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Math AP

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Advanced Placement Mathematics at Archbishop O’Leary

Philosophy

The general philosophy of Advanced P​​lacement (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 10Grade 11Grade 12
Semester 1Semester 2Semester 1Semester 2Semester 1Semester 2

Math 10CAP in

either semester

Math 20-1APMath 30-1AP

Math 31AP

Calculus or

Math 35AP Statistics

Learning Strategies 35

AP Exams written in early May.

 

Math 10 Advanced Placement  

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 RadicalsSimplifying Radicals, Exponent Rules
3. TrigonometryPrimary Trigonometric Ratios
5. PolynomialsFactoring
6. Linear Relations and FunctionsInterval Notation
7. Linear Equations and GraphsWriting equations of lines and perpendicular lines
8/9. Systems of EquationsLinear-Linear, Linear-Quadratic, Quadratic-Quadratic
1/2. MeasurementMemorization of formulas for area, volume, surface area


 

 ​Math 20-1 Advanced Placement     

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 Representations

Even Function vs Even Degree Polynomial

Intervals of increase and decrease

4. Quadratic Equations

Zeros of a function

Quadratic formula memorized

5. Radical Expressions
and Equations
Rationalizing numerators and denominators
6. Rational Expressions 
and Equations
Simplifying rational expressions involving operations
7. Absolute Value and
Reciprocal Functions

Piecewise definition of Absolute Value

Absolute value of functions

1. Sequences and SeriesSum of an infinite geometric sequence
2. TrigonometryExact values of special trigonometric ratios
8. Systems of Equations
& Inequalities
Quadratic-Quadratic Systems
9. Linear and Quadratic
Inequalities
Inequalities involving quadratics

 

 

Math 30-1 Advanced Placement      

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 Functions

Transformations of Functions

Inverse Functions

Interval Notation

3. Polynomial Functions

Continuity

Transformations with cubic functions

Symmetry

Cubic functions classified as odd functions

 

2. Radical Functions and

9. Rational Functions

Asymptotes

Continuity

Discontinuity

7. Exponential Functions and

8. Logarithmic Functions

e, Euler's number

Transformations of Exponential Functions

4. 5. 6. Trigonometry

Exact Values of special trig ratios

Trigonometric equations vs identities

Sum, Difference, Double, Half, Pythagorean Theorems

 

10. Function Operations

Composition of Inverse Functions

Operations of any 2 functions algebraically and graphically

11. Permutations, Combinations & the Binomial TheoremBinomial Theorem Related to Composition of Functions​


 


 

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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

 

Want to know more about the AP program in Canada?
Check out AP Canada's Website.    http://apcanada.collegeboard.org/

 

For more insight into the AP program as a worldwide program, please visit AP Central.

http://apcentral.collegeboard.com/home​​​​