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  2. AP World History: Modern - Wikipedia

    en.wikipedia.org/wiki/AP_World_History:_Modern

    However, students may begin writing during this time; most students take notes on the documents in order to plan out the DBQ. Students are advised to spend 45 minutes writing the DBQ and then 40 writing the LEQ, but there are no rules on when each essay must be worked on. There are three prompts for the LEQ, but only one needs to be chosen.

  3. AP European History - Wikipedia

    en.wikipedia.org/wiki/AP_European_History

    Advanced Placement (AP) European History (also known as AP Euro, APEH, or EHAP), is a course and examination offered by the College Board through the Advanced Placement Program. This course is for high school students who are interested in a first year university level course in European history .

  4. Document-based question - Wikipedia

    en.wikipedia.org/wiki/Document-based_question

    The document based question was first used for the 1973 AP United States History Exam published by the College Board, created as a joint effort between Development Committee members Reverend Giles Hayes and Stephen Klein. Both were unhappy with student performance on free-response essays, and often found that students were "groping for half ...

  5. Advanced Placement exams - Wikipedia

    en.wikipedia.org/wiki/Advanced_Placement_exams

    Advanced Placement (AP) examinations are exams offered in United States by the College Board and are taken each May by students. The tests are the culmination of year-long Advanced Placement (AP) courses, which are typically offered at the high school level. AP exams (with few exceptions [1]) have a multiple-choice section and a free-response ...

  6. AP United States History - Wikipedia

    en.wikipedia.org/wiki/AP_United_States_History

    The AP U.S. History course is designed to provide the same level of content and instruction that students would face in a freshman-level college survey class. It generally uses a college-level textbook as the foundation for the course and covers nine periods of U.S. history, spanning from the pre-Columbian era to the present day. The percentage ...

  7. Logarithmically concave function - Wikipedia

    en.wikipedia.org/wiki/Logarithmically_concave...

    Every concave function that is nonnegative on its domain is log-concave. However, the reverse does not necessarily hold. An example is the Gaussian function f(x) = exp(−x 2 /2) which is log-concave since log f(x) = −x 2 /2 is a concave function of x. But f is not concave since the second derivative is positive for | x | > 1:

  8. Squared triangular number - Wikipedia

    en.wikipedia.org/wiki/Squared_triangular_number

    A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.

  9. Fatou's lemma - Wikipedia

    en.wikipedia.org/wiki/Fatou's_lemma

    A suitable assumption concerning the negative parts of the sequence f 1, f 2, . . . of functions is necessary for Fatou's lemma, as the following example shows. Let S denote the half line [0,∞) with the Borel σ-algebra and the Lebesgue measure.