Topic Quiz A.6: Equations of lines

Area

Area of a square s = length of a side

A = s^2

Area of a rectangle l = length, w = width

A = lw

Area of a parallelogram b = base, h = height (straight up from the base, not the slanted side)

A = bh

Area of a triangle b = base, h = height

A = \tfrac{1}{2}bh

Area of a trapezoid b_1 and b_2 = the two parallel sides, h = height

A = \tfrac{1}{2}h(b_1 + b_2)

Area of a circle r = radius (half of the diameter); \pi \approx 3.14

A = \pi r^2

Perimeter and circumference

Perimeter of a square s = length of a side

P = 4s

Perimeter of a rectangle l = length, w = width

P = 2l + 2w

Perimeter of a triangle s_1, s_2, s_3 = the three side lengths

P = s_1 + s_2 + s_3

Circumference of a circle the distance around a circle; r = radius, d = diameter, \pi \approx 3.14

C = 2\pi r = \pi d

Surface area (SA) and volume (V)

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

Rectangular prism l = length, w = width, h = height

SA = 2lw + 2lh + 2wh \qquad V = lwh

Right prism B = area of the base, p = perimeter of the base, h = height

SA = ph + 2B \qquad V = Bh

Cylinder r = radius of the base, h = height

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

SA = \tfrac{1}{2}ps + B \qquad V = \tfrac{1}{3}Bh

Cone r = radius of the base, s = slant height, h = height

SA = \pi rs + \pi r^2 \qquad V = \tfrac{1}{3}\pi r^2 h

Sphere r = radius

SA = 4\pi r^2 \qquad V = \tfrac{4}{3}\pi r^3

Data

Mean (average) add all the values of the data set, then divide by how many values there are

\text{mean} = \dfrac{\text{total of the values}}{\text{number of values}}

Median

the middle value when the data are in order; with an even number of values, it is the mean of the two middle values

Algebra

Slope of a line (x_1, y_1) and (x_2, y_2) = two points on the line

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)

y = mx + b

Point-slope form of a line m = slope, (x_1, y_1) = a point on the line

y - y_1 = m(x - x_1)

Standard form of a quadratic equation a, b, c are numbers and a \ne 0

y = ax^2 + bx + c

Quadratic formula solves ax^2 + bx + c = 0

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)

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

I = Prt

Distance = rate × time d = distance, r = rate (speed), t = time

d = rt

Total cost

\text{total cost} = (\text{number of units}) \times (\text{price per unit})