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The products of small numbers may be calculated by using the squares of integers; for example, to calculate 13 × 17, one can remark 15 is the mean of the two factors, and think of it as (15 − 2) × (15 + 2), i.e. 15 2 − 2 2.
This is an accepted version of this page This is the latest accepted revision, reviewed on 13 January 2025. Educational assessment For other uses, see Exam (disambiguation) and Examination (disambiguation). Cambodian students taking an exam in order to apply for the Don Bosco Technical School of Sihanoukville in 2008 American students in a computer fundamentals class taking an online test in ...
It contains 8 multiple-choice questions, and 4 open questions. The second round takes place at twelve different universities. It contains 5 questions where the answer is a certain number and 2 open questions. There are a few optional training days and then the third round takes place at the Eindhoven University of Technology. It contains 5 open ...
Mathematics Written Each student is given the same questions, and their answers are scored in the same way. The teacher gives different questions to different students: an easy test for poor students, another test for most students, and a difficult test for the best students. Music Audition: All musicians play the same piece of music.
Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [ 1 ] Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers ), or defined as generalizations of the ...
If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and whose third vertex is where the line that is parallel to the parabola's axis and that passes through the midpoint of the base intersects the parabola, and so on.