GEOMETRY AND DISCRETE MATH MGA4U Mrs. E. Benoit-Rooms 217/ 218

http:/lwww.geocities.com/eaabenoit

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Are you in the right course? Here are a few indications.

a. You MUST have achieved a credit in MCR3U, preferably with a very good to excellent mark

b. It is likely that you are seriously considering a university degree in mathematics, physics, engineering or another major which lists MGA4U as a prerequisite to entry.

c. You have excellent attendance and do homework each night (45 minutes is the bare minimum despite a whirlwind schedule).

d. Your 3U and 2D notebooks are so well done that you can easily review 3U and 2D materials independently by reviewing your own notes. You have already reviewed these notes so that the previous ideas are both fresh and mature--therefore ready to use in this class,

c. You communicate mathematical ideas well and enjoy the precision that mathematical notation gives to your communication. You grasp new mathematical ideas easily but quickly build on this foundation by "pushing the pencil." Practice is necessary both to help the ideas mature and also to give you the facility to work quickly and precisely. You are a hard worker and always attempt ALL assigned problems on your own.

8. You bounce back from any "failure" to complete a task correctly. This is feedback indicating where more work is needed.
9. You are well organized and keep track of "weak" areas so that you can seek help both during class and outside of class.

j. You are in the habit of both prereading and reviewing course material frequently.

k. Over the course of the semester you are able to retain the material previously taught.

2. ATTENDANCE is essential. The course moves extremely quickly.

All absences are the responsibility of the student, supported by parental notes and field trips lists as appropriate.

PLANNED ABSENCES: it is the student's responsibility to inform the teacher as early as possible of planned absences such as doctor's appointments and field trips. Please notify the teacher in writing to avoid confusion (the initial notice may /should come from you, even if your are not 18, then followed up by a parental note or field trip list). The student is responsible for obtaining class notes from another student and making up any assignments, etc., in a timely fashion (prior arrangement with the teacher is a necessity). Class work is always the priority during class.

UNPLANNED ABSENCES: usually this is illness. Make sure that you have the phone numbers of several "buddies" in the class to check on the progress of the course. Also check the homework page. Bring a parental note (to be kept in the subject teacher's records) explaining the absence even if the absence has been called in.

MISSED TESTS, QUIZZES, ASSIGNMENTS. Remember that class work is always the priority during class time so it is your responsibility to seek out the teacher to make any necessary arrangements in a timely fashion.

--If the absence is (or should have been!) planned, you must make prior arrangements with the teacher who will decide whether the test, quiz or assignment will be made up before your absence or after your absence. If the date of the absence is getting close, make sure you know when you are to make up the missed marks.

--If the absence is not planned (usually illness), get your quiz (8:40) or test(8:00) at Room 218 from any math teacher on the day you return and attach your parental note to the quiz or test when you hand it in. If there is a serious and legitimate reason why this is not possible, see the subject teacher with your parental note either at 8:50 or 12:30 on the day of your return.

**Cheek "Big Blue" on teacher's desk in 217 for handbacks and handouts.

3. EVALUATION.

Term Work: 70% of the course mark

Term work will be evaluated in these categories

Knowledge/Understanding --- 45% of the term mark; Application --- 30% of the term mark;

Thinking/Inquiry/Problem Solving --- 15% of the term mark; Communication--- 10% of the term mark

End of semester evaluation will include a final examination and other components (which may include items such as performance tasks and summative class tests). The summative evaluation portion will cover all topics presented during the entire course. The following expectations should also be used as a review list during the term and for exam preparation.

TEXT: Harcourt Mathematics 12 Geometry and Discrete Mathematics Peter Crippin, Jock MacKay, Neal Reid: Harcourt Canada Ltd., 2002. Replacement cost: $70

COURSE: Mathematics MGA 4U

I have read the above document and I am aware that both progress and marks will be affected should these requirements not be met. 1 have also read the absence and missed test/assignment policy in the student agenda.

Geometry and Discrete Mathematics (MGA4U)

Also see: http:/www.edu.gov.on.ca/document/curricul/secondary/grade1112/math/math.html#MGA4U

This course enables students to broaden mathematical knowledge and skills related to abstract mathematical topics and to the solving of complex problems. Students will solve problems involving geometric and Cartesian vectors, and intersections of lines and planes in three-space. They will also develop an understanding of proof, using deductive, algebraic, vector, and indirect methods. Students will solve problems involving counting techniques and prove results using mathematical induction.

