maths alevel formulas

* O C E / 2 6 2 9 0 *

Data, Formulae and Relationships Booklet
(Revised Version 2.1)

GCE Advanced Level and Advanced Subsidiary

Physics A
Physics units G481, G482, G484, G485

Instructions to Exams Officer/Invigilator
•

Do not send this Data Sheet for marking; it should be retained in the centre or destroyed.

These data, formulae and relationships are for the use of candidates following the Physics A specification.
Clean copies of this booklet must be available in the examination room, and must be given up to the invigilator at the end of the examination.
Copies of this booklet may be used for teaching.

© OCR 2010
GCE Physics A

DC (SLM) 26290/8
CST255

Data
Values are given to three significant figures, except where more are useful. speed of light in a vacuum

c

3.00 × 108 m s–1

permittivity of free space

ε0

8.85 × 10–12 C2 N–1 m–2 (F m–1)

elementary charge

e

1.60 × 10–19 C

Planck constant

h

6.63 × 10–34 J s

gravitational constant

G

6.67 × 10–11 N m2 kg–2

Avogadro constant

NA

6.02 × 1023 mol–1

molar gas constant

R

8.31 J mol–1 K–1

Boltzmann constant

k

1.38 × 10–23 J K–1

electron rest mass

me

9.11 × 10–31 kg

proton rest mass

mp

1.673 × 10–27 kg

neutron rest mass

mn

1.675 × 10–27 kg

alpha particle rest mass

mα

6.646 × 10–27 kg

acceleration of free fall

g

9.81 m s–2

© OCR 2010
GCE Physics A

CST255

Conversion factors unified atomic mass unit

1 u = 1.661 × 10–27 kg

electron-volt

1 eV = 1.60 × 10–19 J
1 day = 8.64 × 104 s
1 year ≈ 3.16 × 107 s
1 light year ≈ 9.5 × 1015 m

Mathematical equations arc length = rθ circumference of circle = 2pr area of circle = pr 2 curved surface area of cylinder = 2prh volume of cylinder = pr 2h surface area of sphere = 4pr2
4
volume of sphere = pr 3
3
Pythagoras’ theorem: a2 = b2 + c2
For small angle θ ⇒ sinθ ≈ tanθ ≈ θ and cosθ ≈ 1 lg(AB) = lg(A) + lg(B)
A
lg( ) = lg(A) – lg(B)
B
ln(xn) = n ln(x) ln(ekx) = kx

© OCR 2010
GCE Physics A

CST255

Formulae and relationships
Unit 1 –