Edexcel A Level Maths Inverse Formula Sheet

EDEXCEL A LEVEL MATHS - INVERSE FORMULA BOOKLET
All the formula + identities NOT in the formula booklet that you need to know.
BASIC GCSE EQUATIONS LAWS OF INDICES TRIGONOMETRY

Quadratic Equation: 𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛 Trig Definitions:
−𝑏 ± √𝑏2 − 4𝑎𝑐 𝑎𝑚 sin 𝜃

𝑥= = 𝑎𝑚−𝑛 ≡ tan 𝜃
2𝑎 𝑎𝑛 cos 𝜃
Cosine Rule: (𝑎𝑚 ) 𝑛 = 𝑎𝑚𝑛 1

≡ cosec 𝜃
sin 𝜃
𝑎2 = 𝑏2 + 𝑐 2 − 2𝑏𝑐 cos 𝐴 (𝑎𝑏)𝑛 = 𝑎𝑛 𝑏𝑛
1
2 2 2 1 ≡ sec 𝜃
𝑏 +𝑐 −𝑎 cos 𝜃
cos 𝐴 = 𝑎𝑚 = 𝑚√𝑎
2𝑏𝑐 cos 𝜃 1
−𝑚
1 ≡ ≡ cot 𝜃
Sine rule: 𝑎 = 𝑚 sin 𝜃 tan 𝜃
𝑎
𝑎 𝑏 𝐶
= = Pythagorean Identities:
sin 𝐴 sin 𝐵 sin 𝐶 LAWS OF LOGARITHMS
sin2 𝜃 + cos 2 𝜃 ≡ 1
𝑥
Area of a triangle: 𝑎 = 𝑦 ⟹ 𝑥 = log𝑎 (𝑦)
1 + cot 2 𝜃 ≡ cosec 2 𝜃
1 log 𝑎(𝑥) + log 𝑎 (𝑦) = log 𝑎 (𝑥𝑦)
𝐴= 𝑎𝑏 sin 𝐶 tan2 𝜃 + 1 ≡ sec 2 𝜃
2
𝑥
log 𝑎(𝑥) − log 𝑎 (𝑦) = log 𝑎 ( ) Double angle formulae:
COORDINATE GEOMETRY 𝑦
For straight line between (𝑥1 , 𝑦1 )
log 𝑎 (𝑥 𝑦 ) = ylog 𝑎 (𝑥) sin 2𝜃 = 2 sin 𝜃 cos 𝜃
and (𝑥2 , 𝑦2 ):
𝑦 −𝑦 log 𝑎 (𝑎) = 1 cos 2𝜃 = cos 2 𝜃 − sin2 𝜃
Gradient, 𝑚 = 𝑥2 −𝑥1
2 1 = 2 cos 2 𝜃 − 1
log 𝑎 (1) = 0 = 1 − 2 sin2 𝜃
Length = √(𝑥2 − 𝑥1 ) + (𝑦2 − 𝑦1 )
1
Midpoint: (
𝑥1 +𝑥2 𝑦1 +𝑦2
, ) log 𝑎 ( ) = − log 𝑎(𝑥) 2 tan 𝜃
2 2 𝑥 tan 2𝜃 =
1 − tan2 𝜃
Lines perpendicular if: 𝑚1 𝑚2 = −1
VECTORS
Equation of a straight line: RADIANS
⃑⃑⃑⃑⃑ = 𝑂𝐵
𝐴𝐵 ⃑⃑⃑⃑⃑ − 𝑂𝐴
⃑⃑⃑⃑⃑
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ) Definition:
1
𝑎̂ = 𝑎
Equation of a circle (centre (𝒂, 𝒃), |𝑎| 180°
radius 𝒓): 1rad =
𝑖
𝜋
(𝑥 − 𝑎 )2 + (𝑦 − 𝑏 )2 = 𝑟 2 For 𝑎 = [ 𝑗 ], |𝑎| = √𝑖 2 + 𝑗 2 + 𝑘 2 Arc length:
𝑘
Circle theorems: 𝑙 = 𝑟𝜃
• The perpendicular bisector of a chord will SEQUENCES + SERIES Sector area:
pass through the centre of a circle.
General forms of arithmetic and 1 2
• A tangent to a circle is perpendicular to
the radius of the circle at the point of geometric series: 𝐴= 𝑟 𝜃
intersection. 2
Arithmetic:
• The angle in a semicircle is 90°/ π/2 rad. 𝑢 𝑛 = 𝑎 + (𝑛 − 1)𝑑 FACTOR THEOROM
Geometric: If 𝑓 (𝑝) = 0 then (𝑥 − 𝑝) is a

