ASVAB

How to find an average

sum of all values Average = ---------------------- number of values

Area of a Triangle

A = 1/2 bh

Find the area of a circular park whose radius is 4.9 meters.

A = π (4.9)² A = 24.01π

Area of a Circle

A = π r²

Circumference of a circle

C = 2πr

How far will a wheel with a radius of 3.5 feet travel in 500 revolutions? (Use 2/7 for π .)

C = 2πr C = 2(2/7)(3.5) = 2/1 (22/7) (3 1/2) = 2/1 (22/7) (7/2) = 1/1 (22/1) (1/1) = 22/1 = 22 Distance traveled by the wheel in one revolution is 22 feet. Therefore, the distance traveled in 500 revolutions will be: 500 x 22 = 11,000 feet.

Rate formula

Distance = Rate x Time

Find the total length of fencing required to fence the outer edges of a rectangular park that is 35 meters by 25 meters.

P= 2 x (l + w) P = 2(35 + 25) = 2 x 60 = 120

Perimeter of a Rectangle

Perimeter = 2 x (length + width)

What is the mode in this set of numbers: 2, 5, 9, 6, 2, 3, 3, 8, 2?

The mode is the value that appears most often. The number 2 appears three times, so it is the mode.

Find the hypotenuse of a right triangle whose legs are 15 meters and 8 meters.

This is a geometry question that deals with right triangles. To improve your skills, review the "Right Triangles" lesson. Since the triangle is a right triangle and you know the lengths of two of the sides, you can use the Pythagorean Theorem to solve for the length of the hypotenuse. Remember that in the Pythagorean Theorem, a and b represent the legs and c represents the hypotenuse: a² + b² = c² 8² + 15² = c² 64 + 225 = c² 289 = c² √289 = 17

The area of a triangle is 32 square centimeters and its height is 8 centimeters. Find its base.

This is a geometry question that deals with the area of a triangle. To improve your skills, review the "Triangles" lesson. The formula for the area of a triangle is A = 1/2 bh. Plug the known values into the formula and solve for the base: 32 = 1/2 b(8) 32 = 8b/2 32 = 4b 32/4 = 4b/4 8 = b

Find the volume, in cubic centimeters, of a cylindrical pipe that has a radius of 5 cm and a height of 14 cm.

This is a geometry question that deals with the volume of a cylinder. To improve your skills, review the "Solid Geometry" lesson. The volume formula for a cylinder is: V = π r²h. The question tells you that the radius (r) of the cylindrical pipe is 5 cm and its height (h) is 14 cm. Substitute the values in the formula: V = π(5²)(14) = π(25)(14) = 350π

If 3 + x ≥ 4x - 5 what is the value of x?

This is an algebra question that deals with inequalities. To improve your skills, review the "Inequalities" lesson. To solve the inequality, you must get x by itself on one side: 3 + x ≥ 4x - 5 3 + x + 5 ≥ 4x - 5 + 5 8 + x ≥ 4x 8 +x - x ≥ 4x - x 8 ≥ 3x / 3 8/3 ≥ x 8/3 ≥ x is the same as x ≤ 8/3.

A certain number of tickets is sold at $10 per ticket, and the remaining tickets are sold at $8 per ticket. If 105 total tickets are sold and the amount collected is $922, find the number of tickets sold for $10.

This is an algebra question that deals with solving for more than one variable. To improve your skills, review the "Solving Equations" and "Working with Variables" lessons. Let x equal the number of tickets sold at $10 per ticket and y equal the number of tickets sold at $8 per ticket. The total number of tickets sold is x + y. Since you're told that the total number of tickets sold is 105, it follows that x + y = 105. The total amount earned by selling the tickets is $10x + $8y. According to the second condition, the total amount collected from the tickets sold is $922. So, 10x + 8y = 922. Since you are looking for the number of tickets sold at $10, you need to find the value of x. Solve the first equation for y, and then replace y in the second equation with the result from the first equation. x + y = 105 x + y - x = 105 - x y = 105 - x Now replace y in the second equation: 10x + 8y = 922 10x + 8(105 - x) = 922 10x + 840 - 8x = 922 2x = 840 = 922 - 840 2x = 82 2x/2 = 82/2 x = 41 Therefore, 41 tickets were sold at $10 per ticket.

Janna wants to fly her new kite in the nearest neighborhood park. If Prospect Park is 8 blocks from her house, and Kimberly Park is 5 blocks less than 1.5 times as far from her house as Prospect Park, which of the following is true?

This is an arithmetic question in the form of a word problem. To improve your skills, review the "Word Problems" lesson. The first step is to translate the English into math. Prospect Park is 8 blocks from Janna's house, so you can write that as P = 8. Kimberly Park is 5 blocks less than 1.5 times the distance to Prospect Park, or 5 less than 1.5 times P, so you can write K = 1.5P - 5. Now you can solve the second equation for K by plugging in 8 for P: K = 1.5P - 5 = 1.5(8) - 5 = 12 - 5 = 7 Kimberly Park is 7 blocks from Janna's house. Since Prospect Park is 8 blocks from Janna's house, Kimberly Park is 8 - 7 =1 block closer.

In an English class, the class average on a recent test was a score of 85. If the sum of all the test scores was 1,785, how many students are in the class?

This is an arithmetic question that deals with averages. To improve your skills, review the "Averages" lesson. The average test score is 85, and the sum of all the test scores is 1,785. Plug these into the average formula to find the number of values: sum of all values Average = ---------------------- number of values 1,785 85 = -------- x 85x = 1,785 (divide both sides by 85) x = 21

At a gas station, Richard pays $28.91 for 9.8 gallons of gas. What is the price he pays per gallon?

This is an arithmetic question that deals with dividing decimals. To improve your skills, review the "Multiplying and Dividing Decimals" lesson. The cost per gallon is the total cost, $28.91, divided by the number of gallons, 9.8. To divide these two decimals, you must make the number you are dividing by into a whole number by moving the decimal one place to the right, and you must also do this for the other number: 9.8 → 98 28.91 → 289.1 Now use long division to solve 289.1 ÷ 98: 289.10 ÷ 98 = 2.95 Richard pays $2.95 per gallon.

5⁴ x 25³ =

This is an arithmetic question that deals with exponents. To improve your skills, review the "Powers" lesson. Since 25 is the same as 5², rewrite the expression so that both terms have the same base: 5⁴ x 25³ = 5⁴⁴ x (5²)³ Now follow the rules of multiplying powers: 5⁴ x (5²)³ = 5⁴ x 5²∗³ = 5⁴ x 5⁶ = 5⁴⁺⁶ =5¹°

7! + 4! =

This is an arithmetic question that deals with factorials. To improve your skills, review the "Factorials" lesson. 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040. 4! = 4 × 3 × 2 × 1 = 24. 7! + 4! = 5,040 + 24 = 5,064.

What is the result when 3.65 is multiplied by 23.3?

This is an arithmetic question that deals with multiplying decimals. To improve your skills, review the "Multiplying and Dividing Decimals" lesson. To multiply two decimals, remove both decimal points and set up the problem with two whole numbers: 365 10950 x 233 73000 --------- --------- 1095 85045 Now figure out where the decimal point should go. Since 3.65 has two digits after the decimal point and 23.3 has one digit after the decimal point, the answer should have 2 + 1 = 3 digits after the decimal point. Therefore the correct answer is 85.045.

A rectangle has a length of 8 inches and a width of 5 inches. If its length is increased by 50% and its width is reduced by 25%, find the percent change in the area of the rectangle.

This is an arithmetic question that deals with percent change. It is also a geometry question that deals with the area of a rectangle. To improve your skills, review the "Percent Increase and Decrease" and "Squares, Rectangles, and Parallelograms" lessons. The area of a rectangle is determined by the formula: Area = Length × Width The area of a rectangle with a length of 8 and a width of 5 is: 8 × 5 = 40. The length is increased by 50%. Take 50%, or 0.5, of the length, 8, and add it to 8: 0.5 × 8 = 4 and 4 + 8 = 12 The new length is 12. The width of the rectangle is decreased by 25%. Take 25%, or 0.25, of the width, 5, and subtract it from 5: 0.25 × 5 = 1.25 and 5 - 1.25 = 3.75 The new width is 3.75. The area of the new rectangle will be the new length multiplied by the new width: 12 × 3.75 = 45. Now find the percent increase in the area of the rectangle by using the formula: Difference in the areas Perecent Increase = ----------------------------- x 100 Original Area Plug in the values to get: 45-40 PI = -------- x 100 40 5 = ---- x 100 40 = 0.125 x 100 = The percent increase is 12.5%.

A train travels at an average speed of 50 miles per hour for 2 1/2 hours. Then it travels at a speed of 70 miles per hour for 1 1/2 hours. How far did the train travel?

This is an arithmetic question that deals with rates. To improve your skills, review the "Rates" lesson. Use the rate formula to find the distance that the train traveled: Distance = Rate × Time. Keep in mind that there are two parts of the total trip because the train traveled at two different speeds for two different amounts of time. Part 1: Multiply 50 miles per hour by 2 1/2 hours to find the distance in miles. 50 x 2 1/2 = 50 x 5/2 (turn 2 1/2 into improper fract) = 50/1 x 5/2 = 250/2 (cross multiply) = 125 Part 2: Multiply 70 miles per hour by 1 1/2 hours to find the distance in miles. 70 x 1 1/2 = 70 x 3/2 = 70/1 x 3/2 = 210/2 = 105 Add these distances together to find the total distance: 125 + 105 = 230 miles.

A pump can drain a completely filled 375-gallon tank in 15 minutes. At this rate, how much longer will it take to drain a completely filled 600-gallon tank?

This is an arithmetic question that deals with rates. To improve your skills, review the "Rates" lesson. First, find the rate at which the pump drains a 375-gallon tank. Remember that rate is equal to amount divided by time. It drains 375 gallons in 15 minutes, so the rate is: 375 ÷ 15 = 25 gallons per minute. Next, use this rate of 25 gallons per minute to determine the time it will take to drain a 600-gallon tank. Remember that time is equal to the amount divided by the rate: 600 ÷ 25 = 24. It will take 24 minutes to drain 600 gallons. There is one more step, because the question asks how much longer it takes to drain the 600-gallon tank than to drain the 375-gallon tank. Subtract the two times to get the answer: 24 minutes - 15 minutes = 9 minutes

√10 x √6 =

This is an arithmetic question that deals with square roots. To improve your skills, review the "Square Roots" lesson. When multiplying square roots, multiply the values under the square root signs and then simplify: √10 x √6 = √10 x 6 = √60 = √4 x √15 = 2√15

Volume for a cylinder

V = π r²h (pie r squared) times height