Let 10 points (1, 2, ..... 10) on the boundary of sector are given as shown in figure, if maximum number of different triangles that can be formed by joining any three of given points, is a natural number, then digit at its unit
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SHADY SIDE ACADEMY SENIOR SCHOOL
DEPARTMENT OF MATHEMATICS
Problem-Based Mathematics I
MISSION/HISTORY: As part of an on-going curriculum review the Mathematics
Department of Shady Side Academy sent two members of the senior school math faculty to
visit Phillips Exeter Academy [PEA] in 2008 to observe their classes. After this observation
and much reflection, the department decided to adopt this problem-based curriculum. The
materials used in the Mathematics I and II courses are taken directly from PEA. We thank the
teachers at PEA for the use of their materials.
RATIONALE: The Shady Side Academy Mathematics Department Goals are as follows:
Students will develop the habit of using mathematical reasoning based on logical thinking.
Students will develop adequate skills necessary to solve problems mathematically.
Students will recognize that the structure and order of mathematics can be discovered in the
world around us.
Students will recognize the connections of mathematics to other disciplines.
Students will express themselves clearly in mathematical discourse.
Students will be familiar with and proficient in appropriate technology.
Students will achieve their highest mathematical goals.
Students will gain an appreciation for the study of mathematics.
In addition, the teachers in the Department of Mathematics want you to be an articulate
student of mathematics. We want you to be able to speak and write mathematics well. We
want you to be a fearless problem solver so that you approach problems with curiosity and not
trepidation. The Mathematics I classroom is student-centered. The curriculum is problem-
based with an integrated design. You will continually learn new material while reviewing
prior topics.
EXPECTATIONS: In order for you to be successful in this course, the Mathematics
Department has the following suggestions and expectations. First, we expect you to attempt
every problem. More than merely writing the problem number, write an equation or draw a
picture or write a definition; in other words, indicate in some way that you have thought about
and tried the problem. Next, seek help wherever you can find it. We expect you to cooperate
with your peers and teachers. The Mathematics Department is a team of teachers striving to
help all students reach their potential. You are encouraged to ask any teacher for help if your
own is not available. Finally, as stated in the Student Handbook on page 13: “Homework for
Forms III and IV normally is limited to 45 minutes of homework per night per subject on days
when that class meets.” We expect you to spend 45 minutes on mathematics homework to prepare for each class meeting