AP Calculus AB8/12/15

Mrs. Langley

Who Should Take AP Calculus AB?

• Students must successfully complete four years of college preparatory mathematics before enrolling in AP Calculus AB. These are courses typically (but not always) entitled Algebra 1, Algebra 2, Geometry, and Precalculus.

3

The College Board strongly encourages educators to make

equitable access a guiding principle for their AP programs

by giving all willing and academically prepared students the

opportunity to participate in AP.

Equity & Access Policy Statement

AP Course Audit

• Before students can officially carry the AP designation on their transcripts, the teacher must successfully complete the AP course audit.

• The AP course audit was created at the request of colleges to provide a way of recognizing that a course designated AP has been taught in alignment with the current AP Course Description.

Philosophy of AP Calculus

• Students should develop an understanding of the concepts of calculus and have experience with its methods and applications.– The Rule of Four (analytical, verbal, numerical,

graphical)– The BC course is an extension of the AB course

and not just an enrichment of it.• The emphasis of the course should be on broad

concepts and widely applicable methods.• Technology should be used in class, on homework

and projects, and is required for the AP exams.• Calculus should be an integrated whole.

Goals of AP Calculus

• Students must understand calculus analytically, verbally, graphically, and numerically.

• Students should communicate verbally – orally and in writing – about their work.

• Students should use technology to obtain and verify results.

Goals of AP Calculus (cont.)

• The derivative should be understood as a rate of change and as a local linear approximation.

• The definite integral should be understood both as a limit of a Riemann sum and as the net accumulation of a rate of change.

• The Fundamental Theorem of Calculus should be understood as relating the derivative and the definite integral.

Graphing Calculators

• The four capabilities required for AP Calculus are:–Graph a function in an arbitrary

viewing window.–Find the zeros of a function

numerically (i.e., solve equations).–Find the numerical value of the

derivative at a point.–Find the numerical value of a

definite integral.

CAS vs. non-CAS

• Calculators with Computer Algebra Systems (CAS) are allowed on the AP exams.– A large majority of students use graphing

calculators that do not have CAS capabilities.– Students who use CAS calculators score

slightly better on both the calculator and non-calculator sections of the exams.

– Exam questions are written to minimize the difference between students who have CAS calculators and those who do not.

Decimal Representation

• Decimals answers on the AP Calculus Exam must be correct to three places after the decimal point.

• Example: the numerical answer is π– Acceptable responses: π, 3.141, 3.142,

3.141*, 3.142*– Unacceptable responses: 3.14, 3.1, 3,

3.14_ where the third digit is neither a 1 or a 2.

Decimals and Arithmetic

• Students are not required to display answers in decimal forms.

• Students should avoid rounding too soon. If there are intermediate calculations that need to be used later in a problem, that value should be stored with all displayed decimal places and the stored, not the rounded, value should be used in later calculations.

Final Word about Calculators

• Scientific calculators, PDAs, and calculators with typewriter (QWERTY) keyboards are not allowed on the exam.

• Calculator memories need not be cleared before the exam.

• While calculator programs are encouraged during the teaching and learning of calculus, their use should be limited during exams.

Mathematics Before AP Calculus

• The Elementary Functions• The Properties, Algebra, and Graphs

of Functions

The Elementary Functions

• Constant, linear, and other polynomial functions.

• Rational functions• Exponential and logarithmic functions• The six trigonometric functions and

their inverses.• Piecewise-defined functions made up

of the functions above, including the absolute value function.

The Properties, Algebra, and Graphs of Functions

• Domain and range• Periodicity• Standard shapes of the graphs of

elementary functions• Transformations of functions and

symmetry of functions

To Review or Not to Review?

• There are basically two schools of thought when it comes to starting an AP course:– Spend the first few days/weeks

reviewing the necessary precalculus, or– Start with calculus and review as

needed throughout the course.

The Exam Format – Section I

• Section I, Part A: multiple-choice, no calculator allowed, 28 questions in 55 minutes. 5 choices per question.

• Section I, Part B: multiple-choice, calculator required, 17 questions in 50 minutes. Not all of the questions require a calculator. 5 choices per question.

The Exam Format – Section II

• Section II, Part A: Free Response. 2 questions, 30 minutes, calculators are allowed.

• Section II, Part B: Free Response. 4 questions, 60 minutes, calculators are not allowed. Students may return to Section II Part A during this time, but they may not use their calculators.

Forms of the Exams

• US Main Exam – the one given to the majority of test takers in early May.

• International Main Exam – also known as the Overseas Exam, this test is given on the same date to students in Europe, Asia, Africa, and parts of Latin America.

• US Alternate Exam – also known as the Alternate Exam, this test is given to students who cannot take the Operational Exam on the given date. Permission from ETS is needed.

Exam Scoring

• Section I is machine-scored.• Section II is scored by the faculty

consultants (Readers) at the AP Calculus reading in early June.

Exam Scores

• Section I and Section II each contribute 50% of the total score.

• Section I: the score is the number of correct answers to the 45 multiple choice questions.

• Section II: the six free-response questions have a maximum score of 9 points each for a total of 54 points.

• The maximum total score is 1.2 times the multiple choice score plus the free-response score for a total of 108 points.

Exam Grades

• ETS statisticians look at statistical and other data to equate the current exam to previous exams.

• The “cut points” are determined immediately after the reading. These are not released every year.

Definition of Exam Grades

• 5 – Extremely well qualified• 4 – Well qualified• 3 – Qualified• 2 – Possibly qualified• 1 – No recommendation

After the School Year Ends

• Students usually get their scores in July.

• Teachers can access their students’ scores and their AP Instruction Reports online in July.

Questions?