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Diploma Programme

Mathematics HL and further mathematics HL formula booklet For use during the course and in the examinations First examinations 2014

Edited in 2015 (version 2)

© International Baccalaureate Organization 2012

5048

Contents Prior learning

2

Core

3

Topic 1: Algebra

3

Topic 2: Functions and equations

4

Topic 3: Circular functions and trigonometry

4

Topic 4: Vectors

5

Topic 5: Statistics and probability

6

Topic 6: Calculus

8

Options

10

Topic 7: Statistics and probability

10

Further mathematics HL topic 3 Topic 8: Sets, relations and groups

11

Further mathematics HL topic 4 Topic 9: Calculus

11

Further mathematics HL topic 5 Topic 10: Discrete mathematics

12

Further mathematics HL topic 6

Formulae for distributions

13

Topics 5.6, 5.7, 7.1, further mathematics HL topic 3.1 Discrete distributions

13

Continuous distributions

13

Further mathematics

14

Topic 1: Linear algebra

14

Mathematics HL and further mathematics formula booklet

1

Formulae

Prior learning Area of a parallelogram

A= b × h , where b is the base, h is the height

Area of a triangle

= A

1 (b × h) , where b is the base, h is the height 2

Area of a trapezium

= A

1 (a + b) h , where a and b are the parallel sides, h is the height 2

Area of a circle

A = πr 2 , where r is the radius

Circumference of a circle

C = 2πr , where r is the radius

Volume of a pyramid= V

1 (area of base × vertical height) 3

Volume of a cuboid

V =l × w × h , where l is the length, w is the width, h is the height

Volume of a cylinder

V = πr 2 h , where r is the radius, h is the height

Area of the curved surface of a cylinder

A= 2πrh , where r is the radius, h is the height

Volume of a sphere

V=

4 3 πr , where r is the radius 3

Volume of a cone

V=

1 2 πr h , where r is the radius, h is the height 3

Distance between two points ( x1 , y1 ) and ( x2 , y2 )

d=

Coordinates of the midpoint of a line segment with endpoints ( x1 , y1 ) and ( x2 , y2 )

x1 + x2 y1 + y2 , 2 2

Solutions of a quadratic equation

( x1 − x2 ) 2 + ( y1 − y2 ) 2

The solutions of ax 2 + bx + c = 0 are x =

Mathematics HL and further mathematics formula booklet

−b ± b 2 − 4ac 2a

2

Core

Topic 1: Algebra 1.1

The nth term of an arithmetic sequence

un = u1 + (n − 1) d

The sum of n terms of an arithmetic sequence

S n=

The nth term of a geometric sequence

un = u1r n −1

n n ( 2u1 + (n − 1) d )= (u1 + un ) 2 2

The sum of n terms of a u1 (r n − 1) u1 (1 − r n ) , r ≠1 = S = finite geometric sequence n

r −1

1.2

1− r

The sum of an infinite geometric sequence

S∞ =

Exponents and logarithms

a x = b ⇔ x = log a b , where a > 0, b > 0, a ≠ 1

u1 , r

View more...
Mathematics HL and further mathematics HL formula booklet For use during the course and in the examinations First examinations 2014

Edited in 2015 (version 2)

© International Baccalaureate Organization 2012

5048

Contents Prior learning

2

Core

3

Topic 1: Algebra

3

Topic 2: Functions and equations

4

Topic 3: Circular functions and trigonometry

4

Topic 4: Vectors

5

Topic 5: Statistics and probability

6

Topic 6: Calculus

8

Options

10

Topic 7: Statistics and probability

10

Further mathematics HL topic 3 Topic 8: Sets, relations and groups

11

Further mathematics HL topic 4 Topic 9: Calculus

11

Further mathematics HL topic 5 Topic 10: Discrete mathematics

12

Further mathematics HL topic 6

Formulae for distributions

13

Topics 5.6, 5.7, 7.1, further mathematics HL topic 3.1 Discrete distributions

13

Continuous distributions

13

Further mathematics

14

Topic 1: Linear algebra

14

Mathematics HL and further mathematics formula booklet

1

Formulae

Prior learning Area of a parallelogram

A= b × h , where b is the base, h is the height

Area of a triangle

= A

1 (b × h) , where b is the base, h is the height 2

Area of a trapezium

= A

1 (a + b) h , where a and b are the parallel sides, h is the height 2

Area of a circle

A = πr 2 , where r is the radius

Circumference of a circle

C = 2πr , where r is the radius

Volume of a pyramid= V

1 (area of base × vertical height) 3

Volume of a cuboid

V =l × w × h , where l is the length, w is the width, h is the height

Volume of a cylinder

V = πr 2 h , where r is the radius, h is the height

Area of the curved surface of a cylinder

A= 2πrh , where r is the radius, h is the height

Volume of a sphere

V=

4 3 πr , where r is the radius 3

Volume of a cone

V=

1 2 πr h , where r is the radius, h is the height 3

Distance between two points ( x1 , y1 ) and ( x2 , y2 )

d=

Coordinates of the midpoint of a line segment with endpoints ( x1 , y1 ) and ( x2 , y2 )

x1 + x2 y1 + y2 , 2 2

Solutions of a quadratic equation

( x1 − x2 ) 2 + ( y1 − y2 ) 2

The solutions of ax 2 + bx + c = 0 are x =

Mathematics HL and further mathematics formula booklet

−b ± b 2 − 4ac 2a

2

Core

Topic 1: Algebra 1.1

The nth term of an arithmetic sequence

un = u1 + (n − 1) d

The sum of n terms of an arithmetic sequence

S n=

The nth term of a geometric sequence

un = u1r n −1

n n ( 2u1 + (n − 1) d )= (u1 + un ) 2 2

The sum of n terms of a u1 (r n − 1) u1 (1 − r n ) , r ≠1 = S = finite geometric sequence n

r −1

1.2

1− r

The sum of an infinite geometric sequence

S∞ =

Exponents and logarithms

a x = b ⇔ x = log a b , where a > 0, b > 0, a ≠ 1

u1 , r

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