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IB MATHEMATICS SL
Course Description: IB Mathematics SL is an advanced study of
mathematics, designed to prepare the student for the IB Math SL Exam and
additional Calculus, either AP Calculus AB or BC. It is a rigorous course of
study specifically designed for that student who expects to go on to study
subjects which have significant mathematical content. The class will include
a portfolio, consisting of two assignments, one on mathematical
investigation and the other on mathematical modelling.
The following are the 7 Areas of study with approximate recommended
hours of instruction:
Algebra
8 hrs
Functions & Equations
24 hrs
Circular functions & trigonometry
16 hrs
Matrices
10 hrs
Vectors
16 hrs
Statistics & probability
30 hrs
Calculus
36 hrs
Total = 140 hrs
AIMS & SUBTOPICS
1. ALGEBRAIC CONCEPTS
1.1.a Arithmetic sequences & series
a n  a1  (n  1)d
Sn 
n
(a1  a n )
2
1.1.b Geometric sequences & series
an  a1r n 1
a (1  r n )
Sn 
1 r
a
Sn 
for n  , r  1
1 r
1.1.c Sigma Notation
1
1.2.a Exponents & Logarithms
1.2.b Laws of Exponents & Logarithms
1.2.c Change of Base Formula and application
log b a 
log c a
log c b
1.3.a Binomial Theorem: expansion of ( a  b) ,
n N
n
2. FUNCTIONS & EQUATIONS
2.1.a Concept of function f : x  f ( x) with
Domain & Range
2.1.b Composite functions ( f  g )( x)  f ( g ( x))
1
2.1.c Inverse function f
2.2.a The graph of a function = f(x)
2.2.b Window settings on GDC to view both global
and local behavior
2.2.c Solutions of equations graphically with “root”
concept with f(x) = 0 or “intersect”
concept with f(x) = g(x)
2.3.a Transformations of graphs
2.3.a.1
Vertical translations
y = f(x) + b
2.3.a.2
Horizontal translations
y = f(x –a)
2.3.a.3
Vertical dilations (stretches)
y = pf(x)
2.3.a.4
Horizontal dilations
y = f(x/q)
2.3.a.5
X-axis Reflections
y = - f(x)
2.3.a.6
Y-axis Reflections
y = f( -x )
1
2.3.b Graphs of y  f ( x) as a reflection of y = f(x)
in the line y = x
2
2.4.a The reciprocal function y = 1/x and its selfinverse nature
2.5.a The quadratic function f(x) = ax  bx  c
with its graph, the y-intercept (0, c) and
2
b
2a
the axis of symmetry x =
2.5.b The quadratic function in the form
f(x) = a ( x  h)  k with vertex at (h,k)
2
2.5.c The quadratic function in the form
f(x) = a(x – p)(x – q) with
x-intercepts at ( p, 0) and ( q, 0)
2.6.a Solutions to ax  bx  c  0 with use of the
2
b  4ac and the
discriminant
quadratic formula.
2
2.7.a The exponential function y  a , a  0
and its graph
2.7.b The logarithmic function y  log a x, x  0
and its graph
2.7.c Application of
x
log a a x  x and a log a x  x, x  0
2.7.d Solution of a  b using logarithms
x
2.8.a The exponential function y  e
2.8.b The natural log function y  ln x, x  0
x
2.8.c Manipulation/Application of a  e
with
compound interest and growth/decay
models
x
x ln a
3. CIRCULAR FUNCTIONS & TRIGONOMETRY
3.1.a Radian measure versus degree measure of an
angle
3.1.b Length of an arc of a circle s  r
3.1.c Area of a sector of a circle A 
1 2
r 
2
3
3.2.a Definitions of sin  and cos  in terms of the
unit circle
3.2.b Definition of tan  and use of y = x ( tan )
3.2.c The Pythagorean Identity
sin 2   cos 2   1and its
transformations
3.3.a Double angle formulas for sin 2 and cos 2
3.4.a Domain, Range , and graphs of the basic three
circular
functions sin x, cos x, and tan x
3.4.b Composite functions of the form
f(x) = a sin (b(x + c)) + d
3.5.a Solutions of trig equations in a restricted
interval using both graphical and analytic
means
3.5.b Equations of the type a sin(b(x + c)) = k with
graphical interpretation
3.5.c Quadratic equations involving trig functions
