Grade 10 Science: formula sheet

Motion, light, heat, electricity and weather · 37 formulas · metric edition 1

Download the PDF: 2 pages The full study guide: modules, problems, answer key

Module 1 · Motion — Speed, Distance, Time

Science 10-1 Speed, Distance & Time

v = \tfrac{d}{t}

Average speed from distance travelled and elapsed time.

Science 10-2 Displacement from Average Velocity

d = \frac{v_0 + v}{2} \, t

Displacement as the average of initial and final velocities multiplied by the elapsed time, valid…

Module 2 · Light & Geometric Optics

Science 10-3 Wave Speed (v = fλ)

v = f \lambda

The universal wave equation: a wave's speed equals its frequency times its wavelength.

Science 10-4 Period-Frequency Relation

T = \frac{1}{f}

Period and frequency are reciprocals: seconds per cycle versus cycles per second.

Science 10-5 Index of Refraction (n = c/v)

n = \frac{c}{v}

How much a medium slows light: the ratio of c to the speed of light in the medium.

Science 10-6 Snell's Law of Refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

Light bends at an interface so that n sin θ stays the same on both sides.

Science 10-7 Critical Angle for Total Internal Reflection

\sin\theta_c = \frac{n_2}{n_1}

Beyond this angle of incidence, light in the denser medium reflects totally instead of refracting.

Science 10-8 Focal Length of a Spherical Mirror

f = \frac{R}{2}

A spherical mirror focuses parallel rays at half its radius of curvature.

Science 10-9 Thin Lens Equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Relates a thin lens's focal length to its object and image distances.

Science 10-10 Lens Magnification (m = −d_i/d_o)

m = -\frac{d_i}{d_o}

Image magnification from the ratio of image to object distance; the minus sign tracks inversion.

Science 10-11 Magnification from Heights (m = h_i/h_o)

m = \frac{h_i}{h_o}

Magnification as the ratio of image height to object height.

Science 10-12 Lens Power in Diopters

P = \frac{1}{f}

The optician's unit: lens power in diopters is the reciprocal of focal length in metres.

Module 3 · Heat & Temperature

Science 10-13 Sensible Heat (Q = mcΔT)

Q = m c \Delta T

Heat needed to change a mass's temperature: mass times specific heat times the temperature change.

Science 10-14 Latent Heat

Q = m L

Heat absorbed or released when a mass changes phase at constant temperature.

Science 10-15 Thermal Linear Expansion

\Delta L = \alpha L_0 \Delta T

Length change of a solid caused by a temperature change, via the linear expansion coefficient.

Science 10-16 Heat Conduction Rate

P = \tfrac{k A \Delta T}{d}

Steady-state heat flow through a slab by Fourier's law of conduction.

Module 4 · Electricity — Circuits & Power

Science 10-17 Electric Charge (Q = It)

Q = I t

Total charge transferred by a steady current flowing for a given time.

Science 10-18 Ohm's Law

V = I R

Relates the voltage across a conductor to the current through it and its resistance.

Science 10-19 Two Resistors in Series

R_{t} = R_{1} + R_{2}

Total resistance of two resistors connected end to end is simply their sum.

Science 10-20 Two Resistors in Parallel

R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

Total resistance of two resistors connected side by side: product over sum, always less than either…

Science 10-21 Electrical Power (P = VI)

P = V I

Power delivered to a component as the product of the voltage across it and the current through it.

Science 10-22 Electrical Power (P = I²R)

P = I^{2} R

Power dissipated as heat in a resistance carrying a current (Joule heating).

Science 10-23 Electrical Energy (E = Pt)

E = P t

Energy consumed by a device drawing constant power over a period of time.

Science 10-24 Energy Cost from a Utility Rate

C_e = E \, p_e

Cost of the energy a system consumes: kilowatt-hours or fuel BTUs times the utility rate, for tower…

Module 5 · Weather, Climate & the Atmosphere

Science 10-25 Pressure (P = F/A)

P = \frac{F}{A}

Pressure as perpendicular force spread over an area.

Science 10-26 Hydrostatic Pressure (P = ρgh)

P = \rho g h

Gauge pressure at depth h in a fluid of density ρ, using g = 9.80665 m/s².

Science 10-27 Barometric Pressure with Altitude

P = P_0 \, e^{-Mgz/RT}

Atmospheric pressure at a height above a reference level, for an isothermal layer.

Science 10-28 Relative Humidity from Vapour Pressure

\varphi = \frac{p_v}{p_{ws}}

Relative humidity as what it actually is: the vapour pressure present divided by the saturation…

Science 10-29 Saturation Vapour Pressure (Magnus / Alduchov–Eskridge)

p_{ws} = 610.94 \exp\!\left(\frac{17.625\,t}{t + 243.04}\right)

The vapour pressure of water at saturation, from temperature alone, by the Alduchov–Eskridge Magnus…

Science 10-30 Dew Point (Magnus Approximation)

T_d = \frac{c\,\gamma}{b - \gamma}, \quad \gamma = \ln\!\frac{\mathrm{RH}}{100} + \frac{b\,T}{c + T}

Dew point from air temperature and relative humidity by the Magnus formula with the WMO's Sonntag…

Science 10-31 Humidex (Canadian Humidity Index)

H = T + 0.5555\,(e - 10), \quad e = 6.11\,e^{5417.753\left(\frac{1}{273.16} - \frac{1}{T_d}\right)}

Environment Canada's humidex: air temperature raised by the excess vapour pressure computed from…

Science 10-32 Wind Chill (2001 North American Formula)

T_{wc} = 13.12 + 0.6215\,T - 11.37\,V^{0.16} + 0.3965\,T\,V^{0.16}

The wind chill index adopted by Canada and the United States in 2001, from air temperature and wind…

Science 10-33 Heat Index (Rothfusz Regression)

\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2

The US National Weather Service heat index, Rothfusz's nine-term regression through Steadman's…

Science 10-34 Albedo and Reflected Radiation

G_r = \alpha\,G

Shortwave radiation reflected by a surface, as its albedo times the incident irradiance.

Science 10-35 Environmental Lapse Rate

\Gamma = \frac{T_1 - T_2}{z_2 - z_1}

How fast the air cools with height, from two temperatures at two altitudes.

Science 10-36 Flash-to-Bang Distance to a Lightning Strike

d = \left(331.3 + 0.606\,T_C\right) t

Light arrives effectively instantly and sound does not, so the gap between the flash and the…

Science 10-37 Speed of Sound in Air

v = 331.3 + 0.606\, T_C

The speed of sound in dry air grows about 0.6 m/s for every degree Celsius above freezing.