CURRICULUM SUMMARY – January to March 2016
SUBJECT: Mathematics SL and HL
Week Learning objectives:
YEAR GROUP: IB1
Activities (in brief)
TEACHERS: Agata Piskorz and Anna Tokarz
Students will understand and use:
1
2
3
4
5
QUADRATICS
 Quadratic optimization
 Solution of f(x)=g(x) where f and g are linear
or quadratic.
 (HL only):polynomial functions and their
graphs
 Quadratic function – revision
 (HL only): the factor and remainder theorems
 (HL only): the fundamental theorem of
algebra
EXPONENTS AND LOGARTHMS
Students will understand and use:
 Laws of exponents.
 Algebraic expansion and factorisation with
exponents
 Exponential equations
 Exponential functions.
 (HL only): polynomial equations
 Logarithms, logarithms in base 10, natural
logarithms.
 Laws of logarithms including change of base
 Exponential and logarithmic equations.
 Logarithmic function.
 (HL only): roots of polynomial equations


Rational functions
(HL only): polynomial inequalities
Solving equations, both graphically and analytically.
Using of technology to solve a variety of equations, including those where there is no appropriate
analytic approach.
(HL only):investigating graphs and properties of polynomial functions; noting the graphical
significance of repeated factors
Quadratic functions -solving practical and theoretical problems.
(HL only): application of the factor and remainder theorems in various contexts;
(HL only): discovering the relationship between the degree of a polynomial function and the
possible numbers of x-intercepts
Exponents including rational exponents - revision.
Solving simple exponential equations.
Exponential functions graphs.
Exponential growth and decay – solving practical problems.
(HL only): solving polynomial equations graphically
(HL only): solving polynomial equations algebraically over the set of complex numbers, noting
existence of complex conjugate roots
Discovering the laws of logarithms.
Using laws of logarithms.
Solving exponential equations – using logarithms.
Use of technology to solve a variety of equations, including those where there is no appropriate
analytical approach.
(HL only): deriving and using theorems about the sum and product of roots of a polynomial
equations, including complex roots
Investigating the reciprocal function, its properties and graph , transforming the reciprocal
function graph. Finding intercepts and asymptotes of rational functions.
(HL only): practice in using graphical and algebraic methods of solving polynomial inequalities up
to degree 3; practice of effective use of GDC in solving “misleading” equations or inequalities
graphically.
Solving past papers questions
Solving Review Sets from the book.
Writing a test.
6
7
8
SEQUENCES AND SERIES
Students will understand and use:
 definition of a sequence, the general term (
n-th term ) of a sequence,
 definition of arithmetic and geometric
sequences, the formula for the n-th term of
an arithmetic sequence,
 (HL only): number sequence as an example of
a function with positive integers domain
 the formula for the n-th term of a geometric
sequence
 the sum of an arithmetic sequence -arithmetic
series, the formula for the sum of the first n
terms,
 (HL only): limit of a number sequence and limit
of a function
 (HL only): continuous function
 the sum of an geometric sequence, geometric
series,
 the sum of an infinite geometric series,
 examples of applications: compound interest
and population growth,
 (HL only): concept of convergent and
divergent number series
9
THE BINOMIAL THEOREM
Students will understand and use:
10


expansion of a  b  , n  1, 2 ,3 ,4

expansion of a  b  , n  N .
Generating terms of a sequence using term-to-term and position-to-term definitions of the
sequence.
Specifying sequences by using words, using an explicit formula (general term – n-th term
formula).
Showing that a sequence is arithmetic.
Showing that a sequence is geometric.
Finding the formula for the general term of an arithmetic or geometric sequence.
(HL only): checking monotonicity of a number sequence using definition or ratio of consecutive
terms in general form
Using sigma notation
Deriving the formula for the sum of an arithmetic series.
(HL only): calculating limits of number sequences
(HL only): calculating limits of piece-wise functions to check if they are continuous.
Finding sums of the arithmetic and geometric series.
Solving growth and decay problems.
Using the compound interest formula I  C (1 
r
) nk  C and using the GDC
k  100
(HL only): examples of testing series convergence
SEQUENCES revision – solving problems at class and at home;
writing a test;
discussing results of the test;
n
(HL only): systems of linear equations, up to
three equations with three unknowns
n
Deriving the expansion for n=2,3, 4.
(HL only): analysing examples of systems of equations with a unique solution, infinity of solutions
or no solutions; writing a general solution for systems with infinity of solutions; solving systems
algebraically and using GDC;
n
k 
Determining the   by Pascal’s triangle, by the formula and by the use of the GDC
Solving past papers questions
Solving Review Sets from the book.
Writing a test.