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Number of Questions Time allotted Exam Weight Section I, Part A: Multiple Choice Questions: 55 questions: 55 minutes: 40% Section I, Part B: Short-Answer Questions: 3 questions (2 required questions + 1 chosen from 2 others) 40 minutes: 20% Section II Part A: Document-Based Question: 1 question: recommended 60 minutes (includes 15-minute ...
Property 3 is redundant; it follows by applying 2 to 1. In practical terms, it is often advantageous to be able to recognize the canonical forms. There is also a practical, algorithmic question to consider: how to pass from a given object s in S to its canonical form s*? Canonical forms are generally used to make operating with equivalence ...
In our example, we can say with certainty that 2 and 3 are prime, and thus we have proved our result. The primality certificate is the list of ( p , a p ) {\displaystyle (p,a_{p})} pairs, which can be quickly checked in the corollary.
For example, if a = 2 and p = 7, then 2 7 = 128, and 128 − 2 = 126 = 7 × 18 is an integer multiple of 7. If a is not divisible by p, that is, if a is coprime to p, then Fermat's little theorem is equivalent to the statement that a p − 1 − 1 is an integer multiple of p, or in symbols: [1] [2] ().
Formerly, the test was scored by awarding 1 point for correct answers, while taking off a 1/4 point for incorrect answers. No points were taken away for blank answers. However, the College Board discontinued the policy for all AP Exams in 2011; now, they only award 1 point for each correct answer, with no 1/4 point deductions.
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The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score. [26] The free response section is hand-graded by hundreds of AP teachers and professors each June. [27]
The Lang–Trotter conjecture (1976) of Serge Lang and Hale Trotter states the asymptotic number of primes p with a given value of a p, [16] the trace of Frobenius that appears in the formula. For the typical case (no complex multiplication , trace ≠ 0) their formula states that the number of p up to X is asymptotically