# Advanced Placement Mathematics at Archbishop O’Leary

## Philosophy

The general philosophy of Advanced Placement (AP) Mathematics is to build enduring mathematical understanding whereby students are required to study the why and how of mathematics in addition to mastering the necessary procedures and skills.

Mathematical practices for AP students to accomplish the learning objectives and build conceptual understanding include:

1. Reasoning with definitions and theorems
2. Connecting concepts
3. Implementing algebraic/computational processes
4. Connecting multiple representations
5. Building notational fluency
6. Communicating mathematics precisely

AP Mathematics courses emphasize a multi-representational approach to teaching and learning, with concepts and problems expressed graphically, numerically, analytically, and verbally.

# Use of Technology

Technology will be used regularly by students and teachers to reinforce the relationships among the multiple representations of concepts. Students are encouraged to use technology to explore, experiment, confirm written work, and to assist in interpreting results and supporting conclusions. It is a common practice for students to justify the reasonableness of a calculated answer as well as verify the accuracy of the result through various techniques. The Development Committee of AP Calculus has found it necessary to make certain requirements of the technology students' use for AP Calculus Exams. At Archbishop O'Leary, we support the Development Committee's recommendation that students use the highest level of technology on the list of approved calculators, TI Nspire CX.

The Advanced Placemment (AP)  program provides students with the opportunity to develop the skills they need to succeed in university, from improved study habits, to exam-writing experience, to workload and time management.

# Course Sequence

Students registered in AP Mathematics are encouraged to take Math 10C AP in Grade 10, and then Math 20-1AP and Math 30-1AP both in Grade 11. This would allow room in the student's schedule to complete AP Calculus or AP Statistics in Grade 12.

The Math AP sequence of courses is designed for students who enjoy math and its challenges. Students must be motivated, committed, and consistent in their study of Mathematical Theory as topics and concepts will be examined in more depth and with multiple representations in comparison to the regular Alberta Education curriculum standards. Evaluation of student ability will be based on the respective course assessment standards of Alberta Education.

## AP Maths Sample Schedule

 Grade 10 Grade 11 Grade 12 Semester 1 Semester 2 Semester 1 Semester 2 Semester 1 Semester 2 Math 10CAP ineither semester Math 20-1AP Math 30-1AP Math 31APCalculus orMath 35AP Statistics Learning Strategies 35AP Exams written in early May.

The General Philosophy of AP Mathematics will be followed in this course.

This course will emphasize a multi-representational approach to teaching and learning, with concepts and problems expressed graphically, numerically, analytically, and verbally.

 Topic Concepts to be Enriched or Emphasized 4. Exponents and Radicals Simplifying Radicals, Exponent Rules 3. Trigonometry Primary Trigonometric Ratios 5. Polynomials Factoring 6. Linear Relations and Functions Interval Notation 7. Linear Equations and Graphs Writing equations of lines and perpendicular lines 8/9. Systems of Equations Linear-Linear, Linear-Quadratic, Quadratic-Quadratic 1/2. Measurement Memorization of formulas for area, volume, surface area

The General Philosophy of AP Mathematics will be followed in this course.

This course will emphasize a multi-representational approach to teaching and learning, with concepts and problems expressed graphically, numerically, analytically, and verbally.

 Topic Concepts to be Enriched or Emphasized 3. Quadratic Functions Multiple RepresentationsEven Function vs Even Degree PolynomialIntervals of increase and decrease 4. Quadratic Equations Zeros of a functionQuadratic formula memorized 5. Radical Expressionsand Equations Rationalizing numerators and denominators 6. Rational Expressions and Equations Simplifying rational expressions involving operations 7. Absolute Value andReciprocal Functions Piecewise definition of Absolute ValueAbsolute value of functions 1. Sequences and Series Sum of an infinite geometric sequence 2. Trigonometry Exact values of special trigonometric ratios 8. Systems of Equations& Inequalities Quadratic-Quadratic Systems 9. Linear and QuadraticInequalities Inequalities involving quadratics

The General Philosophy of AP Mathematics will be followed in this course.

This course will emphasize a multi-representational approach to teaching and learning, with concepts and problems expressed graphically, numerically, analytically, and verbally.

 1. Transformations Visualization of Graphs of FunctionsTransformations of FunctionsInverse FunctionsInterval Notation 3. Polynomial Functions ContinuityTransformations with cubic functionsSymmetryCubic functions classified as odd functions 2. Radical Functions and9. Rational Functions AsymptotesContinuityDiscontinuity 7. Exponential Functions and8. Logarithmic Functions e, Euler's numberTransformations of Exponential Functions 4. 5. 6. Trigonometry Exact Values of special trig ratiosTrigonometric equations vs identitiesSum, Difference, Double, Half, Pythagorean Theorems 10. Function Operations Composition of Inverse FunctionsOperations of any 2 functions algebraically and graphically 11. Permutations, Combinations & the Binomial Theorem Binomial Theorem Related to Composition of Functions ## Mathematics 31AP Calculus AB

Students enrolled in Math 31AP will complete the Alberta Mathematics 31 Calculus program during the first semester of Grade 12. Topics will be enriched with multiple representations to provide a deeper understanding of the concepts. There will be a focus on providing complete solutions to free response problems by justifying answers with reference to theorems and rules. Students must enroll in Learning Strategies 35 during the second semester to continue to study calculus concepts not covered in Math 31 and prepare for the AP Calculus AB exam in May. Upon successful completion of the AP Calculus AB exam in May, students may receive university credit equivalent to a first year math course. This course is recommended for university faculties such as engineering, advanced math, and sciences programs to give students an advantage in first year post-secondary institutions requiring calculus.

PRE-REQUISITE REQUIRED Successful completion of Math 20-1. It is recommended that students complete Math 30-1AP prior to studying Math 31AP, however due to scheduling restrictions, Math 30-1 and Math 31AP may be taken concurrently during the first semester of Grade 12.

## Mathematics 35AP Statistics

Student enrolled in this course will complete the Alberta Mathematics 35 Statistics program during the first semester of Grade 12. Students should have a strong grasp of mathematical processes and possess a sufficient mathematical maturity. Curriculum for this course will provide students with a non­calculus based introduction to statistics. Students must enroll in Learning Strategies 35 during the second semester to continue to study statistics concepts beyond Alberta Math 35 curriculum and to prepare for the AP Statistics exam in May This course may be delivered individually on-line depending on enrollment.

PRE-REQUISITE REQUIRED Successful completion of Math 20-1. It is recommended that students complete Math 30-1 prior to studying statistics, however due to scheduling restrictions, Math 30-1 and Math 35AP may be taken concurrently during first semester of Grade 12.

## Learning Strategies 35 AP Calculus

This course is an extension of Math 31AP Calculus into the second semester. Students will complete the study of AP Calculus AB that extends beyond Math 31 Calculus. Students will be given the opportunity for extensive preparation to write the AP Calculus AB exam in early May.

Depending on enrollment, this course may also include an extension of Math 35 AP Statistics and preparation for the AP Statistics exam in early May.

For more information on the AP program and what it could mean for you, check out the University of Alberta's AP information. http://www.admissions.ualberta.ca/en/AP-IB/AP-advanced-placement.aspx