GED Math Formula Sheet

Area

Area of a square s = length of a side Lesson: A = s^2
Area of a rectangle l = length, w = width Lesson: A = lw
Area of a parallelogram b = base, h = height (straight up from the base, not the slanted side) Lesson: A = bh
Area of a triangle b = base, h = height Lesson: A = \tfrac{1}{2}bh
Area of a trapezoid b_1 and b_2 = the two parallel sides, h = height Lesson: A = \tfrac{1}{2}h(b_1 + b_2)
Area of a circle r = radius (half of the diameter); \pi \approx 3.14 Lesson: A = \pi r^2

Perimeter of a square s = length of a side Lesson: P = 4s
Perimeter of a rectangle l = length, w = width Lesson: P = 2l + 2w
Perimeter of a triangle s_1, s_2, s_3 = the three side lengths Lesson: P = s_1 + s_2 + s_3
Circumference of a circle the distance around a circle; r = radius, d = diameter, \pi \approx 3.14 Lesson: C = 2\pi r = \pi d

p = perimeter of the base with area B; \pi \approx 3.14

Rectangular prism l = length, w = width, h = height Lesson: SA = 2lw + 2lh + 2wh \qquad V = lwh
Right prism B = area of the base, p = perimeter of the base, h = height Lesson: SA = ph + 2B \qquad V = Bh
Cylinder r = radius of the base, h = height Lesson: SA = 2\pi rh + 2\pi r^2 \qquad V = \pi r^2 h
Pyramid B = area of the base, p = perimeter of the base, s = slant height, h = height Lesson: SA = \tfrac{1}{2}ps + B \qquad V = \tfrac{1}{3}Bh
Cone r = radius of the base, s = slant height, h = height Lesson: SA = \pi rs + \pi r^2 \qquad V = \tfrac{1}{3}\pi r^2 h
Sphere r = radius Lesson: SA = 4\pi r^2 \qquad V = \tfrac{4}{3}\pi r^3

Mean (average) add all the values of the data set, then divide by how many values there are Lesson: \text{mean} = \dfrac{\text{total of the values}}{\text{number of values}}
Median Lesson: the middle value when the data are in order; with an even number of values, it is the mean of the two middle values

Slope of a line (x_1, y_1) and (x_2, y_2) = two points on the line Lesson: m = \dfrac{y_2 - y_1}{x_2 - x_1}
Slope-intercept form of a line m = slope, b = y-intercept (where the line crosses the y-axis) Lesson: y = mx + b
Point-slope form of a line m = slope, (x_1, y_1) = a point on the line Lesson: y - y_1 = m(x - x_1)
Standard form of a quadratic equation a, b, c are numbers and a \ne 0 Lesson: y = ax^2 + bx + c
Quadratic formula solves ax^2 + bx + c = 0 Lesson: x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Pythagorean theorem in a right triangle: a, b = the two legs, c = the hypotenuse (the longest side, across from the right angle) Lesson: a^2 + b^2 = c^2
Simple interest I = interest, P = principal (the amount saved or borrowed), r = rate per year as a decimal, t = time in years Lesson: I = Prt
Distance = rate × time d = distance, r = rate (speed), t = time Lesson: d = rt
Total cost Lesson: \text{total cost} = (\text{number of units}) \times (\text{price per unit})

The real test does not give you these. They come up often, so know them before test day.

Percent Lesson: \text{percent} = \dfrac{\text{part}}{\text{whole}} \times 100\%
Percent change a positive answer is an increase, a negative answer is a decrease Lesson: \text{percent change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%
Distance between two points the Pythagorean theorem on the coordinate plane Lesson: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Midpoint of a segment the point halfway between (x_1, y_1) and (x_2, y_2) Lesson: M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)
Parallel and perpendicular lines perpendicular slopes are negative reciprocals, for example 2 and -\tfrac{1}{2} Lesson: \text{parallel: } m_1 = m_2 \qquad \text{perpendicular: } m_1 \cdot m_2 = -1
Angles of a triangle the angles on a straight line add up to 180^\circ; around a point, to 360^\circ Lesson: \angle A + \angle B + \angle C = 180^\circ
Probability always between 0 (impossible) and 1 (certain) Lesson: P(\text{event}) = \dfrac{\text{favorable outcomes}}{\text{total outcomes}}
Mode and range Lesson: mode = the value that appears most often; range = largest value - smallest value
Rules of exponents Lesson: a^m \cdot a^n = a^{m+n} \qquad \dfrac{a^m}{a^n} = a^{m-n} \qquad (a^m)^n = a^{mn}