Grammar Hero Reference Sheet

Slope of a Line

Slope = Rise/Run = change in Y/Change in X

Quadratic Formula

note: ax^2+bx+c=0 and a =/ 0

Standard Form of a Linear Equation

Ax+By=C where A, B, and C are real numbers and A & B are not both zero.

Slope-Intercept Form

y=mx+b, where m is the slope and b is the y-intercept of the line.

Point-Slope form

y-y1=m(x-x1)

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

Pythagorean Theorem

a²+b²=c²

Area of a Triangle

A=1/2bh

b = the base of any triangle

h = perpendicular height of any triangle

Distance Formula

M = point halfway between points (x1, y1) and (x2, y2)

Simple Interest Formula

I=PRT (Interest = Principal (i.e., loan or investment amount * Rate of interest in decimal form * Time in terms of YEARS)

Distance, Rate, and Time

d = rt

Rate and time must be in proportional units (e.g., if rate is given in terms of miles per hour, time must be in terms of hours)

Percent Change

PC = (New Value - Old Value)/(Old Value) * 100

If PC is POSITIVE, there was an increase.

If PC is NEGATIVE, there was a decrease.

Order of Operations

PEMDAS

Multiplication/Division and Addition/Subtraction have EQUAL PRECEDENCE, so their calculations are performed as they appear in the expression from left to right.

Perimeter (except circles)

Simply add up all of its sides.

P=2a+2b=2(a+b)

Note: The perimeter of a CIRCLE is its circumference.

Mean (statistics)

Sum of all data points/number of data points

Range (statistics)

Maximum value-minimum value

Mode (statistics)

Most frequently occurring value in a data set.

Median (statistics)

The value in the middle of a data set when arranged in order from smallest to largest value.

If there is an odd number in the middle, that is the median.

If there is an even number, the median is the average of the two middle values.

Area of a Circle

A=πr²

Circumference of a Circle

C=2πr

OR

C=πd

Weight and Mass

1 ton = ….

1 pound = …

1 ton = 2,000 pounds

1 pound = 16 ounces

Capacity

8 fl oz = …

1 cup = …

2 pints = …

4 quarts =…

8 fl oz = 1 cup

2 cup = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

Multiplication/Division with Positive and Negative Numbers

• + +

• - -

• + -

• - +

Area and Perimeter Formulas of a Square

Perimeter: P=4s

Area = A = s^2

Area and Perimeter Formulas of a Rectangle

P = 2l + 2w

A = lw

Area and Perimeter Formulas of a Trapezoid

P = a + b1 + c + b2

A = 1/2(b1+b2)*h

Volume and Surface Area of a Cube

V = a^3

SA = 6a^2

Volume and Surface Area of a Rectangular Solid

V = lwh

SA = 2lw + 2wh + 2lh

Volume and Surface Area of a Cylinder

V= πr^2h

SA=2πr(h) + 2πr^2

Volume and Surface Area of a Sphere

V=(4/3)πr^3

SA= 4πr^2

Volume of a Rectangular Pyramid

V=1/3abh

ab = area if base of pyramid

Volume of a Cone

V=1/3πr²h

Probability(A)

P(A)=Desired Outcome/Total Number of Outcomes

Probability(Not A)

= 1 - P(A)

Probability(A and B)

P(A) * P*(B)

Probability(A or B) (exclusive)

P(A) + P(B)

Probability(A or B) (non-exclusive)

P(A) + P(B) - P(A and B)

Zero-Exponent Rule

Anything raised to the power of 0 = 1

Power Rule

To raise a power to a power you need to multiply the exponents.

Negative Exponent Rule

Negative exponents in the NUMERATOR get moved to the DENOMINATOR and become positive exponents.

Negative exponents in the DENOMINATOR get moved to the NUMERATOR and become positive exponents.

Product Rule of Exponents

when multiplying two terms with the same base, KEEP the base and ADD the exponents together

Quotient Rule of Exponents

when you are dividing and the bases are the same, KEEP the same base and SUBTRACT the exponents

Adding and Subtracting Fractions

A/B + C/D = (ad)+(cb)/b*d)

just cross multiply :)

Multiplying Fractions

Multiply straight across, then simplify as needed

Dividing Fractions

Keep, change, flip

Combined Rates and Work

Complementary Angles

Two angles whose sum is 90 degrees

Supplementary Angles

Two angles whose sum is 180 degrees

Properties of Radicals

Factorials (e.g. 8!)

To find the factorial of any integer, multiply it by every positive integer below it, e.g.:

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Divisibility Rules

Divisibility Rules for PRIME numbers

If a number is divisible by 2, 3, 4, 5, 6, 9, or 10, then it CANNOT be prime.

Fundamental Counting Principle

if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.

Converting Celsius to Fahrenheit

Converting Fahrenheit to Celsius