3.6.a Solving Right triangle: finding all parts
3.6.b Law of Cosines
3.6.c Law of Sines and the Ambiguous Case
3.6.d The area of a triangle using A 
1
ab sin C
2
with application
4. MATRICES
4.1.a Definition of a matrix with understanding of the
terms “element”, “row”, “column”, and “order”
4.2.a Algebra of Matrices: Addition, Subtraction,
Multiplication by a scalar
4.2.b Multiplication of matrices
4.2.c Identity and Zero matrices
4.3.a Determinant of a square matrix
4.3.b Calculation of 2 X 2 and 3 X 3 determinants
4.3.c Inverse of a 2 X 2 matrix
4.3.d Conditions for the existence of the inverse of a
matrix
4
4.4.a Solution of systems of linear equations using
inverse matrices with a maximum of three
equations in three unknowns
5. Vectors
5.1.a Vectors in two dimensions and 3-D
5.1.b Components of a vector with column
representation
 v1 
v  v2   v1i  v2 j  v3k with i,j, & k
 
v3 
unit vectors
5.1.c Algebraic and Geometric approaches to:
5.1.c.1
Sum and Difference of two
vectors
5.1.c.2
Multiplication by a scalar, kv
5.1.c.3
Magnitude of a vector
5.1.c.4
Unit vectors, base vectors i, j ,
and k
5.1.c.5
Position vectors OA  a
5.2.a Scalar product or dot product of two vevtors:
v  w  v w cos ; v  w  v1w1  v2 w2  v3w3
5.2.b
5.2.c
5.3.a
5.3.b
5.4.a
Parallel and perpendicular vectors
Angle between two vectors
Representation of a line r = a + tb
The angle between two lines
Distinguishing between intersecting and parallel
lines
5.4.b Finding points where lines intersect
6. STATISTICS & PROBABILITY
6.1.a Concepts of population, sample, random sample
and frequency distribution of discrete and continuous
data
5
6.2.a Presentation of data including:
6.2.a.1
Frequency tables & diagrams
6.2.a.2
Box & whisker plots
6.2.a.3
Grouped data
6.2.a.4
mid-interval values
6.2.a.5
interval width
6.2.a.6
upper and lower interval
boundaries
6.2.a.7
frequency histograms
6.3.a Mean, Median, Mode, Quartiles, & Percentiles
6.3.b Range, inter-quartile range, variance, and standard
deviation
6.4.a Cumulative frequency and cumulative frequency
graphs used to find median, quartiles, and
percentiles
6.5.a Concepts of trial, outcomes, equally likely
outcomes, sample space, and event
6.5.b Probability of an event P( A) 
n( A)
n(U )
6.5.c Complementary events A and A’ (not A);
P(A) + P(A’) = 1
6.6.a Combined events, the formula:
P( A  B)  P( A)  P( B)  P( A  B) where
P( A  B)  0 for mutually exclusive events
6.7.a Conditional Probability, the formula:
P( A B) 
P( A  B)
P( B)
6.7.b Independent Events, the definition:
P( A B)  P( A)  P( A B')
6.8.a Use of Venn diagrams to solve problems
6.9.a Concept of discrete random variables and their
probability distributions
6.9.b Expected value (mean), E(X) for discrete data
6.10.a Binomial distribution
6.10.b Mean of the binomial distribution
6
6.11.a Normal distribution
6.11.b Properties of the normal distribution
6.11.c Standardization of normal variables
7. CALCULUS - an informal introductory approach is used in
developing the history of and utility for modern day
calculus
A. The derivative definitions:
f(x) - f(a)
’
1. f (a) = lim -------------x --->a x - a
f(x + h) - f(x)
2. f (x ) = lim
----------------h ---> 0
h
’
B. derivatives of elementary functions
C. derivatives of sums, products, and quotients
D. the chain rule
E. derivatives of implicitly defined functions
F. related rates applications
G. use of graphing calculator to explore the tangent
question
H. instantaneous change vs. average rate of change => the
tangent vs. the secant
I. Indefinite integration with application to acceleration
and velocityfunctions
J. Integration by substitution
K. Numerical approximation techniques including the
trapezoidal rule
7