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Mathematics

**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, 9^{th} graders begin at the Academy by taking
Geometry (or Accelerated Algebra II, if they completed Geometry in 8^{th}
grade). Students who enter having taken
both Accelerated Algebra II and Geometry will be placed into AP Statistics.

** Course Descriptions:**

**GEOMETRY**** – (1.0 credit; 9 ^{th}
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 ; 9 ^{th}
or 10^{th} 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 9 ^{th},
10^{th}, 11^{th} 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 (11 ^{th}/12^{th} 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; 11 ^{th}/12^{th}
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;
11 ^{th}/12^{th} 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; 11 ^{th}/12^{th}
grades)**

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.