Mathematics formulae
Circle
Mathematics formulae Laws of indices a ×a =a m
n
m
an =
am = am−n an 1 a−n = n a
m+n
√ n
am
r
(a ) = a m n
mn
a0 = 1 Area = πr 2
Areas of plane figures
Circumference = 2πr
Rectangle
Radian measure: 2π radians = 360 degrees Sector of a circle s
b
q
l
r
Area = l × b
θ◦ (2πr) = rθ (θ in rad) 360 ◦ θ 1 area = (θ in rad) (πr 2 ) = r 2 θ 360 2 arc length s =
Parallelogram
h
Volumes and surface areas of regular solids
b
Rectangular prism (or cuboid)
Area = b × h Trapezium
a h
l
h b
Volume = l × b × h
b
Area =
Surface area = 2(bh + hl + lb)
1 (a + b)h 2
Cylinder Triangle
r
h
h
b
Area =
1 ×b×h 2
Science for Engineering. 978-1-138-82688-5, © John Bird. Published by Taylor & Francis. All rights reserved.
Volume = π r 2 h Total surface area = 2π rh + 2π r 2
Right-angled triangles Pyramid
Theorem of Pythagoras b2 = a2 + c2 A h b
c A
If area of base = A and perpendicular height = h then: Volume =
B
C
a
Trigonometric ratios
1 ×A×h 3
c b a cos C = b c tan C = a sin C =
Total surface area = sum of areas of triangles forming sides + area of base
Cone
Non right-angled triangles A l h
c
b
r
1 2 πr h 3 Curved surface area = πrl Volume =
B
Sine rule
Total surface area = πrl + π r 2
Cosine rule
C
a b c = = sin A sin B sin C a2 = b2 + c2 − 2bc cos A
Area of any triangle
Sphere
r
4 3 πr 3 Surface area = 4πr 2 Volume =
a
(i)
1 × base × perpendicular height 2
(ii)
1 1 1 ab sin C or ac sin B or bc sin A 2 2 2
Graphs Equation of a straight line
y = mx + c
Mathematics formulae Laws of indices a ×a =a m
n
m
an =
am = am−n an 1 a−n = n a
m+n
√ n
am
r
(a ) = a m n
mn
a0 = 1 Area = πr 2
Areas of plane figures
Circumference = 2πr
Rectangle
Radian measure: 2π radians = 360 degrees Sector of a circle s
b
q
l
r
Area = l × b
θ◦ (2πr) = rθ (θ in rad) 360 ◦ θ 1 area = (θ in rad) (πr 2 ) = r 2 θ 360 2 arc length s =
Parallelogram
h
Volumes and surface areas of regular solids
b
Rectangular prism (or cuboid)
Area = b × h Trapezium
a h
l
h b
Volume = l × b × h
b
Area =
Surface area = 2(bh + hl + lb)
1 (a + b)h 2
Cylinder Triangle
r
h
h
b
Area =
1 ×b×h 2
Science for Engineering. 978-1-138-82688-5, © John Bird. Published by Taylor & Francis. All rights reserved.
Volume = π r 2 h Total surface area = 2π rh + 2π r 2
Right-angled triangles Pyramid
Theorem of Pythagoras b2 = a2 + c2 A h b
c A
If area of base = A and perpendicular height = h then: Volume =
B
C
a
Trigonometric ratios
1 ×A×h 3
c b a cos C = b c tan C = a sin C =
Total surface area = sum of areas of triangles forming sides + area of base
Cone
Non right-angled triangles A l h
c
b
r
1 2 πr h 3 Curved surface area = πrl Volume =
B
Sine rule
Total surface area = πrl + π r 2
Cosine rule
C
a b c = = sin A sin B sin C a2 = b2 + c2 − 2bc cos A
Area of any triangle
Sphere
r
4 3 πr 3 Surface area = 4πr 2 Volume =
a
(i)
1 × base × perpendicular height 2
(ii)
1 1 1 ab sin C or ac sin B or bc sin A 2 2 2
Graphs Equation of a straight line
y = mx + c
