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# 009 common equations and formulas for asvab math

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• 1. COMMONEQUATIONS ANDFORMULAS FORASVAB MATHwww.mystudyguides.com
• 2. Common Equation and Formulas for ASVAB MathMultiplication Table * 1 2 3 4 5 6 7 8 9 10 11 12 1 1 (12) 2 3 4 5 6 7 8 9 10 11 12 2 2 4 (22) 6 8 10 12 14 16 18 20 22 24 3 3 6 9 (32) 12 15 18 21 24 27 30 33 36 4 4 8 12 16 (42) 20 24 28 32 36 40 44 48 5 5 10 15 20 25 (52) 30 35 40 45 50 55 60 6 6 12 18 24 30 36 (62) 42 48 54 60 66 72 7 7 14 21 28 35 42 49 (72) 56 63 70 77 84 8 8 16 24 32 40 48 56 64 (82) 72 80 88 96 9 9 18 27 36 45 54 63 72 81 (92) 90 99 108 10 10 20 30 40 50 60 70 80 90 100(102) 110 120 11 11 22 33 44 55 66 77 88 99 110 121(112) 132 12 12 24 36 48 60 72 84 96 108 120 132 144(122) The table above is the standard multiplication table taught to most students. The diagonal line of cells that bisects the table is the line of perfect squares. This is the result of multiplying a number by itself once. www.mystudyguides.com
• 3. Common Equation and Formulas for ASVAB MathPrimes Prime numbers are numbers that only have two factors: 1 and the number itself. Here is a list of prime numbers from 1 to 100. 1, 2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. The most commonly referenced prime numbers will be from 1 through 19. www.mystudyguides.com
• 4. Common Equation and Formulas for ASVAB MathFirst Outer Inner Last (F.O.I.L) This method is handy technique for distributing. Use this when you have an equation that is in factored form already, and you need to distribute it back out. First Outer Inner Last (x+2)(2x-3) Multiply the first terms. x*2x =2x2 Multiply the outer terms. x*(-3)= -3x Multiply the inner terms. 2*2x=4x Multiply the last terms. 2*(-3)= -6 Now put them together in descending order of powers and simplify. 2x2 – 3x + 4x – 6 And your completed answer is: 2x2 +x – 6 Now to factor that, you’ll need to look at the term with the largest power of x, as well as the constant. www.mystudyguides.com
• 5. Common Equation and Formulas for ASVAB MathF.O.I.L 2x2 tells us that there are two factors (x2 = x times itself once. If it were x3 we would know that there are three factors.) Since the coefficient of x2 is 2, and the factors of 2 are 1 and 2, we know that the answer will have this in it. (x )(2x ) Now look at -6. We know that because the end result is a ( – ) number, that we will be multiplying a negative times a positive. We also know that the factors of 6 are 1,2,3, and 6. We need to find out what factors will result in the middle two terms adding up to +1. After experimenting with these few factors, we can see that the correct factors are 2 and 3, which gives us(x+2)(2x-3). www.mystudyguides.com
• 6. Common Equation and Formulas for ASVAB MathSquares and Rectangle Perimeter The perimeter of this shape is the sum of all of its sides. P=2L+2W In the case of a perfect square, this can be simplified to P=4W, since all four sides are equal. Now, if L=3 and W = 2, we can find the perimeter. P=2L+2W P=2(3)+2(2) P=6+4 P=10 Area The area of a rectangle is the length multiplied to the width: A=L*W In the case of a perfect square, this can be simplified to A=L2, or A=W2, as they are equal. If the length is 2in and the width is 3in, then the area is 6in2. A=L*W A=2in*3in A=6in2 www.mystudyguides.com
• 7. Common Equation and Formulas for ASVAB MathTriangles Perimeter The perimeter of a triangle can be found by adding all three sides. P=A+B+C Area The formula for the area of a triangle is A= ½*B*H where A=area, B=base (side A in the illustration above) and H=height (not shown above, but shown as the vertical straight line in the illustration below). You can find the height by drawing a straight line from the top angle to the base, so that the new triangle is a right triangle, with the angle between the base and the height being the right angle. Remember, the new side, height, cuts the base in half. Here’s that new triangle. Pythagorean Theorem If you are given a right triangle, and the two legs are given, you should be able to find the hypotenuse using this equation c2=a2+b2 www.mystudyguides.com
• 8. Common Equation and Formulas for ASVAB MathTriangles If leg a is given as 2, and leg b is given as 3, we can find the hypotenuse, or c. c2=a2+b2 c2=22+32 c2=13 c=√13 The square root of 13 is not an easy number to define without a calculator, and often the hypotenuse will not be the result of a perfect square. Don’t worry about this. On the test, since you’re not allowed to use a calculator, if you see a question like this, you’ll likely see the answers listed in that same simplified format as the above answer. You should be able to figure out that the hypotenuse is the square root of 13, but no one is going to expect you to calculate the exact square root of 13. www.mystudyguides.com
• 9. Common Equation and Formulas for ASVAB MathCircles With circles, there are a couple of new terms introduced. Circumference is the distance around all the way around the circle on the outside. Here, Circumference=C. Radius is the distance from the exact center of the circle to any point on circle’s perimeter or circumference. Let Radius=r Diameter is the distance of a straight line that touches the circumference of the circle twice, and bisects the center point of the circle. It is twice the radius. Diameter=D, or 2r. Pi is a number that is used to in the calculation of circle area. It is approximately 3.14, but that simply rounded to the nearest hundredth. Pi does not end, nor does it repeat. Pi=π www.mystudyguides.com
• 10. Common Equation and Formulas for ASVAB MathCircles Circumference, Radius, Diameter To find the Circumference of a circle, use this equation: C=πD, or C=2πr. If you are given the radius, you can find the diameter simply by multiplying it by 2 D=2r If you are given the diameter you can find the radius by dividing it by 2, or multiplying by ½. r= D/2, or r= ½ D Area You can find the area of a circle by multiplying pi and the radius squared. A=πr2 www.mystudyguides.com
• 11. Common Equation and Formulas for ASVAB MathRectangular Solid Surface Area The surface area is the areas of all of the planes added together. Surface area = S S=2(WH+LH+HL) Volume The volume of a rectangular solid (V) can be found by multiplying length to width and then to height. It is simply area with one more dimension added. V=LWH www.mystudyguides.com
• 12. Common Equation and Formulas for ASVAB MathCones Surface area of a cone is S=π*r*√(r2+h2)+π*r2 Multiply pi and the radius of the base circle to the square root of r2 + h2, and then add it to pi times r2 Volume of a cone is 1/3 *π*r2*h Spheres To find the surface area of a sphere, multiply radius squared by pi and four. S= 4*r2*π To find the volume, multiply 4/3 by pi times the radius cubed. S= 4/3 * π *r3 www.mystudyguides.com
• 13. Common Equation and Formulas for ASVAB MathCylinders To find the surface area of a sphere, multiply radius squared by pi and four. S= 4*r2*π To find the volume, multiply 4/3 by pi times the radius cubed. S= 4/3 * π *r3 www.mystudyguides.com