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HSC exam sheets

Formula and data sheets

These are study transcriptions of the sheets NESA prints at the back of the papers. Use them in practice the way you will in the exam. The official PDF is the authority.

Official HSC papers and formula sheets stay on the NESA site. We do not host those PDFs. Reproduction of whole papers needs NESA rights; until Chad decides that, this page only transcribes the public formula lines and links out.

Physics data and formulae

Use these as you would in the HSC. The official NESA PDF is the authority if anything here is shorter.

Official: NESA Physics data sheet, formulae sheet and periodic table

Constants (selected)

  • Acceleration due to gravity
    g=9.8 m s−2g = 9.8\ \text{m s}^{-2}
  • Speed of light
    c=3.00×108 m s−1c = 3.00 \times 10^{8}\ \text{m s}^{-1}
  • Elementary charge
    e=1.602×10−19 Ce = 1.602 \times 10^{-19}\ \text{C}
  • Electron rest mass
    me=9.109×10−31 kgm_e = 9.109 \times 10^{-31}\ \text{kg}
  • Planck constant
    h=6.626×10−34 J sh = 6.626 \times 10^{-34}\ \text{J s}
  • Coulomb constant
    k=8.99×109 N m2C−2k = 8.99 \times 10^{9}\ \text{N m}^{2}\text{C}^{-2}
  • Universal gravitation
    G=6.67×10−11 N m2kg−2G = 6.67 \times 10^{-11}\ \text{N m}^{2}\text{kg}^{-2}

Motion and mechanics

  • Average velocity
    v=ΔxΔtv = \frac{\Delta x}{\Delta t}
  • Equations of motion
    v=u+ats=ut+12at2v2=u2+2asv = u + at \quad s = ut + \tfrac{1}{2}at^{2} \quad v^{2} = u^{2} + 2as
  • Newton II
    ΣF=ma\Sigma F = ma
  • Weight
    F=mgF = mg
  • Work
    W=Fscos⁡θW = Fs\cos\theta
  • Kinetic energy
    Ek=12mv2E_k = \tfrac{1}{2}mv^{2}
  • Gravitational potential energy
    Ep=mghE_p = mgh
  • Impulse
    I=FΔt=ΔpI = F\Delta t = \Delta p
  • Momentum
    p=mvp = mv
  • Centripetal
    a=v2rF=mv2ra = \frac{v^{2}}{r} \quad F = \frac{mv^{2}}{r}
  • Torque
    τ=rFsin⁡θ\tau = rF\sin\theta
  • Newton gravitation
    F=GMmr2F = \frac{GMm}{r^{2}}
  • Orbital
    v=GMrr3T2=GM4π2v = \sqrt{\frac{GM}{r}} \quad \frac{r^{3}}{T^{2}} = \frac{GM}{4\pi^{2}}

Waves, electricity, light

  • Wave equation
    v=fλv = f\lambda
  • Ohm
    V=IRV = IR
  • Coulomb
    F=14πε0q1q2r2F = \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^{2}}
  • Electric field
    E=Fq=VdE = \frac{F}{q} = \frac{V}{d}
  • Magnetic force on a charge
    F=qvBsin⁡θF = qvB\sin\theta
  • Magnetic force on a wire
    F=IlBsin⁡θF = IlB\sin\theta
  • Faraday
    E=−NΔΦΔt\mathcal{E} = -N\frac{\Delta\Phi}{\Delta t}
  • Photon
    E=hf=hcλE = hf = \frac{hc}{\lambda}
  • Photoelectric
    hf=ϕ+12mvmax⁡2hf = \phi + \tfrac{1}{2}mv_{\max}^{2}
  • Time dilation / length contraction
    t=t01−v2/c2l=l01−v2/c2t = \frac{t_0}{\sqrt{1-v^{2}/c^{2}}} \quad l = l_0\sqrt{1-v^{2}/c^{2}}

Mathematics Standard reference sheet

The same one-page sheet is provided in the Standard 1 and Standard 2 exams. Transcribed for study. The official PDF is the authority.

