Diploma Programme

Mathematical studies SL formula booklet For use during the course and in the examinations First examinations 2014

Published March 2012 © International Baccalaureate Organization 2012 Mathematical studies SL formula booklet

5042

1

Contents Prior learning

2

Topics

3

Topic 1—Number and algebra

3

Topic 2—Descriptive statistics

3

Topic 3—Logic, sets and probability

4

Topic 5—Geometry and trigonometry

5

Topic 6—Mathematical models

6

Topic 7—Introduction to differential calculus

6

Mathematical studies SL formula booklet

1

Prior learning 5.0

Area of a parallelogram Area of a triangle

Area of a trapezium

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

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

= A

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

= A

Area of a circle

A = πr 2 , where r is the radius

Circumference of a circle

C = 2πr , where r is the radius

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

Mathematical studies SL formula booklet

( x1 − x2 ) 2 + ( y1 − y2 ) 2

2

Topics

Topic 1—Number and algebra 1.2

Percentage error

vA − vE × 100% , where vE is the exact value and vA is the vE approximate value of v

1.7

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

1.8

ε=

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 = n geometric sequence r −1 1− r 1.9

Compound interest

kn

r   FV = PV × 1 +  , where FV = future value, PV = present  100k  value, n = number of years, k = number of compounding periods per year, r% = nominal annual rate of interest

Topic 2—Descriptive statistics 2.5

Mean of a set of data

k

x=

2.6

Interquartile range

Mathematical studies SL formula booklet

∑fx i =1

i i

n

k

, where n = ∑ f i i =1

IQR = Q3 − Q1

3

Topic 3—Logic, sets and probability 3.3

3.6

3.7

Truth tables

Probability of an event A

q

¬p

p∧q

p∨q

p∨q

T

T

F

T

T

F

T

T

T

F

F

F

T

T

F

F

F

T

T

F

T

T

T

F

F

F

T

F

F

F

T

T

P( A) =

number of outcomes in A total number of outcomes

Complementary events

P( A′) = 1 − P( A)

Combined events

P( A ∪ B )= P( A) + P( B ) − P( A ∩ B )

Mutually exclusive events

P( A ∩ B ) = 0

Independent events

P( A ∩ B ) = P( A) P( B )

Conditional probability

Mathematical studies SL formula booklet

p⇒q p⇔q

p

P(A | B ) =

P( A ∩ B ) P( B )

4

Topic 5—Geometry and trigonometry 5.1

Equation of a straight line Gradient formula

5.3

Sine rule

Cosine rule

Area of a triangle

5.5

y = mx + c ; ax + by + d = 0 m=

y2 − y1 x2 − x1

a b c = = sin A sin B sin C a 2 = b 2 + c 2 − 2bc cos A ; cos A =

b2 + c2 − a 2 2bc

1

ab sin C , where a and b are adjacent sides, C is the 2 included angle A=

Area of the curved surface of a cylinder

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

Surface area of a sphere

A = 4π r 2 , where r is the radius

Area of the curved surface of a cone

A= πrl , where r is the radius, l is the slant height

Volume of a pyramid

1 V = Ah , where A is the area of the base, h is the 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

Volume of a sphere

Volume of a cone

Volume of a prism

Mathematical studies SL formula booklet

V=

4 3 πr , where r is the radius 3

V=

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

V = Ah, where A is the area of cross-section, h is the height

5

Topic 6—Mathematical models 6.3

Equation of the axis of symmetry for the graph of the quadratic function y = ax 2 + bx + c

x= −

b 2a

Topic 7—Introduction to differential calculus 7.2

Derivative of axn

f ( x) = ax n

Derivative of a sum

f ( x) = ax n , g ( x) = bx m

Mathematical studies SL formula booklet



f ′( x) = nax n −1 ⇒

f ′( x) + g ′( x) = nax n −1 + mbx m −1

6

New Formula Sheet.pdf

Mathematical studies SL formula booklet 1. Contents. Prior learning 2. Topics 3. Topic 1—Number and algebra 3. Topic 2—Descriptive statistics 3. Topic 3—Logic, sets and probability 4. Topic 5—Geometry and trigonometry 5. Topic 6—Mathematical models 6. Topic 7—Introduction to differential calculus 6. Page 2 of 7 ...

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