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IB Mathematics SL (MA, AS) Grades
Offered: 11-12 Credit:
1.0 for 1 year 2.0 for 2 years Course description:
Mathematics SL is a one year (plus a four hour quarterly
Saturday class) course for juniors and seniors who already possess knowledge
of basic mathematical concepts, and who are equipped with the skills needed
to apply simple mathematical techniques correctly. The majority of these students will expect
to need a sound mathematical background as they prepare for future studies in
subjects such as chemistry, economics, psychology and business
administration. Some students will
take this class just for the intellectual challenge. The course will be expanded to adequately
cover the material necessary to pass the AP Students will experience internationalism through mathematics
by having teacher directed discussions of a) the differences in notation, b)
the lives of mathematicians set in a historical and/or social context, c)the
cultural context of mathematical discoveries, d) the ways in which specific
mathematical discoveries were made and the techniques used to make them, e)
how the attitudes of different societies towards specific areas of
mathematics are demonstrated, f) the universality of mathematics as a means
of communication. Students will
experience fully integrated mathematics e.g. when they learn matrices and
then learn statistics they will then see statistical problems using matrices,
everything they learn can be crossed with anything else they have learned in
the past. This will result in
continual review of past material and an attitude of learning full mastery
not just passing this week’s test.
Each type of problem will be analyzed from an algebraic approach, from
a numerical approach and from a graphical approach to enhance full
mastery. We have graphing calculators
in classroom sets for each class as well as calculators to rent for the year
for anyone who cannot afford to buy a calculator but wishes to have one at
home. We have a few math reference
books in our math department and more in our media center. We have funding set aside to purchase
whatever books are deemed helpful. We
are just across the street from Prior to entering the Mathematics SL class the students will
have the opportunity to take Algebra 2 and Precalculus classes with strong
vector development and integrated topics.
Provo High has a strong background in the use of technology especially
graphing calculators in teaching math and solving problems. We will expand this knowledge and use into
the IB Program. Topics:
1.
Algebra a.
Arithmetic and geometric sequences and series b. Exponents and logarithms c.
Binomial Theorem 2.
Functions and Equations a.
Concept of function, domain and range, image, composite
functions, inverse function b. Graph of a function, use of
GDC to investigate properties of graphs and their solutions c.
Transformations of graphs: translations, stretches; reflections in the
axes d. Reciprocal function, its
graph; its self-inverse nature e.
Quadratic function, graph, axis of symmetry, vertex
form, factored form—x-intercepts f.
Solutions to quadratic functions, quadratic formula,
use of its discriminant g. Exponential and logarithmic
functions 3.
Circular Functions and Trigonometry a.
Circles, radian measure, arc length, sector area b. Define sin & cos terms of
unit circle c.
Double angle formulae d. Periodic nature of trig
functions, their domains, ranges and graphs e.
Solutions to trig equations over finite interval f.
Solution of triangles, cosine rule, sine rule, area of
triangle 4.
Matrices a.
Definition – element, row, column, and order b. Matrix algebra -- =, +, -, X
scalar, X by another matrix, identity & zero matrices c.
2x2 & 3x3 determinants, inverse of 2x2 matrix,
conditions for inverse existence d. Solution to systems of linear
equations using inverse matrices 5.
Vectors a.
Vectors as displacements in 2 and 3 dimensions b. Scalar product of two vectors
– perpendicular vectors, parallel vectors, and the angle between vectors c.
Line as r = a + ib, the angle between two lines d. Distinguishing between
coincident and parallel lines, finding where lines intersect 6.
Statistics and Probability a.
Concept of population, sample, random sample and
frequency distribution of discrete and continuous data b. Presentation of data: frequency tables and diagrams, box and
whisker plots c.
Measures of central tendency: mean, median, ode; quartiles, percentiles;
range; interquartile range; variance; standard deviation d. Cumulative frequency e.
Concepts of trial, outcome, equally likely outcomes,
sample space (U) and event; probability of an event, complementary events f.
Combined events g. Conditional probability h. Venn diagrams, tree diagrams
and tables of outcomes to solve problems i.
Concept of discrete random variables and their
probability distributions expected value (mean), E(X) for discrete data j.
Binomial distribution; mean of the binomial
distribution k.
Normal distribution; its properties; standardization of
normal variables 7.
Calculus a.
Limits and convergence b. Differentiation of a sum and a
real multiple of the functions in VII. A, chain rule, product rule, quotient
rule, second derivative c.
Local maxima & minima points, first & second
derivatives in optimization problems d. Indefinite integration as
anti-differentiation; indefinite integrals of exponential, and trig
functions, the composite of any of these with the linear function ax + b e.
Anti-differentiation with a boundary condition to
determine the constant term; definite integrals; areas under curves; areas
between curses; volumes of revolution f.
