displacement, you must caculate the volume of the cylinder. To calculate the volume of a cylinder, use the formula: V=pr^2h. The displacement is 7.0686 cubic inches.

1C-5
The first step in solving this problem is to calculate the volume of the tank. This is done by multiplying the length times the width times the height. The volume is 10 cubic feet. Using the given relationship of 7.5 gal. = 1 cu. ft., you can determine the number of gallons the tank will hold by multiplying the volume times 7.5 gallons. The tank holds 75 gallons.

1C-6
The first step in solving this problem is calculate the volume of the tank. This is done by converting all dimensions to inches and then multiplying the length times the width times the height. The volume is 2,041.875 cubic inches. Using the given relationship of 231 cubic inches = 1 gallon, you can determine the number of gallons the tank will hold by dividing the volume by 231 cubic inches. The tank holds 8,84 gallons. 8.83 is the closest.

1C-7
When asked to compute displacement, you must calculate the volume of cylinder. To calculate the volume of a cylinder, use the formula: V=pr^2h. The displacement of each cylinder is 50.5 cubic inches. To determine the displacement of the engine, multiply the displacement by the number of cylinders. The engine displacement is 202 cubic inches. 200 is the closest.

1C-8
When calculating the volume of an object multiply the length times the width times the height. The volume is 4,331.25 cubic inches.

1C-9
When asked to compute displacement, you must calculate the volume of the cylinder. To calculate the volume of a cylinder, use the formula: V=pr^2h. The displacement of each cylinder is 43.295. To determine the displacement of the entire engine, multiply the displacement of each cylinder by the number of cylinders. The engine displacement 259.77.

1C-10
The surface area of a cube is equal to the surface area of one side multiplied by six. Surface area = (7.25 in.^2)x6 or 315.375 sq. in. Cubing 7.25 inches gives you the cube volume of 381.078 cu. in., but the questions asks for surface area, not volume.

1C-11
TO compute the area of a trapezoid, use the formula A = 1/2(b1+b2)h. The answer is 52.5 square feet.

1C-12
The area of a triangle is calculate using the formula A = 1/2 bh. The area of the triangle is 6 sq. in.

1C-13