IB Math SL Summer Assignment 2019-2020

The IB Math SL curriculum covers six different mathematical topics (algebra, functions, trigonometry, vectors, statistics, and calculus). Three of these six topics were thoroughly covered in your Pre-Calculus class (algebra, functions, and trigonometry). In an effort to best prepare you for the IB paper exams at the end of the year, three topics need to be reviewed during the summer. This will leave the class with more time during the school year to focus on statistics and calculus.

The summer assignment will be broken up into three sections in which I have written a suggested timeline in which they should be completed:

 Topic 1: Algebra- finish by June 22nd  Topic 2: Functions- finish by July 13th  Topic 3: Trigonometry- finish by July 31st

Every topic should be turned in by the first day of class. Please complete all work in sequential order on separate paper and write your final answers on the actual assignment.

The summer assignment will be worth a quiz grade and there will be a test over this material within the first three weeks of the school year.

To assist you in each topic, here are links to video tutorials: https://sites.google.com/a/roundrockisd.org/kyle-bell/ib-math-sl-summer-assignment https://osc-ib.com/ib-revision-videos

I also suggest using notes from your previous Pre-Calculus course along with the attached formula booklet for reference. This formula booklet is what you will be allowed to use on the paper exam.

If you have any questions, you can email me at [email protected] and I will return your email as soon as I can. Have a wonderful summer! I look forward to seeing you next year! Mr. Anand Name:

Topic 1: Algebra

Topic 2: Functions

*The circle indicates the origin.

Topic 3: Trigonometry

Diploma Programme

Mathematics SL formula booklet

For use during the course and in the examinations

Published March 2012 5045 Mathematical studies SL: Formula booklet 1

Contents

Prior learning 2 Topics 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 5 Topic 6—Calculus 6

Mathematics SL formula booklet 1 Formulae Prior learning

Area of a parallelogram A  b  h

1 Area of a triangle A  (b  h)

1 Area of a trapezium A  (a  b) h 2

2 Area of a circle A  r

Circumference of a circle C  2r

Volume of a pyramid 1 V  (area of base  vertical height) 3

Volume of a cuboid (rectangular prism) V  l  w  h

Volume of a cylinder V  r2h

Area of the curved surface of a cylinder A  2rh

Volume of a sphere 4 3 V  r 3

Volume of a cone V r h

2 2 2 Distance between two points (x1, y1, z1) and d  (x  x )  ( y  y )  (z  z ) (x2 , y2 , z2 )

Coordinates of the midpoint of a line segment  x1  x2 y1  y2 z1  z2  with endpoints (x , y , z ) and (x , y , z )  , ,  1 1 1 2 2 2  2 2 2 

Mathematics SL formula booklet 2 Topics

Topic 1—Algebra

th 1.1 The n term of an un  u1  (n 1)d arithmetic sequence n n The sum of n terms of an S  (2u  (n 1)d )  (u  u ) arithmetic sequence n 2 1 2 1 n

th n1 The n term of a u  u r n 1 geometric sequence

The sum of n terms of a u (rn 1) u (1  rn ) 1 1 Sn   , r  1 finite geometric sequence r 1 1  r u The sum of an infinite S  1 , r  1 geometric sequence  1  r

1.2 Exponents and logarithms ax  b  x  log b a

Laws of logarithms logc a  logc b  logc ab a log a  log b  log c c c b log a  r log a c r c

log a Change of base log a  c b log b c

Binomial coefficient  n  n! 1.3     r  r ! n  r !

n n  n  n1  n  nr r n Binomial theorem (a  b)  a  a b   a b   b      1   r 

Mathematics SL formula booklet 3 Topic 2—Functions and equations

2.4 Axis of symmetry of 2 b f (x)  ax  bx  c  axis of symmetry x  

graph of a quadratic 2a function

2.6 Relationships between ax  ex ln a

logarithmic and x loga x log a  x  a a exponential functions

2 2.7 Solutions of a quadratic 2 b  b  4ac equation ax  bx  c  0  x  , a  0 2a

Discriminant   b2  4ac

Topic 3—Circular functions and trigonometry

3.1 Length of an arc l   r

Area of a sector 1 2 A   r 2

sin 3.2 Trigonometric identity tan  cos

3.3 Pythagorean identity cos2   sin2   1 Double angle formulae sin 2  2sin cos cos 2  cos2   sin2   2 cos2  1  1  2sin2 

2 2 2 3.6 Cosine rule a  b  c c 2 a 2 b 2 2ab cos C ; cos C  2ab

Sine rule a b c   sin A sin B sin C

1 Area of a triangle A  ab sin C 2

Mathematics SL formula booklet 4 Topic 4—Vectors

2 2 2 4.1 Magnitude of a vector v  v  v  v 1 2 3

4.2 Scalar product v  w  v w cos

v  w  v1w1  v2w2  v3w3

v  w Angle between two cos  vectors v w

4.3 Vector equation of a line r = a + tb

Topic 5—Statistics and probability

5.2 Mean of a set of data n  fi xi i1 x  n  fi i1

n( A) 5.5 Probability of an event A P( A)  n(U )

Complementary events P( A)  P( A)  1

5.6 Combined events P( A  B)  P( A)  P(B)  P( A  B)

Mutually exclusive events P( A  B)  P( A)  P(B)

Conditional probability P(A  B)  P(A) P(B | A)

Independent events P( A  B)  P( A) P(B)

5.7 Expected value of a discrete E( X )     x P( X  x) random variable X x

 n  r nr 5.8 Binomial distribution X ~ B(n, p)  P( X  r)  p (1  p) , r  0, 1, , n    r 

E( X )  np Mean

Var( X )  np(1  p) Variance

5.9 Standardized normal x   z  variable 

Mathematics SL formula booklet 5 Topic 6—Calculus

dy  f (x  h)  f (x)  6.1 Derivative of f (x) y  f (x)   f (x)  lim   dx h0 h  

n n n1 6.2 Derivative of x f (x)  x  f (x)  nx

Derivative of sin x f (x)  sin x  f (x)  cos x

Derivative of cos x f (x)  cos x  f (x)   sin x

1 Derivative of tan x f (x)  tan x  f (x)  cos2 x

x x x Derivative of e f (x)  e  f (x)  e

1 Derivative of ln x f (x)  ln x  f (x)  x

dy dy du Chain rule y  g(u) , u  f (x)    dx du dx

dy dv du Product rule y  uv   u  v dx dx dx

Quotient rule du dv v  u u dy dx dx y    2 v dx v

6.4 Standard integrals n1 x xn dx   C, n  1  n  1 1  dx  ln x  C, x  0 x

sin x dx  cos x  C 

cos x dx  sin x  C

x x e dx  e  C

6.5 Area under a curve b between x = a and x = b A  y dx a

Volume of revolution b V  πy2 dx about the x-axis from x = a  a to x = b

t 6.6 Total distance travelled 2 distance  v(t) dt from t1 to t2  t1

Mathematics SL formula booklet 6

Mathematics SL formula booklet 7