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Core Rules Flashcards

Learn the essential rules needed for Pure Maths (27 cards)

1
Q

d/DX a^x

A

a^x ln(a)

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2
Q

Area of a circle

A

πr^2

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3
Q

Circumference of a circle

A

2πr

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4
Q

Area of a sector

A

1/2 × r^2 × X (in radians)

x/360 × πr^2 (in degrees)

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5
Q

Area of a triangle

A

1/2 × A × B × SinC

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5
Q

Area of a triangle

A

1/2 × A × B × SinC

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6
Q

Integrate cosX/sinX

A

ln(sinX) + c

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7
Q

Differentiate ln(x)

A

1/x

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8
Q

Integrate 1/3x

A

ln(x)/3 + c

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9
Q

3/x integrated

A

3ln(x) + c

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10
Q

Cos(X) differentiated

A

-Sin(X)

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11
Q

Differentiate Sin(X)

A

Cos(X)

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12
Q

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

A

U = cos(X)

-(CosX)^2/2-C

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13
Q

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

A

1

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14
Q

1+(tanX)^2 = ?

A

(SecX)^2

1/(CosX)^2

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15
Q

(CotX)^2+ 1 = ?

A

(CosecX)^2

1/(SinX)^2

16
Q

Cosine rule for angles

A

CosA = b^2 + c^2 - a^2 ÷ 2bc

17
Q

Sine rule (for sides)

A

a/SinA = b/SinB

18
Q

Sine rule for angles

A

SinA/a = SinB/b

19
Q

Cosine rule for sides

A

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

20
Q

Product rule

A

dy/dx = vdu/dx + udv/dx

21
Q

Arithmetic formula for terms

A

A_n =a + d(n-1)

22
Q

Geometric formula for terms

23
Q

2(sinX)^2

24
1+Cos2X
2(CosX)^2
25
Prove √3 is irrational by contradiction
A and B have a common factor
26
Area of trapezium
1/2(a+b)h