GROUP 5 –
MATHEMATICS 4 CREDITS
All students at UAIS must complete four credits of Mathematics in
four years, and students must enter the Academy having already successfully
completed both semesters of Algebra I.
Typically, 9th graders begin at the Academy by taking
Geometry (or Accelerated Algebra II, if they completed Geometry in 8th
grade). Students who enter having taken
both Accelerated Algebra II and Geometry will be placed into AP Statistics.
Course Descriptions:
GEOMETRY – (1.0 credit; 9th
grade)
The study of Geometry includes math vocabulary, organization of proofs, logic
and reasoning, points, lines, planes and angles, parallel lines and planes,
transformations and congruence, congruent triangles, similar polygons, trigonometry
and the unit circle, non-right triangles, circles, areas of plane and solid
figures, volumes and surface areas of solids, using formulas in solving
problems, visualizing geometric situations, and using geometric ideas in real
situations. The objective of this course is to provide the student with the
requisite foundation for the study of advanced algebra and trigonometry.
Students will utilize knowledge of the subject in a variety of experiences and
assessments. The course will integrate a variety of teaching and learning strategies
including practical application, literature and a variety of other means of
learning geometry.
ACC ALGEBRA II –(1.0 credit ; 9th
or 10th grades)
The goal of Algebra II is to build upon the concepts taught in Algebra I and
Geometry while adding new concepts to the students’ repertoire of mathematics.
In Algebra I, students studied the concept of functions in various forms such
as linear, quadratic, polynomial, and exponential. Algebra II continues the
study of exponential and logarithmic functions and further enlarges the catalog
of function families to include rational and trigonometric functions. In
addition to extending the algebra strand, Algebra II will extend the numeric
and logarithmic ideas of accuracy, error, sequences, and iteration. The topic
of conic sections fuses algebra with geometry. Students will also extend their
knowledge of univariate and bivariate statistical applications. It is also the
goal of this model to help students see the connections in the mathematics that
they have already learned. For example, students will not only gain an in-depth
understanding of circular trigonometry, but will also understand its
connections to triangular trigonometry.
AP STATISTICS –(1.0 credit 9th,
10th, 11th or 12th grades)
Statistical literacy is a main goal of this class. Therefore,
verbal communication of concepts, vocabulary and ideas amongst students is an
essential part of the course design. Students work together to develop
competency in the subject through communications during group work, activities
and class discussions. Along with verbal interaction, students display
statistical literacy through written work. Everything from chapter outlines and
book work, to more formal assessments are used to evaluate students’ level of
understanding. Portfolio work including case studies and a statistical analysis
project are major components of the course. A course in statistics and
probability beyond the core curriculum is built around four themes: data
exploration and study design, probability models and their application,
statistical inference, and model assessment. Pre-requisite requirements to take AP
Statistics at UAIS include both Geometry and ACC Algebra II.
IB MATH STUDIES SL (1 & 2) –2.0
credits (11th/12th grades)
This course is available at SL only. The course concentrates on mathematics
that can be applied to contexts related as far as possible to other subjects
being studied, to common real-world occurrences and to topics that relate to
home, work and leisure situations. The course includes project work, a feature
unique within this group of courses: students must produce a project, a piece
of written work based on personal research, guided and supervised by the
teacher. The project provides an opportunity for students to carry out a
mathematical investigation in the context of another course being studied, a
hobby or interest of their choice using skills learned before and during the
course. This process allows students to ask their own questions about
mathematics and to take responsibility for a part of their own course of
studies in mathematics. It caters for students 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 skills and a rudimentary knowledge of basic
processes. Topics covered include Number and Algebra, geometry and trigonometry
Statistics, and Financial mathematics.
IB MATH SL (1 & 2) –(2.0 credits; 11th/12th
grades)
This course caters to students who already possess knowledge of core
mathematical concepts from Algebra I and Algebra II and who are equipped with
the skills needed to apply core 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. The course focuses on introducing important
mathematical concepts through the development of mathematical techniques. The
intention is to introduce students to these concepts in a comprehensible and
coherent way, rather than insisting on mathematical rigor. Students should
wherever possible apply the mathematical knowledge they have acquired to solve
realistic problems set in an appropriate context.
The internally assessed component, the exploration, offers students a framework
for developing independence in their mathematical learning by engaging in
mathematical investigation and mathematical modeling. Students are provided
with opportunities to take a considered approach to these activities and to
explore different ways of approaching a problem. The exploration also allows
students to work without the time constraints of a written examination and to
develop the skills they need for communicating mathematical ideas. This course
does not have the depth found in the mathematics HL course. Students wishing to
study subjects with a high degree of mathematical content should therefore opt
for the mathematics HL course rather than a mathematics SL course.
IB MATH HL (1 & 2) – ( 2.0 credits;
11th/12th grades)
This course caters for students with a good background in mathematics who are
competent in a range of analytical and technical skills. The majority of these
students will be expecting to include mathematics as a major component of their
university studies, either as a subject in its own right or within courses such
as physics, engineering and technology. Others may take this subject because
they have a strong interest in mathematics and enjoy meeting its challenges and
engaging with its problems.
The nature of the subject is such that it focuses on developing important
mathematical concepts in a comprehensible, coherent and rigorous way. This is
achieved by means of a carefully balanced approach. Students are encouraged to
apply their mathematical knowledge to solving problems set in a variety of
meaningful contexts. Development of each topic should feature justification and
proof of results. Students embarking on this course should expect to develop
insight into mathematical form and structure, and should be intellectually
equipped to appreciate the links between concepts in different topic areas.
They should also be encouraged to develop the skills needed to continue their
mathematical growth in other learning environments.
The internally assessed component, the portfolio, offers students a framework
for developing independence in their mathematical learning through engaging in
mathematical investigation and mathematical modeling. Students will be provided
with opportunities to take a considered approach to these activities, and to
explore different ways of approaching a problem. The portfolio also allows
students to work without the time constraints of a written examination and to
develop skills in communicating mathematical ideas.
This course is a demanding one, requiring students to study a broad range of
mathematical topics through a number of different approaches and to varying
degrees of depth. Students wishing to study mathematics in a less rigorous
environment should therefore opt for one of the standard level courses,
mathematics SL or mathematical studies SL.
IB FURTHER MATHS HL (1 & 2) –(2.0 credits; 11th/12th
grades)
Co-requisite: IB Math HL and teacher/parent approval
This course caters for students with a good background in mathematics who have
attained a high degree of competence in a range of analytical and technical
skills, and who display considerable interest in the subject. Most of these
students will intend to study mathematics at university, either as a subject in
its own right or as a major component of a related subject. The course is
designed specifically to allow students to learn about a variety of branches of
mathematics in depth and also to appreciate practical applications.
The nature of the subject is such that it focuses on different branches of
mathematics to encourage students to appreciate the diversity of the subject.
Students should be equipped at this stage in their mathematical progress to
begin to form an overview of the characteristics that are common to all
mathematical thinking, independent of topic or branch. All categories of
student can register for mathematics HL only or for further mathematics SL only
or for both. However, candidates registering for further mathematics SL will be
presumed to know the topics in the core syllabus of mathematics HL and to have
studied one of the options, irrespective of whether they have also registered
for mathematics HL.
Examination questions are intended to be comparable in difficulty with those
set on the four options in the mathematics HL course. The challenge for
students will be to reach an equivalent level of understanding across these
four topics.