asvab formulas

What is the sum of two or more numbers?

Formula: \text{Sum} = a + b (+ c \dots)

What is the difference between two numbers?

Formula: \text{Difference} = a - b

What is the product of two numbers?

Formula: \text{Product} = a \times b

What is the quotient of two numbers?

Formula: \text{Quotient} = a \div b

How do you add two fractions with the same denominator?

Formula: \frac{a}{b} + \frac{c}{b} = \frac{a + c}{b}

How do you subtract fractions with the same denominator?

Formula: \frac{a}{b} - \frac{c}{b} = \frac{a - c}{b}

How do you multiply two fractions?

Formula: (\frac{a}{b})(\frac{c}{d}) = \frac{ac}{bd}

How do you divide fractions?

Formula: (\frac{a}{b}) \div (\frac{c}{d}) = (\frac{a}{b})(\frac{d}{c})

How do you convert a decimal to a percent?

Formula: \text{Decimal} \times 100 = \text{Percent}

How do you convert a percent to a decimal?

Formula: \text{Percent} \div 100 = \text{Decimal}

What is the formula for finding a percent of a number?

Formula: \text{Percent} \times \text{Number}

What is the formula for percent increase or decrease?

Formula: \frac{\text{New} - \text{Old}}{\text{Old}} \times 100

How do you compare two quantities using a ratio?

Formula: a : b = \frac{a}{b}

How do you solve a proportion?

Formula: \frac{a}{b} = \frac{c}{d} \rightarrow ad = bc

What is the area of a rectangle?

Formula: A = l \times w

What is the area of a square?

Formula: A = s^2

What is the area of a triangle?

Formula: A = \frac{1}{2}bh

What is the area of a circle?

Formula: A = \pi r^2

What is the formula for the perimeter of a rectangle?

Formula: P = 2l + 2w

What is the formula for the circumference of a circle?

Formula: C = 2\pi r or C = \pi d

What is the volume of a rectangular prism?

Formula: V = lwh

What is the volume of a cube?

Formula: V = s^3

What is the volume of a cylinder?

Formula: V = \pi r^2 h

What is the sum of angles on a straight line?

180^\circ

What is the sum of angles in a triangle?

180^\circ

What is the measure of a right angle?

90^\circ

How do you solve for x in the addition problem x + a = b?

Formula: x = b - a

How do you solve for x in the multiplication problem ax = b?

Formula: x = b \div a

What is the Distributive Property formula?

a(b + c) = ab + ac

How do you simplify by combining like terms?

Formula: ax + bx = (a + b)x

What is the formula for distance?

\text{Distance} = \text{Rate} \times \text{Time} (d = rt)

What is the formula for work rate problems?

\text{Work Rate} = \frac{1}{\text{Time}}

What is the sum of two or more numbers?

Formula: \text{Sum} = a + b (+ c \dots)

What is the difference between two numbers?

Formula: \text{Difference} = a - b

What is the product of two numbers?

Formula: \text{Product} = a \times b

What is the quotient of two numbers?

Formula: \text{Quotient} = a \div b

How do you add two fractions with the same denominator?

Formula: \frac{a}{b} + \frac{c}{b} = \frac{a + c}{b}

How do you subtract fractions with the same denominator?

Formula: \frac{a}{b} - \frac{c}{b} = \frac{a - c}{b}

How do you multiply two fractions?

Formula: (\frac{a}{b})(\frac{c}{d}) = \frac{ac}{bd}

How do you divide fractions?

Formula: (\frac{a}{b}) \div (\frac{c}{d}) = (\frac{a}{b})(\frac{d}{c})

How do you convert a decimal to a percent?

Formula: \text{Decimal} \times 100 = \text{Percent}

How do you convert a percent to a decimal?

Formula: \text{Percent} \div 100 = \text{Decimal}

What is the formula for finding a percent of a number?

Formula: \text{Percent} \times \text{Number}

What is the formula for percent increase or decrease?

Formula: \frac{\text{New} - \text{Old}}{\text{Old}} \times 100

How do you compare two quantities using a ratio?

Formula: a : b = \frac{a}{b}

How do you solve a proportion?

Formula: \frac{a}{b} = \frac{c}{d} \rightarrow ad = bc

What is the area of a rectangle?

Formula: A = l \times w

What is the area of a square?

Formula: A = s^2

What is the area of a triangle?

Formula: A = \frac{1}{2}bh

What is the area of a circle?

Formula: A = \pi r^2

What is the formula for the perimeter of a rectangle?

Formula: P = 2l + 2w

What is the formula for the circumference of a circle?

Formula: C = 2\pi r or C = \pi d

What is the volume of a rectangular prism?

Formula: V = lwh

What is the volume of a cube?

Formula: V = s^3

What is the volume of a cylinder?

Formula: V = \pi r^2 h

What is the sum of angles on a straight line?

180^\circ

What is the sum of angles in a triangle?

180^\circ

What is the measure of a right angle?

90^\circ

How do you solve for x in the addition problem x + a = b?

Formula: x = b - a

How do you solve for x in the multiplication problem ax = b?

Formula: x = b \div a

What is the Distributive Property formula?

a(b + c) = ab + ac

How do you simplify by combining like terms?

Formula: ax + bx = (a + b)x

What is the formula for distance?

\text{Distance} = \text{Rate} \times \text{Time} (d = rt)

What is the formula for work rate problems?

\text{Work Rate} = \frac{1}{\text{Time}}

What is the average of a set of numbers?

Formula: \text{Average} = \frac{\text{Sum}}{\text{Number of items}}

What is the area of a parallelogram?

Formula: A = b \cdot h

What is the formula for the perimeter of a square?

Formula: P = 4s

What is the volume of a sphere?

Formula: V = \frac{4}{3} \pi r^3

What is the volume of a cone?

Formula: V = \frac{1}{3} \pi r^2 h

What is the formula for Simple Interest?

Formula: I = PRT

where:

• I = interest
• P = principal
• R = rate
• T = time

What is the formula for probability?

Formula: P = \frac{\text{Desired Outcome}}{\text{Total Outcome}}

What is the formula for the slope of a line?

Formula: m = \frac{y2 - y1}{x2 - x1}

What is the equation of a straight line in slope-intercept form?

Formula: y = mx + b

What is the distance formula between two points?

Formula: d = \sqrt{(x1 - x2)^2 + (y1 - y2)^2}

What is the formula for the midpoint of two points?

Formula: (x, y) = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)

What is the formula for the sum of interior angles of a polygon?

Formula: (n - 2) \times 180^\circ

What is the Pythagorean Theorem?

For a right-angle triangle: a^2 + b^2 = c^2

How do you add or subtract logarithms with the same base?

• \logb(mn) = \logb(m) + \log_b(n)
• \logb\left(\frac{m}{n}\right) = \logb(m) - \log_b(n)

What are the core exponent rules?

• (x^m)^n = x^{mn}
• x^m \cdot x^n = x^{m+n}
• \frac{x^m}{x^n} = x^{m-n}

What is the Quadratic Equation Formula?

If ax^2 + bx + c = 0, then:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

How do radicals relate to fractional exponents?

Formula: \sqrt[n]{x} = x^{\frac{1}{n}}

Example:
\sqrt{16} = (16)^{\frac{1}{2}} = 4