Mathematic Formulas
Geometric Formulas
I. Perimeter
a. Rectangle:
b. Regular Polygon:
c. Square:
II. Circumference of Circle
a. Diameter Given:
b. Radius Given:
III. Area
a.
b.
c.
d.
e.
f.
g.
Circle:
Parallelogram:
Rectangle:
Square:
Triangle:
Trapezoid:
Regular Polygon:
P = 2(ℓ+w) or P = 2ℓ + 2w
P = ns
P = 4s
C = πd
C = 2πr
A = πr²
A = bh
A = ℓw or A = bh
A = s²
A = ½bh
A = ½(b1 + b2)h
A = ½aP
IV. Surface Area
a.
b.
c.
d.
e.
f.
g.
Cube:
Prism:
Rectangular Prism:
Cylinder:
Cone:
Sphere:
Regular Pyramid:
S = 6e²
S = Ph + 2B
S = 2(ℓw + ℓh + wh)
S = 2πrh + 2πr²
S = πrℓ + πr²
S = 4πr²
S = ½Pℓ + B
V. Volume
a.
b.
c.
d.
e.
f.
g.
Cylinder:
Cube:
Prism (Gen. Formula):
Pyramid (Gen. Formula):
Rectangular Prism:
Cone:
Sphere:
V = (πr²)h or V = Bh
V = e³
V = Bh
V = ⅓Bh
V = ℓwh
V = ⅓Bh or V = ⅓πr²h
V = 4/3πr³
VI. Variation
a. Direct:
b. Inverse:
y = kx or k = y/x, k ≠ 0
y = k/x or k = xy, k ≠ 0
VII. Nth Term of a Sequence
a. Arithmetic:
b. Geometric:
aⁿ = aⁿ ̄ ¹ + d
aⁿ = aⁿ‾ ¹ • r
VIII. Pythagorean Theorem
a. Right Triangle with hypotenuse c and legs a and b:
i. c² = a² + b²
IX. Trigonometric Ratios
a. Exponential Growth
i. y = ab ͯ, a > 0 and b > 1
b. Exponential Decay
i. y = ab ͯ, a > 0 and 0 < b < 1
c. Acute angle of a right triangle:
i. cosine (cos) = adjacent leg/hypotenuse
ii. sine (sin) = opposite leg/hypotenuse
iii. tangent (tan) = opposite leg/adjacent leg
X. Slope
a. A line with points (x1, y1) and (x2, y2):
i. m = y2 – y1/x2 – x1
XI. Linear Functions
a.
b.
c.
d.
Standard Form:
Slope-intercept form:
Point-slope form:
Slope Formula:
ax + by = c
y = mx + b
y – y1 = m(x – x1)
m = y2 – y1/x2 – x1
e.
XII. Quadratic Equations
a.
b.
c.
d.
Standard Form:
Quadratic Formula:
Discriminant:
Axis of Symmetry:
ax² + bx + c = 0
x = -b ± √b² - 4ac/2a
√b² - 4ac
x = -b/2a
XIII. Nonlinear Functions
a. Absolute-Value Function:
b. Exponential Function:
c. Quadratic Function:
d. Rational Function:
e. Radical Function:
XIV. Distance Formula
a. d = √(x2 – x1)² + (y2 – y1)²
XV. Midpoint Formula
a. M = (x1 + x2/2 , y1 + y2/2)
y = |x|
y = ab ͯ
y = ax² + bx + c
y = a/x
y = √x
Other Formulas
I. Celsius (°C)
a. Formula:
C = 5/9 (F – 32)
II. Fahrenheit (°F)
a. Formula:
F = 9/5 C + 32
III. Simple Interest
a. Breakdown: (principal(p) • rate(r) • time(t)(in years) = Simple Interest(SI))
b. Formula:
SI = p • r • t
IV. Distance
a. Breakdown: (rate(r) • time(t) = Distance(D))
b. Formula:
D=r•t
V. Percentage
a. Breakdown: rate(r) • base(b) = percentage(p)
b. Formula:
P=r•b
VI. Discount
a. Breakdown: (list price(LP) • rate of discount(R of D) = Discount(D))
b. Formula:
D = LP • R of D
VII. Sale Price
a. Breakdown: (regular price(RP) – discount(D) = Sale Price(SP))
b. Formula:
SP = RP - D
VIII. Sales Tax
a. Breakdown: (marked price(MP) • rate of sales tax(R of T) = Sales
Tax(ST))
b. Formula:
ST = MP • R of T
IX. Total Cost
a. Breakdown: (marked price(MP) + sales tax(ST) = Total Cost(TC))
b. Formula:
TC = MP + ST
X. Commission
a. Breakdown: (total sales(TS) • rate of commission(R of C) =
Commission(C))
b. Formula:
C = TS • R of C
XI. Compound Interest Balance
a. Formula:
XII. Half-life
a. Formula:
XIII. Percentage Proportion
a. Formula:
A = P(1 + r/n)ⁿͭ
A = P(0.5)ͭ
part/whole = percent/100