Core Rules

Question 1

d/DX a^x

Answer 1

a^x ln(a)

Question 2

Area of a circle

Answer 2

πr^2

Question 3

Circumference of a circle

Answer 3

2πr

Question 4

Area of a sector

Answer 4

1/2 × r^2 × X (in radians)

x/360 × πr^2 (in degrees)

Question 5

Area of a triangle

Answer 5

1/2 × A × B × SinC

Question 5

Area of a triangle

Answer 5

1/2 × A × B × SinC

Question 6

Integrate cosX/sinX

Answer 6

ln(sinX) + c

Question 7

Differentiate ln(x)

Answer 7

1/x

Question 8

Integrate 1/3x

Answer 8

ln(x)/3 + c

Question 9

3/x integrated

Answer 9

3ln(x) + c

Question 10

Cos(X) differentiated

Answer 10

-Sin(X)

Question 11

Differentiate Sin(X)

Answer 11

Cos(X)

Question 12

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

Answer 12

U = cos(X)

-(CosX)^2/2-C

Question 13

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

Answer 13

1

Question 14

1+(tanX)^2 = ?

Answer 14

(SecX)^2

1/(CosX)^2

Question 15

(CotX)^2+ 1 = ?

Answer 15

(CosecX)^2

1/(SinX)^2

Question 16

Cosine rule for angles

Answer 16

CosA = b^2 + c^2 - a^2 ÷ 2bc

Question 17

Sine rule (for sides)

Answer 17

a/SinA = b/SinB

Question 18

Sine rule for angles

Answer 18

SinA/a = SinB/b

Question 19

Cosine rule for sides

Answer 19

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

Question 20

Product rule

Answer 20

dy/dx = vdu/dx + udv/dx

Question 21

Arithmetic formula for terms

Answer 21

A_n =a + d(n-1)

Question 22

Geometric formula for terms

Answer 22

a_n = ar^n-1

Question 23

2(sinX)^2

Answer 23

1-Cos2X

Question 24

1+Cos2X

Answer 24

2(CosX)^2

Question 25

Prove √3 is irrational by contradiction

Answer 25

A and B have a common factor

Question 26

Area of trapezium

Answer 26

1/2(a+b)h