Core Rules Flashcards by Jack Hughes

Q

d/DX a^x

A

a^x ln(a)

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Q

Area of a circle

A

πr^2

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Q

Circumference of a circle

A

2πr

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Q

Area of a sector

A

1/2 × r^2 × X (in radians)

x/360 × πr^2 (in degrees)

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Q

Area of a triangle

A

1/2 × A × B × SinC

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Q

Area of a triangle

A

1/2 × A × B × SinC

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Q

Integrate cosX/sinX

A

ln(sinX) + c

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Q

Differentiate ln(x)

A

1/x

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Q

Integrate 1/3x

A

ln(x)/3 + c

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Q

3/x integrated

A

3ln(x) + c

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Q

Cos(X) differentiated

A

-Sin(X)

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Q

Differentiate Sin(X)

A

Cos(X)

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Q

How would sin(X)cos(X) be integrated?

A

U = cos(X)

-(CosX)^2/2-C

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Q

(CosX)^2 + (SinX)^2 = ?

A

1

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Q

1+(tanX)^2 = ?

A

(SecX)^2

1/(CosX)^2

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Q

(CotX)^2+ 1 = ?

A

(CosecX)^2

1/(SinX)^2

Q

Cosine rule for angles

A

CosA = b^2 + c^2 - a^2 ÷ 2bc

Q

Sine rule (for sides)

A

a/SinA = b/SinB

Q

Sine rule for angles

A

SinA/a = SinB/b

Q

Cosine rule for sides

A

a^2 = b^2 + c^2 - 2bcCosA

Q

Product rule

A

dy/dx = vdu/dx + udv/dx

Q

Arithmetic formula for terms

A

A_n =a + d(n-1)

Q

Geometric formula for terms

A

a_n = ar^n-1

Q

2(sinX)^2

A

1-Cos2X

Q

1+Cos2X

A

2(CosX)^2

Q

Prove √3 is irrational by contradiction

A

A and B have a common factor

Q

Area of trapezium

A

1/2(a+b)h