Student Tools
Calculators, converter, and formula sheet
Scientific Calculator
Advanced
Expression
Fraction Calculator
ExactUnit Converter
CommonGraphing Calculator
y = f(x)Formula Sheet
ReferenceAlgebra
Slope
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Rate of change between two points.
Slope-intercept form
\(y=mx+b\)
\(m\) is slope, \(b\) is y-intercept.
Point-slope form
\(y-y_1=m(x-x_1)\)
Line through one known point.
Quadratic formula
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
For \(ax^2+bx+c=0\).
Discriminant
\(D=b^2-4ac\)
Determines the number/type of roots.
Vertex x-value
\(x=\frac{-b}{2a}\)
Axis of symmetry for a parabola.
Distance formula
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Distance between two points.
Midpoint
\(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\)
Point halfway between two points.
Geometry
Rectangle
\(A=lw,\ P=2l+2w\)
Area and perimeter.
Triangle
\(A=\frac{1}{2}bh\)
Area using base and height.
Circle
\(A=\pi r^2,\ C=2\pi r\)
Area and circumference.
Pythagorean theorem
\(a^2+b^2=c^2\)
Right triangles only.
Rectangular prism
\(V=lwh\)
Volume.
Cylinder
\(V=\pi r^2h\)
Volume.
Cone
\(V=\frac{1}{3}\pi r^2h\)
Volume.
Sphere
\(V=\frac{4}{3}\pi r^3\)
Volume.
Trigonometry
Sine
\(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\)
Right triangle ratio.
Cosine
\(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)
Right triangle ratio.
Tangent
\(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
Right triangle ratio.
Radians
\(180^\circ=\pi\text{ radians}\)
Degree-radian conversion.
Data and Probability
Mean
\(\bar{x}=\frac{\text{sum of values}}{\text{number of values}}\)
Average.
Weighted mean
\(\bar{x}=\frac{\sum wx}{\sum w}\)
Average with weights.
Percent change
\(\frac{\text{new}-\text{old}}{\text{old}}\times100\%\)
Increase or decrease.
Probability
\(P=\frac{\text{favorable outcomes}}{\text{total outcomes}}\)
Equally likely outcomes.
Science
Density
\(\rho=\frac{m}{V}\)
Mass per volume.
Speed
\(v=\frac{d}{t}\)
Distance over time.
Force
\(F=ma\)
Newton's second law.
Work
\(W=Fd\)
Force times distance.
Kinetic energy
\(KE=\frac{1}{2}mv^2\)
Energy of motion.
Ohm's law
\(V=IR\)
Voltage, current, resistance.
Wave speed
\(v=f\lambda\)
Frequency times wavelength.
Moles
\(n=\frac{m}{M}\)
Mass over molar mass.