Kinematic problems involving displacement, s, velocity,
v, and acceleration, a g. Graphical behavior of
functions; tangents and normals, behavior for large êx ê, horizontal and
vertical asymptotes; significance of the second derivative; distinction
between maximum and minimum points; points of in flexion with zero and
non-zero gradients. h. Solution of equations using
the Newton-Raphson method i.
Estimating definite integrals using trapezoidal
approximation. Portfolio – 36
hours Work on
portfolios and review the written examination papers at the end of the
year. For the portfolio the students
will work to develop at least four pieces of work of which two are
presentable for the internal assessment.
Assessment:
These papers are externally set and externally marked.
Together they contribute 80% of the final mark for the course. These papers
are designed to allow students to demonstrate what they know and what they
can do. Calculators
For both examination papers, students must have access to a
GDC at all times. Regulations covering the types of calculator allowed are
provided in the Vade Mecum. Mathematics SL information booklet
Each student must have access to a clean copy of the information
booklet during the examination. One copy of
this booklet is provided by IBCA as part of the examination papers
mailing. Awarding of marks
Marks may be awarded for method, accuracy, answers and
reasoning, including interpretation. In paper 1 and paper 2, full marks are not necessarily awarded
for a correct answer with no working. Answers must be supported by working
and/or explanations (in the form of, for example, diagrams, graphs or
calculations). Where an answer is incorrect, some marks may be given for
correct method, provided this is shown by written working. All students
should therefore be advised to show their working. Paper 1 1 hr 30 mins 40% This paper consists of 15 compulsory
short-response questions based on the whole syllabus. Syllabus coverage
Question type
·
A small number of steps is needed to
solve each question. ·
Questions may be presented in the
form of words, symbols, diagrams or tables, or combinations of these. Mark allocation
·
This paper is worth 90
marks, representing 40% of the final mark. ·
Questions of varying levels of
difficulty are set. Each question is worth 6 marks. Paper 2 1 hr 30 mins
40% This paper consists of 5 compulsory
extended-response questions based on the whole syllabus. Syllabus coverage
·
Knowledge of all
topics is required for this paper. However, not all topics are necessarily
assessed in every examination session. ·
Individual questions may require
knowledge of more than one topic. ·
The intention of this paper is to
test students’ knowledge of the syllabus in depth. The range of syllabus
topics tested in this paper may be narrower than that tested in paper 1. ·
To provide appropriate syllabus
coverage of each topic, questions in this section are likely to contain two
or more unconnected parts. Where this occurs, the unconnected parts will be
clearly labelled as such. Question type
·
Questions require extended responses
involving sustained reasoning. ·
Individual questions may develop a single
theme or be divided into unconnected parts. ·
Questions may be presented in the
form of words, symbols, diagrams or tables, or combinations of these. ·
Normally, each question reflects an
incline of difficulty, from relatively easy tasks at the start of a question
to relatively difficult tasks at the end of a question. The emphasis is on
problem-solving. Mark allocation
·
This paper is worth 90
marks, representing 40% of the final mark. ·
Questions in this section may be
unequal in terms of length and level of difficulty. Therefore, individual
questions may not necessarily be worth the same number of marks. The exact
number of marks allocated to each question is indicated at the start of each
question. Guidelines
Notation
Of the various notations in use, the IBO has chosen to adopt a
system of notation based on the recommendations of the International
Organization for Standardization (ISO). This notation is used in the
examination papers for this course without explanation. If forms of notation
other than those listed in this guide are used on a particular examination
paper, they are defined within the question in which they appear. Because students are required to recognize, though not
necessarily use, IBO notation in examinations, it is recommended that teachers
introduce students to this notation at the earliest opportunity. Students are
not allowed access to information about this notation in the
examinations. In a small number of cases, students may need to use
alternative forms of notation in their written answers. This is because not
all forms of IBO notation can be directly transferred into handwritten form.
For vectors in particular the IBO notation uses a bold, italic typeface that
cannot adequately be transferred into handwritten form. In this case,
teachers should advise candidates to use alternative forms of notation in
their written work (for example, x→,x¯ or x¯). Students must always use correct
mathematical notation, not calculator notation. Internal
assessment 20% Portfolio A collection
of two pieces of work assigned by the teacher and completed by the student
during the course. The pieces of work must be based on different areas of the
syllabus and represent the two types of tasks:
The portfolio
is internally assessed by the teacher and externally moderated by the IBO.
Procedures are provided in the Vade Mecum. Resources:
Calculus: Graphical, Numerical, Algebraic by Finney,
Demana, Waits, and Kennedy Precalculus with Limits, A Graphing Approach by
Larson, Hostetler, Edwards Pure Mathematics Volumes 1 and 2 by Bostock
and A Concise Course in A Level Statistics by Crawshaw
and Chambers Any reference books the IB committee feels would be beneficial graphing calculators Standards: http://www.ibo.org Helpful
Websites: |
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Provo High School An “IB World School” 1125 N. University Ave. Provo, UT 84604 |
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Phone: 801-373-6550 Fax: 801-374-4880 IB Coordinator:: Lori Rich |
