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GCSE FORMULAEYou need to know this for your exam
(Higher tier only formulae are indicated)
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AREA
Rectangle = l × w
l
w
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AREA
Parallelogram = b × h
b
h a
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AREA
Triangle = b × h
b
h
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AREA
Trapezium = (a+b) × h
b
h
a
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Circles
Circumference = π × diameterC = πd
Diam
eter
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Circles
Circumference = 2 × π × radiusC = 2πr
Centre
Radiu
s
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Circles
Area = π × radius × radius A = πr2
Centre
Radiu
s
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VOLUME
Cuboid = × w × h
𝑙
h
w
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VOLUME
Prism = × length
𝑙
Areaof
cross section
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VOLUME
h
r
Cylinder = area of circle × heightCylinder = πr2h
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VOLUME
Pyramid = area of base × height
h
Higher tier only
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COMPOUND MEASURES
Speed = Distance ÷ Time
The clue is in the units eg speed in m/s, indicates metres ÷ seconds
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COMPOUND MEASURES
Density = Mass ÷ Volume
The clue is in the units eg density in g/cm3, indicates weight in grams ÷ volume in cm3
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COMPOUND MEASURES
Pressure = Force ÷ Area
The clue is in the units eg speed in N/m2, indicates force in Newtons ÷ area in m2
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RIGHT-ANGLED TRIANGLES
Pythagoras
a2 + b2 = h2
(h is always the hypotenuse)
h
a
b
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RIGHT-ANGLED TRIANGLES
Trigonometryhyp
adj
opp
x⁰sin (𝑥 ° )=𝑜𝑝𝑝
h𝑦𝑝
cos (𝑥 ° )= 𝑎𝑑𝑗h𝑦𝑝
tan (𝑥 ° )=𝑜𝑝𝑝𝑎𝑑𝑗
Check your calculator is in degrees
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NON-RIGHT-ANGLED TRIANGLES
Sine Rule
B
C
A
asin ( 𝐴)
=𝑏
sin (𝐵)=
𝑐sin (𝐶 )
Check your calculator is in
degrees
ab
c
Higher tier only
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NON-RIGHT-ANGLED TRIANGLES
Cosine Rule
B
C
A
𝑎2=𝑏2+𝑐2−2𝑏𝑐×𝑐𝑜𝑠 (𝐴)Check your
calculator is in degrees
ab
c
Higher tier only
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NON-RIGHT-ANGLED TRIANGLES
Area of a triangle
B
C
A
Area = Check your
calculator is in degrees
ab
c
Higher tier only
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Algebra
Quadratic Equations Higher tier only
The solutions of ax2+bx+c=0,
where a≠0, are given by: