Root x₁

—

Root x₂

—

Discriminant

—

Vertex

—

a (x² coefficient)

b (x coefficient)

c (constant)

Parabola y = ax² + bx + c

x = (−b ± √(b²−4ac)) / 2a · Discriminant > 0: two real roots · = 0: one root · < 0: complex roots

Mean

—

Median

—

Std Dev (σ)

—

Variance

—

Min

—

Max

—

Add Clear

Distribution (sorted)

n = 0 values · Range = — · Mode = —

Circle

Rectangle

Triangle

Sphere

Cylinder

Cone

Cube

Area

—

Perimeter

—

Volume

—

sin θ

—

cos θ

—

tan θ

—

θ in radians

—

Angle θ45°

Mode

Degrees Radians

sin, cos, tan over 0–360°

Law of cosines: c² = a² + b² − 2ab·cos(C) · Law of sines: a/sin A = b/sin B = c/sin C

Length

Mass

Temperature

Speed

Energy

Pressure

Value

From

To

—

Conversion scale (common values)

Displacement (s)

—

Final velocity (v)

—

Time (t)

—

Initial velocity u (m/s)0 m/s

Acceleration a (m/s²)9.8 m/s²

Time t (s)5 s

Position over time

v = u + at · s = ut + ½at² · v² = u² + 2as

Max Range

—

Max Height

—

Flight Time

—

Optimal Angle

45°

Launch speed (m/s)30 m/s

Launch angle (°)45°

Gravity (m/s²)9.81 m/s²

Trajectory

Range: R = v²sin(2θ)/g · Max height: H = v²sin²θ/2g · Time: T = 2v·sinθ/g

Net Force (N)

—

Acceleration (m/s²)

—

Friction Force (N)

—

Mass (kg)10 kg

Applied force (N)50 N

Friction coeff μ0.3

Incline angle (°)0°

Force vs mass (at current settings)

F = ma · Friction: f = μN · Normal on incline: N = mg·cosθ · Gravity component: mg·sinθ

Kinetic Energy

—

Potential Energy

—

Work Done

—

Power

—

Mass (kg)10 kg

Velocity (m/s)5 m/s

Height (m)10 m

Time (s)5 s

KE and PE at varying heights (same object)

KE = ½mv² · PE = mgh · W = F·d · P = W/t · g = 9.81 m/s²

Voltage (V)

—

Current (A)

—

Resistance (Ω)

—

Power (W)

—

Voltage V (volts)12 V

Resistance R (Ω)10 Ω

Current vs resistance (at fixed voltage)

V = IR · P = IV = V²/R = I²R · Series: R_total = R₁+R₂ · Parallel: 1/R = 1/R₁+1/R₂

Frequency (Hz)

—

Wavelength (m)

—

Period (s)

—

Wave speed (m/s)

—

Frequency (Hz)440 Hz

Wave speed (m/s)343 m/s

Amplitude1.0

Wave profile y = A·sin(2πx/λ)

v = fλ · T = 1/f · Sound in air ≈ 343 m/s · Light = 3×10⁸ m/s

Pressure (Pa)

—

Volume (m³)

—

Temperature (K)

—

Moles (n)

—

Pressure (kPa)101.3 kPa

Volume (L)22.4 L

Moles (n)1 mol

Pressure vs volume (isothermal — Boyle's Law)

PV = nRT · R = 8.314 J/(mol·K) · STP: 0°C, 101.325 kPa · T(K) = T(°C) + 273.15

Molarity (M)

—

Moles

—

Diluted conc (M)

—

Moles of solute0.5 mol

Volume of solution (L)1.0 L

Dilution volume (L)2.0 L

Concentration vs volume

M = n / V · Dilution: M₁V₁ = M₂V₂ · Units: mol/L or mol/dm³

pH

—

pOH

—

[H⁺] mol/L

—

Nature

—

pH value7.0

pH scale

pH = −log[H⁺] · pOH = −log[OH⁻] · pH + pOH = 14 · Kw = [H⁺][OH⁻] = 10⁻¹⁴

Remaining

—

Decayed

—

% Remaining

—

Decay constant λ

—

Initial amount (g)100 g

Half-life (years)10 yr

Elapsed time (years)20 yr

Radioactive decay curve

N(t) = N₀ × (½)^(t/t½) · Decay constant: λ = ln2 / t½ · N(t) = N₀e^(−λt)

Final Population

—

Growth

—

Doubling Time

—

Initial population1,000

Growth rate (%/yr)3%

Years50 yrs

Carrying capacity Koff

Exponential vs logistic growth

Exponential: N(t) = N₀·e^(rt) · Logistic: N(t) = K / (1 + ((K−N₀)/N₀)·e^(−rt))