Pre-AP Math 10: Foundations and Pre-Calc 10; Foundations 20 Welcome to pre-AP Math and congratulations for taking the plunge! There are some fairly obvious things about AP Math and some not-so-obvious things. Both of these groups require some explanation: The obvious things: 1) This Math program is geared toward students who are planning on going to university after high school. 2) AP Math will be more challenging than the other Math courses at Sheldon. 3) Because AP Math is more challenging, keeping up with your work will take on more significance. The not-so-obvious things: 1) Advanced Placement is a program that students from many different countries take and therefore it is a standard and recognizable program throughout North America. 2) At the end of pre-AP Math and AP Calculus you will write the AP exam. 3) The evaluation of your work specifically toward writing the AP exam and your work towards meeting the outcomes of the Saskatchewan Math curriculum will be separately evaluated and only the latter will appear on report cards and transcripts. 4) It will be necessary to move quickly enough that we can be finished F-PC10, Fnd20, Fnd30, PC20, PC30, and Calculus 30 by around late March or early April of your Grade 12 year. Some important points to guide your thinking about the AP program. 1) There are three goals of this program. The first and most important is to offer students a more challenging Math experience. The primary benefits of a more challenging Math course are greater student preparation for difficulties in school work and university courses. The second goal is to have students prepare intensively for the AP exam. Finally, it is a goal for students to pass the AP exam. However, it is important to note that most of the benefits of taking the AP program are realized by students simply by doing the work during the pre-AP courses and preparing for the AP exam. It is great if you pass, but if you don’t you will still likely be much better prepared to take higher level Math at university. According to AP documentation, about 60% of people that take the AP exam pass it but 94% of the people that attempt the exam go on to earn Bachelor’s degrees at university. 2) It may seem like your marks would go down in a tougher Math course, but the opposite is much more likely. This is because during pre-AP courses you will be evaluated on the outcomes of the regular course curricula. For example, all students at Sheldon who take Pre-Calc 20 will be evaluated on the outcomes of Pre-Calc 20 whether they are in pre-AP or not. However, the students in the pre-AP class will be working at a higher standard than the students in other classes so the evaluations will likely seem much simpler for them. 3) In preparation for the AP exam students will do a number of evaluations that differ from the ones that students in other courses do. The AP exam is unique and requires some practice. More specifically, there are parts of the AP exam that are timed, there are parts on which you can’t use a calculator, there

are parts on which you have to use a specific calculator, there are parts that are multiple choice, and there are parts that require the student to explain their reasoning process. It is very important, if students wish to pass the AP exam, to be prepared for these situations. Therefore students will perform training evaluations designed to prepare them for the AP exam. These evaluations will start early in the pre-AP courses and will continue throughout the program. It is important to note however that these evaluations will not factor into report cards, official marks, or official transcripts. Instead, AP students will get separate feedback on these evaluations so that they can gauge their preparedness for the AP exam. Evaluation Course work (exams/assignments/etc) – 70% Midterm exam – 10% Final exam – 20% **Important to note that there will be several pieces of evaluation each semester that will not count in the above grading scheme but will be reported separately. Course Material Below is the current course material schedule from pre-AP in Grade 10 straight through to the beginning of Calculus in Grade 12 (tentatively late October or early November of your Grade 12 year).

Pre-AP Math Grade 10 1) Grade 9 skills review - Order of operations - Equation Solving - Solving word problems using single variable equations - Skills with polynomials and exponent laws incl binomial expansion etc. 2) Factoring - GCF/LCM/PPN - Factoring the GCF from a polynomial expression - Difference of squares, trinomial squares, and trinomials with a lead coefficient of 1 - Trinomials with a lead coefficient that is not 1 3) Irrationals - Basic concept of a root - Simplifying square roots - Simplifying cube roots, fourth roots, etc and writing mixed radical expressions as entire radicals - Estimating the values of roots - Applying exponent laws to radicals 4) Linear Equations part 1 - Coordinate geometry - Points and the idea of a relation between the x and y values of points - Graphing using a table of values - Slope and intercepts - Graphing using intercepts - Linear relations - Vertical and horizontal lines and their equations

5) Linear Equations part 2 - Slope intercept form and standard form - Using slope intercept form to graph - Creating equations for lines - Applications of linear equations to real world relations 6) Systems of Linear Equations - Solving systems graphically - Solving systems using substitution and elimination - Solving word problems using systems 7) Systems of Linear Inequalities - Graphing single variable equations on a number line

- Solve systems of linear inequalities incl shading and solid/dotten lines. Explain why points within different areas solve the inequaility.

8) Quadratic Equations - Graphing the basic quadratic and a discussion of the parts of the parabola - Characteristics of the parabola: Opening direction, width, vertex, intercepts, axis of symmetry - Vertex-graphing form 9) Trigonometry - Basic trig: sin, cos, tan, Pythagorean Theorem, and angle sum of a triangle - Solving triangles - Applications of basic trig - Special triangles - Introduction of sine and cosine laws - The ambiguous case - application of sine and cosine laws 10) Reasoning - Deductive and inductive reasoning and proofs - Applications of reasoning to ratios, rates, and proportions - Set Theory - Triangle congruency proofs 11) Statistics - Basic stats: Measures of central tendency - Normal distribution and z-scores - Interpretation of statistical data

Pre AP Math Grade 11 1) Skills review - Linear and Quadratic Equations (briefly discuss reciprocal functions) - Systems of Linear Equations - Simplifying Irrationals (briefly discuss rational exponents) - Factoring 2) Factoring and Rational Expressions continued - Factoring sums and differences of cubes - Factoring polynomials with degree > 2 - Simplifying rational expressions - Multiplying and dividing rational expressions - Adding and subtracting rational expressions

3) Graphing Higher Degree Polynomials and Rational Expressions 4) Equation Solving - Absolute value equations - Radical equations 5) Solving Quadratic Equations and Quadratic Inequalities - Square root method - Completing the square method - Quadratic formula - Applications to inequalities 6) Sequence and Series - Arithmetic and geometric sequences - Arithmetic and geometric series - Infinite series 7) Odds and Probability 8) Permutations and Combinations 9) Working with Exponentials and Logs - Graphing exponentials - Solving exponential equations - Graphing logarithmic equations - Manipulating logarithmic expressions - Solving log equations

Pre AP Math Grade 12 1) Trig on the Unit Circle - The six trig functions as defined on the unit circle - Radian measure and conversions with degrees - Exact values of trig functions - Using trig functions to find angles 2) Graphing Trig Functions and Their Inverses 3) Solving Trig Identities 4) Conics

AP Calculus 30

- Hopefully it will be possible to start the Calculus course as of November in students’ first semester of Grade 12. This will give enough time to extend the course in ways necessary for the AP exam, and to finish by the end of March or beginning of April. Most of April will be used for review and rehearsal for the AP exam which is written in May.