CAPS formula sheet
Learn them by topic first. Then open the actual NSC information sheet — the one that does not say which topic a formula belongs to.
Grade 11
Mathematics information sheet
This is the sheet in Mathematics Paper 1 and Paper 2. The exam does not say which topic a formula belongs to — you choose.
- x=(−b ± b²−4ac)2a
- A=P(1 + ni)
- A=P(1 − ni)
- A=P(1 + i)ⁿ
- A=P(1 − i)ⁿ
- F=x [((1 + i)ⁿ − 1) / i]
- P=x [1 − (1 + i)⁻ⁿ]i
- Tₙ=a+(n − 1)d
- Sₙ=n2 [2a + (n − 1)d]
- Tₙ=arⁿ⁻¹
- Sₙ=a(rⁿ − 1)(r − 1)r ≠ 1
- S∞=a(1 − r)−1 < r < 1
- f'(x)=limh→0[f(x + h) − f(x)]h
- ddx [xⁿ]=n xⁿ⁻¹
- ∫ xⁿ dx=xⁿ⁺¹(n + 1)+Cn ≠−1
- Area=∫ab f(x) dx
- d=√[(x₂ − x₁)² + (y₂ − y₁)²]
- M=((x₁ + x₂)/2 ; (y₁ + y₂)/2)
- m=(y₂ − y₁)(x₂ − x₁)
- (x − a)²+(y − b)²=r²
- ⁿPᵣ=n!(n − r)!
- ⁿCᵣ=n![r!(n − r)!]
Data for Physical Sciences
Copied from the sheet in Physics Paper 1 and Chemistry Paper 2. Constants are named. Formulae are not labelled with a topic — you must recognise which line to copy.
TABLE 1: PHYSICAL CONSTANTS
- g=9.8 m·s⁻²
- c=3.0×10⁸ m·s⁻¹
- μ₀=4π×10⁻⁷ T·m·A⁻¹
- ε₀=8.85×10⁻¹² F·m⁻¹
- k=9.0×10⁹ N·m²·C⁻²
- e=1.6×10⁻¹⁹ C
- mₑ=9.11×10⁻³¹ kg
- mₚ=1.67×10⁻²⁷ kg
- h=6.63×10⁻³⁴ J·s
- G=6.67×10⁻¹¹ N·m²·kg⁻²
- R=8.31 J·K⁻¹·mol⁻¹
- NA=6.02×10²³ mol⁻¹
- F=9.65×10⁴ C·mol⁻¹
- T₀=273 K
- p₀=1.01×10⁵ Pa
TABLE 2: FORMULAE
- vf=vi+a Δt
- Δx=vi Δt+½ a (Δt)²
- vf²=vi²+2 a Δx
- Fnet=m a
- p=m v
- Fnet Δt=Δp
- w=m g
- ΔEk=Wnet
- Ek=½ m v²
- Ep=m g h
- W=F Δx cos θ
- P=WΔt=F v
- F=G m₁ m₂r²
- g=G Mr²
- v=f λ
- T=1f
- fL=fs (v ± vL)(v ± vs)
- E=h forE=h cλ
- sin θ=m λa
- n=cv
- n₁ sin θ₁=n₂ sin θ₂
- F=k Q₁ Q₂r²
- E=k Qr²
- V=Wq
- E=Vd
- R=VI
- emf=I(R + r)
- Rs=R₁+R₂+…
- 1Rp=1R₁+1R₂+…
- q=I Δt
- W=V q=V I Δt=I² R Δt=V² ΔtR
- P=I V=I² R=V²R
- Φ=B A cos θ
- ε=−N ΔΦΔt
- ε=ℓ v Borε=ℓ v B sin θ
- F=I ℓ B sin θ
- Vrms=Vmax√2Irms=Imax√2
TABLE 2 (continued)
- n=mM
- c=nVorc=mMV
- n=VVm
- p V=n R T
- (p₁ V₁)T₁=(p₂ V₂)T₂
- Kc=[C]ᶜ [D]ᵈ[A]ᵃ [B]ᵇ
- pH=−log [H₃O⁺]
- kw=[H₃O⁺][OH⁻]=1×10⁻¹⁴at25 °C
- E°cell=E°cathode−E°anode
- E°cell=E°reduction+E°oxidation
- q=m c ΔT
- n=V I ΔtF
Mathematical Literacy information sheet
Formulas you may need. The paper does not say which topic each line belongs to — you choose.
Finance
- part=(percent / 100)×whole
- VAT=0.15×price excluding VAT
- total including VAT=price×1.15
- A=P(1 + in)
- A=P(1 + i)ⁿ
- cost=fixed charge+(rate × units)
Measurement and maps
- P=2(L + W)
- A=L×W
- V=L×W×H
- Acircle=π r²Vcyl=π r² h
- 1 m³=1 000 ℓ
- real distance=map distance×scale
Data and chance
- mean=(sum of values)n
- IQR=Q₃−Q₁
- P(E)=n(E)n(S)
- E(X)=Σ (value × probability)