Official: NESA Mathematics Standard 1 and 2 reference sheet

Measurement

  • Trapezium
    A=12h(a+b)A = \tfrac{1}{2}h(a+b)
  • Pythagoras
    c2=a2+b2c^{2} = a^{2} + b^{2}
  • Sine rule
    asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
  • Cosine rule
    c2=a2+b2−2abcos⁡Cc^{2} = a^{2} + b^{2} - 2ab\cos C
  • Area of a triangle
    A=12absin⁡CA = \tfrac{1}{2}ab\sin C
  • Sphere surface / volume
    SA=4πr2V=43πr3SA = 4\pi r^{2} \quad V = \tfrac{4}{3}\pi r^{3}
  • Cylinder / prism
    V=AhV = Ah

Financial mathematics

  • Simple interest
    I=PrnI = Prn
  • Compound interest
    FV=PV(1+r)nFV = PV(1+r)^{n}
  • Annuity future value
    FV=M(1+r)n−1rFV = M\frac{(1+r)^{n}-1}{r}
  • Annuity present value
    PV=M1−(1+r)−nrPV = M\frac{1-(1+r)^{-n}}{r}

Statistics and algebra

  • Mean
    xˉ=∑xn\bar{x} = \frac{\sum x}{n}
  • z-score
    z=x−μσz = \frac{x-\mu}{\sigma}
  • Empirical rule
    68%/95%/99.7%within1/2/3standarddeviations68\% / 95\% / 99.7\% within 1 / 2 / 3 standard deviations
  • Gradient
    m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2-x_1}
  • Gradient–intercept
    y=mx+by = mx + b
  • Float
    float=LST−EST\text{float} = \text{LST} - \text{EST}

Engineering Studies formulae

Study transcription of the public HSC Engineering Studies formulae sheet printed at the back of the paper. The official NESA PDF is the authority if anything here is shorter. g = 9.8 m s⁻² unless the question states otherwise.

Official: NESA HSC Engineering Studies formulae sheet

Statics and machines

  • Weight
    W=mgW = mg
  • Moment of a force
    M=FdM = Fd
  • Mechanical advantage
    MA=LE\text{MA} = \dfrac{L}{E}
  • Velocity ratio
    VR=dEdL\text{VR} = \dfrac{d_E}{d_L}
  • Efficiency
    η=MAVR×100%\eta = \dfrac{\text{MA}}{\text{VR}} \times 100\%
  • Static friction
    F=μNF = \mu N
  • Angle of friction
    tan⁡ϕ=μ\tan\phi = \mu

Stress, strain and bending

  • Normal stress
    σ=FA\sigma = \dfrac{F}{A}
  • Normal strain
    ε=ΔLL\varepsilon = \dfrac{\Delta L}{L}
  • Young's modulus
    E=σεE = \dfrac{\sigma}{\varepsilon}
  • Shear stress
    τ=FA\tau = \dfrac{F}{A}
  • Hooke (elastic)
    σ=Eε\sigma = E\varepsilon
  • Factor of safety
    FoS=σyield or ultimateσworking\text{FoS} = \dfrac{\sigma_{\text{yield or ultimate}}}{\sigma_{\text{working}}}
  • Bending stress
    σ=MyI\sigma = \dfrac{My}{I}

Energy, fluids and flight

  • Work
    W=FsW = Fs
  • Kinetic energy
    Ek=12mv2E_k = \tfrac{1}{2}mv^{2}
  • Gravitational potential energy
    Ep=mghE_p = mgh
  • Power
    P=Wt=FvP = \dfrac{W}{t} = Fv
  • Hydrostatic pressure
    P=ρghP = \rho gh
  • Pascal's principle
    F1A1=F2A2\dfrac{F_1}{A_1} = \dfrac{F_2}{A_2}
  • Bernoulli (incompressible)
    P+12ρv2+ρgh=constantP + \tfrac{1}{2}\rho v^{2} + \rho gh = \text{constant}
  • Lift
    L=12ρv2ACLL = \tfrac{1}{2}\rho v^{2} A C_L
  • Drag
    D=12ρv2ACDD = \tfrac{1}{2}\rho v^{2} A C_D

Electricity

  • Ohm's law
    V=IRV = IR
  • Electrical power
    P=VI=I2R=V2RP = VI = I^{2}R = \dfrac{V^{2}}{R}
  • Series resistance
    RT=R1+R2+⋯R_T = R_1 + R_2 + \cdots
  • Parallel resistance
    1RT=1R1+1R2+⋯\dfrac{1}{R_T} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots
  • Electrical energy
    W=VItW = VIt

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