Prerequisite: Functions and Relations, Grade 11, University Preparation

• represent vectors as directed line segments;

• perform the operations of addition, subtraction, and scalar multiplication on geometric vectors;

• determine the components of a geometric vector and the projection of a geometric vector;

• model and solve problems involving velocity and force;

• determine and interpret the dot product and cross product of geometric vectors;

• represent Cartesian vectors in two-space and in three-space as ordered pairs or ordered triples;

• perform the operations of addition, subtraction, scalar multiplication, dot product, and cross product on Cartesian vectors.

Determining Intersections of Lines and Planes in Three-Space

By the end of this course, students will:

• determine the vector and parametric equations of lines in two-space and the vector, parametric, and symmetric equations of lines in three-space;

• determine the intersections of lines in three-space;

• determine the vector, parametric, and scalar equations of planes;

• determine the intersection of a line and a plane in three-space;

• solve systems of linear equations involving up to three unknowns, using row reduction of matrices, with and without the aid of technology;

• interpret row reduction of matrices as the creation of a new linear system equivalent to the original;

• determine the intersection of two or three planes by setting up and solving a system of linear equations in three unknowns;

• interpret a system of two linear equations in two unknowns and a system of three linear equations in three unknowns geometrically, and relate the geometrical properties to the type of solution set the system of equations possesses;

• solve problems involving the intersections of lines and planes, and present the solutions with clarity and justification.

2- PROOF AND PROBLEM SOLVING --Overall Expectations By the end of this course, students will:

• demonstrate an understanding of the principles of deductive proof (e.g., the role of axioms; the use of "if . . then" statements; the use of "if and only if' statements and the necessity to prove them in both directions; the fact that the converse of a proposition differs from the proposition) and of the relationship of deductive proof to inductive reasoning;

• prove some properties of plane figures (e.g., circles, parallel lines, congruent triangles, right triangles), using deduction;

• prove some properties of plane figures (e.g., the midpoints of the sides of a quadrilateral are the vertices of a parallelogram; the line segment joining the midpoints of two sides of a triangle is parallel to the third side) algebraically, using analytic geometry;

• prove some properties of plane figures, using vector methods;

• prove some properties of plane figures, using indirect methods;

• demonstrate an understanding of the relationship between formal proof and the illustration of properties that is carried out by using dynamic geometry software.

By the end of this course, students will:

• solve problems by effectively combining a variety of problem-solving strategies (e.g., brainstorming, considering cases, choosing algebraic/geometric/vector or direct/indirect approaches, working backwards, visualizing by using concrete materials or diagrams or software, iterating, varying parameters, creating a model, introducing a coordinate system);

• generate multiple solutions to the same problem;

• use technology effectively in making and testing conjectures;

• solve complex problems and present the solutions with clarity and justification.

By the end of this course, students will:

• solve problems of significance, working independently, as individuals and in small groups;

• Solve problems requiring effort over extended periods of time;

• demonstrate significant learning and the effective use of skills in tasks such as solving challenging problems, researching problems, applying mathematics, creating proofs, using technology effectively, and presenting course topics or extensions of course topics.

3. DISCRETE MATHEMATICS -- OVERALL EXPECTATIONS By the end of this course, students will:

By the end of this course, students will:

• solve problems, using the additive and multiplicative counting principles;

• express the answers to permutation and combination problems, using standard combinatorial symbols [e.g., , P(n, r)];

• evaluate expressions involving factorial notation, using appropriate methods (e.g., evaluate mentally, by hand, by using a calculator);

• solve problems involving permutations and combinations, including problems that require the consideration of cases;

• explain solutions to counting problems with clarity and precision;

• describe the connections between Pascal's triangle, values of , and values for the binomial coefficients;

• solve problems, using the binomial theorem to determine terms in the expansion of a binomial.

By the end of this course, students will:

• demonstrate an understanding of the principle of mathematical induction;

• use sigma notation to represent a series or the sum of a series;

• prove the formulas for the sums of series, using mathematical induction;

• prove the binomial theorem, using mathematical induction;