Snr specialist maths 20 formula sheet PDF

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Specialist Mathematics Formula sheet

Mensuration circumference of a circle

฀ ฀ = 2฀฀฀฀

area of a circle

area of a parallelogram

฀ ฀ = ฀฀ℎ

area of a trapezium

area of a triangle

฀ ฀ = ฀฀ℎ

total surface area of a cone

฀ ฀ = ฀฀฀฀฀฀ + ฀฀฀฀ 2

total surface area of a cylinder

฀ ฀ = 2฀฀฀฀ℎ + 2฀฀฀฀2

surface area of a sphere

฀ ฀ = 4฀฀฀฀2

volume of a cone

1

2

1

฀ ฀ = ฀฀฀฀ 2 ℎ 3

volume of a prism volume of a sphere

฀ ฀ = ฀฀ℎ

฀ ฀ = ฀฀฀฀ 2

volume of a cylinder volume of a pyramid

4

฀ ฀ = ฀฀฀฀ 3

1

฀ ฀ = (฀ ฀ + ฀฀)ℎ 2

฀ ฀ = ฀฀฀฀2 ℎ 1

฀ ฀ = ฀฀ℎ 3

3

Calculus

฀฀฀฀+1 � ฀฀฀ ฀ ฀฀฀฀ = + ฀฀ ฀฀+1

฀฀ ฀ ฀ ฀฀ = ฀฀฀฀฀฀−1 ฀฀฀฀

฀฀ ฀฀ ฀ ฀ = ฀฀ ฀ ฀ ฀฀฀฀ 1 ฀฀ ln(฀฀) = ฀฀ ฀฀฀฀

฀฀ sin(฀฀) = cos(฀฀) ฀฀฀฀

฀฀ cos(฀฀) = − sin(฀฀) ฀฀฀฀

฀฀ tan(฀฀) = sec 2 (฀฀) ฀฀฀฀

฀฀ 1 ฀฀ sin−1 � � = 2 ฀฀฀฀ ฀฀ √฀฀ − ฀฀2

฀฀ ฀฀ −1 cos−1 � � = ฀฀฀฀ ฀฀ √฀฀2 − ฀฀2 ฀฀ ฀฀ ฀฀ tan−1 � � = 2 ฀฀ + ฀฀2 ฀฀฀฀ ฀฀

� ฀฀ ฀ ฀ ฀฀฀฀ = ฀฀ ฀ ฀ + ฀฀

1 ฀฀฀฀ = ln|฀฀| + ฀฀ ฀฀

�

� sin(฀฀) ฀฀฀฀ = − cos(฀฀) + ฀฀ � cos(฀฀) ฀฀฀฀ = sin(฀฀) + ฀฀ � sec 2 (฀฀) ฀฀฀฀ = tan(฀฀) + ฀฀ � � �

1

√฀฀2

−

−1

฀฀2

√฀฀2 − ฀฀2 ฀฀2

Specialist Mathematics Formula sheet

฀฀ ฀฀฀฀ = sin−1 � � + ฀฀ ฀฀

฀฀ ฀฀฀฀ = cos−1 � � + ฀฀ ฀฀

฀฀ ฀฀ ฀฀฀฀ = tan−1 � � + ฀฀ 2 + ฀฀ ฀฀

Queensland Curriculum & Assessment Authority Page 2 of 5

Calculus

chain rule

product rule

quotient rule

integration by parts

volume of a solid of revolution

Simpson’s rule

simple harmonic motion

acceleration

If ℎ(฀฀) = ฀฀�฀฀(฀฀)� then

ℎ′ (฀฀) = ฀฀ ′ �฀฀(฀฀)�฀฀′(฀฀)

If ℎ(฀฀) = ฀฀(฀฀)฀฀(฀฀) then ℎ′ (฀฀) = ฀฀(฀฀)฀฀′ (฀฀) + ฀฀ ′ (฀฀)฀฀(฀฀) If ℎ(฀฀) =

฀฀(฀฀)

฀฀(฀฀)

then

ℎ′ (฀฀) =

฀฀ ฀฀) ฀฀(฀฀) − ฀฀(฀฀)฀฀′(฀฀) (฀฀(฀฀))2 ′(

If ฀ ฀ = ฀฀(฀฀) and ฀ ฀ = ฀฀(฀฀) then ฀฀฀฀ ฀฀฀฀ ฀฀฀฀ × = ฀฀฀฀ ฀฀฀฀ ฀฀฀฀ ฀฀฀฀

฀฀฀฀ ฀฀฀฀ ฀฀ (฀฀฀฀) = ฀ ฀ + ฀ ฀ ฀฀฀฀ ฀฀฀฀

฀฀฀฀ ฀฀฀฀ ฀ ฀฀฀฀฀ − ฀฀฀฀฀฀ ฀฀ ฀฀ � �= ฀฀ 2 ฀฀฀฀ ฀฀

฀฀฀฀ ฀฀฀฀ � ฀฀ ฀฀฀฀ = ฀฀฀฀ − � ฀฀ ฀฀฀฀ ฀฀฀฀ ฀฀฀฀

� ฀฀(฀฀)฀฀′(฀฀) ฀฀฀฀ = ฀฀(฀฀)฀฀(฀฀) − � ฀฀′(฀฀)฀฀(฀฀) ฀฀฀฀

฀฀

about the ฀฀-axis

฀ ฀ = ฀฀ � [฀฀(฀฀)]2 ฀฀฀฀

about the ฀฀-axis

฀ ฀ = ฀฀ � [฀฀(฀฀)]2 ฀฀฀฀

฀฀

∫฀ ฀฀(฀฀฀) If

฀

฀

฀฀

฀฀

฀

฀

[฀฀(฀฀ ฀฀฀฀ ≈ 0 ) + 4[฀฀(฀฀1 ) + ฀฀(฀฀3 ) + ⋯ ] + 2[฀฀(฀฀2 ) + ฀฀(฀฀4 ) + ⋯ ] + ฀฀(฀฀฀฀ )]

3

฀฀2฀฀ = −ω2 ฀฀ then ฀ ฀ = ฀ ฀ sin(ω฀ α฀)+or ฀ ฀ = ฀ ฀ cos(ω฀ ฀β+ ) ฀฀฀฀2

฀฀ 2 = ω2 (฀฀2 − ฀฀2 )

1 ฀฀= ฀฀

2฀฀ ฀฀= ω

฀฀฀฀ ฀฀ 1 2 ฀฀฀฀ ฀฀2 ฀฀ = 2 = ฀฀ = � ฀฀ � ฀฀= ฀฀฀฀ ฀฀฀฀ ฀฀฀฀ ฀฀฀฀ 2

Real and complex numbers complex number forms

฀ ฀ = ฀ ฀ + ฀฀฀฀ = ฀฀(cos(฀฀) + ฀ ฀ sin(฀฀)) = ฀฀ cis(฀฀)

modulus

|฀฀| = ฀ ฀ = �฀฀2 + ฀฀ 2

argument

arg(฀฀) = θ , tan(฀฀) =

product

฀฀1 ฀฀2 = ฀฀1 ฀฀2 cis(฀฀1 + ฀฀2 )

quotient De Moivre’s theorem

฀฀ , −฀฀...