𝑢𝑛 = 𝑎𝑟 𝑛−1 factor of 𝑓(𝑥)
DIFFERENTIATION CODING
𝑥−𝑎
𝒇(𝒙) 𝒇′(𝒙) for coding 𝑦= :
𝑏
𝑎𝑥 𝑛 𝑎𝑛𝑥 𝑛−1 𝑥̅ − 𝑎 𝜎𝑥
𝑦̅ = 𝜎𝑦 =
𝑒 𝑘𝑥
𝑘𝑒 𝑘𝑥 𝑏 𝑏
sin(𝑘𝑥) 𝑘 cos(𝑘𝑥)
PROBABILITY
cos(𝑘𝑥) −𝑘 sin(𝑘𝑥)
Mutually exclusive events:
1
ln(𝑘𝑥 )
𝑘𝑥 𝑃 (𝐴 ∪ 𝐵 ) = 𝑃 (𝐴 ) + 𝑃 (𝐵 )
𝐴𝑘𝑥 𝑘(ln 𝐴)𝐴𝑘𝑥
For independent events:
Chain rule:
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) × 𝑃(𝐵)
𝑑
(𝑓(𝑔(𝑥)) = 𝑔′(𝑥) ∙ 𝑓′(𝑔(𝑥))
𝑑𝑥
NORMAL DISTRIBUTION
Product rule:
Standard normal coding:
𝑑
(𝑓(𝑥)𝑔(𝑥)) = 𝑓(𝑥)𝑔′(𝑥)
𝑑𝑥 𝑋−𝜇
+ 𝑓 ′ (𝑥)𝑔(𝑥) 𝑍=
𝜎
Approximating binomial:
INTEGRATION (Where p is close to 0.5 and n is large)
𝒇(𝒙) ∫ 𝒇(𝒙) 𝒅𝒙 𝑋~𝑁(𝑛𝑝, 𝑛𝑝(1 − 𝑝))*

*continuity correction needed.
𝑥𝑛 𝑥 𝑛+1
(n≠-1) Sample means distribution:
𝑛+1
(𝑎𝑥 + 𝑏)𝑛+1 for 𝑋~𝑁(𝜇, 𝜎 2 )
(𝑎𝑥 + 𝑏)𝑛
𝑎 (𝑛 + 1) 𝜎2
𝑋̅~𝑁 (𝜇, )
1 𝑘𝑥 𝑛
𝑒 𝑘𝑥 𝑒
𝑘
1 FORCES
sin(𝑘𝑥) − cos(𝑘𝑥 )
𝑘 Newton’s 2nd Law:
1 𝐹 = 𝑚𝑎
cos(𝑘𝑥) sin(𝑘𝑥 )
𝑘
Weight:
1
ln |𝑥| 𝑊 = 𝑚𝑔
𝑥
Friction:
𝑘𝑥 𝐴𝑘𝑥
𝐴 𝐹 ≤ 𝜇𝑅
𝑘 ln 𝐴
𝑓 ′ (𝑥 )
ln |𝑓 (𝑥 )|
𝑓 (𝑥 )
PARAMETRIC EQUATIONS
𝑑𝑦 𝑑𝑦 𝑑𝑡
= ×
𝑑𝑥 𝑑𝑡 𝑑𝑥
𝑑𝑥
∫ 𝑦 𝑑𝑥 = ∫ 𝑦 ∙ 𝑑𝑡
𝑑𝑡

Edexcel A Level Maths Inverse Formula Sheet

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EDEXCEL A LEVEL MATHS - INVERSE FORMULA BOOKLET

BASIC GCSE EQUATIONS LAWS OF INDICES TRIGONOMETRY

−𝑏 ± √𝑏2 − 4𝑎𝑐 𝑎𝑚 sin 𝜃

Cosine Rule: (𝑎𝑚 ) 𝑛 = 𝑎𝑚𝑛 1

Geometric: If 𝑓 (𝑝) = 0 then (𝑥 − 𝑝) is a

𝒇(𝒙) ∫ 𝒇(𝒙) 𝒅𝒙 𝑋~𝑁(𝑛𝑝, 𝑛𝑝(1 − 𝑝))*

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