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IB Math Studies SL (MA, AS) Grades
Offered: 11-12 Credit:
1.0 for 1 year 2.0 for 2 years Course description:
Mathematics Studies is a one year (plus a four hour quarterly
Saturday class) course for juniors with varied backgrounds and
abilities. More specifically, it is
designed to build confidence and encourage an appreciation of mathematics in
students who do not anticipate a need for mathematics in their future
studies. Students taking this course
need to be already equipped with fundamental skill and a rudimentary
knowledge of basic processes. There
will be a four hour quarterly Saturday
class. 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 trig functions
and then learn statistics they will then see statistical problems using trig
functions, 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 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
Topics:
I.
Introduction to the Graphic Display
Calculator (GDC) A.
Arithmetic calculations, use of the GDC to graph a variety of
functions, window, zoom, trace,
common buttons explained, entering data lists I.
Number and algebra A.
Natural numbers, integer, rational numbers, and real numbers B.
Approximation: decimal places; significant figures; percentage errors;
estimation C.
Scientific notation D.
SI – the metric system E.
Arithmetic sequences and series plus applications F.
Geometric sequences and series plus applications E.
Solutions of pairs of linear equations in two variables using GDC
solutions of quadratic equations: by factorizing; by using a GDC III. Sets, Logic and Probability A.
Basic concepts of set theory: subsets; intersection; union; complement B.
Venn diagrams and simple applications. C.
Sample space: event, A; complementary event, A’ D.
Basic concepts of symbolic logic: definitions of a proposition;
symbolic notation of propositions E.
Compound statements; translation between verbal statements, symbolic
form and
Venn diagrams; knowledge and use of “exclusive disjunction” and
distinction between it
and “disjunction” F.
Truth tables, concepts of logical contradiction and tautology G.
Definition of implication: converse; inverse; contrapositive; logical
equivalence H.
Equally likely events.
Probability of an event A.
Probability of a complementary
event I. Venn diagrams; tree diagrams; tables of
outcomes; solution of problems using “with replacement” and “ with
replacement” J. Laws of probability: combined events,
mutually exclusive events, independent events, conditional probability IV. Functions A. Concept of a function as a mapping,
domain and range, mapping diagrams B.
Linear functions and their graphs C.
The graph of the quadratic function; properties of symmetry, vertex,
intercepts D. Exponential expressions: graphs and
properties, growth and decay, basic concept of asymptotic behavior E.
Graphs and properties of sine and cosine functions; amplitude and
period F.
Accurate graph drawing G.
Use of GDC to sketch and analyze some simple, unfamiliar functions H. Use of GDC to solve equations involving
simple combinations of some simple, unfamiliar functions. I.
Geometry and Trigonometry A.
Coordinates– two dimensions: points; lines; midpoints; distances
between points B.
Equation of a line in E2: y = mx + c and ax + by + d = 0
gradient; intercepts; points of intersection of lines; parallel and
perpendicular lines C.
Right-angled trig; use of ratios of sine, cosine and tangent D.
Sine rule; cosine rule, area of triangle as E.
Geometry of three-dimensional shapes: cuboid; prism; pyramid;
cylinder; sphere;
hemisphere; cone; Lengths of lines joining vertices, vertices with
midpoints and midpoints
with midpoints; sizes of angles between two lines and between lines and planes II.
Statistics A.
Classification of data as discrete or continuous B.
Simple discrete data: frequency tables; frequency polygons C.
Grouped discrete or continuous data: frequency tables; mid-interval
values; upper and lower
boundaries D.
Cumulative frequency tables for grouped discrete data and for grouped
continuous data; cumulative
frequency curves; Box and Whisker Plots; Percentiles; Quartiles E.
Measures of central tendency for simple discrete data: mean, median,
mode; For grouped discrete and
continuous data: approximate mean; modal group; 50th percentile F.
Measures of dispersion: range; interquartile range; standard deviation G.
Scatter diagrams; line of best fit, by eye, passing through the mean
point. Bivariate data: the concept of
correlation. Pearson’s product-moment
correlation coefficient;
Interpretation of positive, zero and negative correlations H.
The regression line for y on x; use of the regression line for
prediction purposes I.
The Chi squared test for independence: formulation of null and
alternative hypotheses;
significance levels; contingency tables; expected frequencies; degrees
of freedom; use of tables for
critical values; p-values III.
Introductory Differential Calculus A.
Gradient of the line through two points that lie on the graph of a
function Behavior of the gradient of the line
through two points on the graph of a function as one point nears the other Tangent to a curve B.
Differentiation of polynomials and second and third derivatives of
same C.
Gradients of curves for given values of x. Values of x where f”(x) is given equation of the tangent at a given
point D.
Increasing and decreasing functions; graphical interpretation of
f”(x)>0, f”(x) = 0 and
f”(x)<0 E.
Values of x where the gradient of a curve is 0 (zero); solution of
f”(x) = 0 Local maximum and minimum points. VIII Financial
Mathematics A.
Currency conversions B.
Simple interest C.
Compound interest; depreciation D.
Construction and use of tables: loan and repayment schemes; investment
and saving schemes; inflation Project Work on project and review the
written examination papers at the end of the year. The project is an individual piece of work involving the
collection of information or the generation of measurements, and the analysis
and evaluation of the information or measurements. Assessment:
Students will be assessed by internal and external
measures. The internal assessment will
be based on a student portfolio containing two pieces of exemplary work one
in mathematical investigation and the other in mathematical modeling. Students will be given at least two assignments
in each category. The external assessment will consist of two written papers to
be given at the end of the school year.
Students will be allotted a total of three hours to complete the two
papers. Paper one– fifteen compulsory
short-response questions based on the whole syllabus, one and one half hours
to complete. Paper two– five
compulsory extended-response questions based on the whole syllabus, one and
one half hours to complete. In addition to the internal and external assessments, students
will take frequent tests and quizzes throughout the year for the purpose of
providing feedback to both student and teacher regarding progress toward the
aims and objectives of the course. ASSESSMENT
DETAILS
External assessment details --3 hrs 80% General
Paper 1 and paper 2
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. Mathematical studies 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, full marks are awarded for each correct answer
irrespective of the presence or absence of working. In 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. 1 Paper 1--1 hr 30
mins 40% This paper consists of 15 compulsory
short-response questions. Syllabus coverage
·
Knowledge of all
topics is required for this paper. However, not all topics are necessarily
assessed in every examination session. ·
The intention of this paper is to
test students’ knowledge across the breadth of the syllabus. However, it
should not be assumed that the separate topics are given equal
emphasis. 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. 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. 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. Internal assessment 20% Project The project
is an individual piece of work involving the collection of information or the
generation of measurements, and the analysis and evaluation of the
information or measurements.
Resources:
Mathematical Studies 3rd Edition by Fabio
Cirrito, IBID Press Precalculus with Limits, A Graphing Approach by
Larson, Hostetler, Edwards Mathematical Ideas, Addison Wesley, 2001 Discrete Mathematics Across the Curriculum K-12, NCTM, 1991 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 |
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