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Grade 10 Science — formula sheet

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

The full booklet — learning zone, problems, answer key
Speed, Distance & Time
v=dtv = \tfrac{d}{t}
Displacement from Average Velocity
d=v0+v2 td = \frac{v_0 + v}{2} \, t
Wave Speed (v = fλ)
v=fλv = f \lambda
Period-Frequency Relation
T=1fT = \frac{1}{f}
Index of Refraction (n = c/v)
n=cvn = \frac{c}{v}
Snell's Law of Refraction
n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2
Critical Angle for Total Internal Reflection
sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}
Focal Length of a Spherical Mirror
f=R2f = \frac{R}{2}
Thin Lens Equation
1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
Lens Magnification (m = −d_i/d_o)
m=−didom = -\frac{d_i}{d_o}
Magnification from Heights (m = h_i/h_o)
m=hihom = \frac{h_i}{h_o}
Lens Power in Diopters
P=1fP = \frac{1}{f}
Sensible Heat (Q = mcΔT)
Q=mcΔTQ = m c \Delta T
Latent Heat
Q=mLQ = m L
Thermal Linear Expansion
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T
Heat Conduction Rate
P=kAΔTdP = \tfrac{k A \Delta T}{d}
Electric Charge (Q = It)
Q=ItQ = I t
Ohm's Law
V=IRV = I R
Two Resistors in Series
Rt=R1+R2R_{t} = R_{1} + R_{2}
Two Resistors in Parallel
Rt=R1R2R1+R2R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}
Electrical Power (P = VI)
P=VIP = V I
Electrical Power (P = I²R)
P=I2RP = I^{2} R
Electrical Energy (E = Pt)
E=PtE = P t
Energy Cost from a Utility Rate
Ce=E peC_e = E \, p_e
Pressure (P = F/A)
P=FAP = \frac{F}{A}
Hydrostatic Pressure (P = ρgh)
P=ρghP = \rho g h
Barometric Pressure with Altitude
P=P0 e−Mgz/RTP = P_0 \, e^{-Mgz/RT}
Relative Humidity from Vapour Pressure
φ=pvpws\varphi = \frac{p_v}{p_{ws}}
Saturation Vapour Pressure (Magnus / Alduchov–Eskridge)
pws=610.94exp⁡ ⁣(17.625 tt+243.04)p_{ws} = 610.94 \exp\!\left(\frac{17.625\,t}{t + 243.04}\right)
Dew Point (Magnus Approximation)
Td=c γb−γ,γ=ln⁡ ⁣RH100+b Tc+TT_d = \frac{c\,\gamma}{b - \gamma}, \quad \gamma = \ln\!\frac{\mathrm{RH}}{100} + \frac{b\,T}{c + T}
Humidex (Canadian Humidity Index)
H=T+0.5555 (e−10),e=6.11 e5417.753(1273.16−1Td)H = T + 0.5555\,(e - 10), \quad e = 6.11\,e^{5417.753\left(\frac{1}{273.16} - \frac{1}{T_d}\right)}
Wind Chill (2001 North American Formula)
Twc=13.12+0.6215 T−11.37 V0.16+0.3965 T V0.16T_{wc} = 13.12 + 0.6215\,T - 11.37\,V^{0.16} + 0.3965\,T\,V^{0.16}
Heat Index (Rothfusz Regression)
HI=c1+c2T+c3R+c4TR+c5T2+c6R2+c7T2R+c8TR2+c9T2R2\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
Albedo and Reflected Radiation
Gr=α GG_r = \alpha\,G
Environmental Lapse Rate
Γ=T1−T2z2−z1\Gamma = \frac{T_1 - T_2}{z_2 - z_1}
Flash-to-Bang Distance to a Lightning Strike
d=(331.3+0.606 TC)td = \left(331.3 + 0.606\,T_C\right) t
Speed of Sound in Air
v=331.3+0.606 TCv = 331.3 + 0.606\, T_C