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  • ...ade School (Grades 3, 4, 5, 6, 7, 8 + Algebra 1) and High School (Regional and State Finals). ...abulated. The top 10 schools at each grade level will receive certificates and be recognized in the ICTM Bulletin.
    8 KB (1,182 words) - 13:26, 3 April 2024
  • ...y of algebra involves familiarity with introductory topics to a high level and a multitude of new topics. ** [[Sum and difference of powers]]
    2 KB (198 words) - 15:06, 7 December 2024
  • .... the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdots </math> and the sequence is <math>c_0, c_1, c_2,\ldots</math>. ...derived using the [[Geometric sequence#Infinite|sum formula for geometric series]] <cmath>\frac{1}{1-x} = \sum_{k=0}^{\infty} x^k = 1 + x + x^2 + x^3 + \do
    4 KB (659 words) - 11:54, 7 March 2022
  • ...1, 3, 9, -27</math> and <math>-3, 1, 5, 9, \ldots</math> are not geometric sequences, as the ratio between consecutive terms varies. .../math>, <math>b</math>, and <math>c</math> are in geometric progression if and only if <math>b / a = c / b</math>.
    4 KB (649 words) - 20:09, 19 July 2024
  • ...0, 7, 14</math> and <math>4, 12, 36, 108, \ldots</math> are not arithmetic sequences, as the difference between consecutive terms varies. ...math>, <math>b</math>, and <math>c</math> are in arithmetic progression if and only if <math>b - a = c - b</math>.
    4 KB (736 words) - 01:00, 7 March 2024
  • .../math> can be written in the form <math>m/n</math> where <math>m_{}</math> and <math>n_{}</math> are relatively prime positive integers, find <math>m+n</m ...of <math>1</math> to <math>4</math> <tt>H</tt>'s separated by <tt>T</tt>'s and end with <math>5</math> <tt>H</tt>'s. Since the probability that the sequen
    7 KB (1,087 words) - 12:09, 17 November 2024
  • ...e <math>m</math>, <math>n</math>, and <math>p</math> are positive integers and <math>m</math> is not divisible by the square of any prime. Find <math>100m ...es be <math>x</math>. Then, the common ratio is <math>\frac{1}{8x}</math>, and the first term is <math>8x^2</math>.
    4 KB (710 words) - 15:06, 2 June 2024
  • ...math>g_n</math> are the <math>n</math>th terms of arithmetic and geometric sequences, respectively. ...</math>, where <math>d</math> is the common difference of <math>a_n</math> and <math>r</math> is the common ratio of <math>g_n</math>. Or, <math>\frac{a_n
    2 KB (477 words) - 18:39, 17 August 2020
  • Find <math>a + b</math> if <math>a</math> and <math>b</math> satisfy <math>3a + 7b = 1977</math> and <math>5a + b = 2007</math>.
    30 KB (4,794 words) - 22:00, 8 May 2024
  • ...and Wendy their oldest daughter. Tony is the youngest child. Twins Joshua and Alexis are <math>12</math> years old. Single-day passes cost <math>\textdollar{33}</math> for adults (Jerry and Hannah), <math>\textdollar{22}</math> for children
    71 KB (11,749 words) - 11:39, 20 November 2024
  • ...The sum of the first series is <math>r_1</math>, and the sum of the second series is <math>r_2</math>. What is <math>r_1 + r_2</math>? ...t that the sums of the given two sequences are <math>\frac a{1-r_1}</math> and <math>\frac a{1-r_2}</math>.
    3 KB (453 words) - 09:22, 6 October 2023
  • We can rigorously define <math>R[x]</math> to be the set of all sequences of elements of <math>R</math> with only finitely many terms nonzero: ...math>. We also do not care about the order in which the terms are written, and indeed often list them in descending order of power. So we would write:
    12 KB (2,010 words) - 23:10, 2 August 2020
  • ...d throughout, and time is devoted to advanced topics like telescoping sums and piecewise functions. (Note: This class is equivalent to the second half of '''Week 2''': Completing the square and the quadratic formula
    1 KB (134 words) - 21:11, 17 January 2023
  • ...re linearly dependent. Indeed, if we define <math>T = \lambda I - A</math> and let <math>\bold{T}^1, \bold{T}^2, \ldots, \bold{T}^n</math> denote the colu ...> such that <math>(\lambda I - A) \bold{v} = \bold{O}</math>. Distributing and re-arranging, <math>A\bold{v} = \lambda\bold{v}</math>, as desired. In the
    19 KB (3,412 words) - 13:57, 21 September 2022
  • ...{1}{m^2}</math> <math>m-1</math> times, <math>\ldots</math>. To make other sequences, we can split <math>m-1</math> <math>\frac{1}{m^i}</math>s into <math>m(m-1 ...., x_{2011}</math> are nonnegative integers. We plug in <math>m = 1</math> and see that <cmath>P(1) = 1 - 1 - 1... -1 = 1-2011 = -2010</cmath> Now, we can
    11 KB (1,811 words) - 19:45, 1 September 2024
  • ...a second sequence of terms by subtracting each term by the following term and taking it modulus 3, i.e. (1-0, 0-1, 1-0, 0-1, ... 0-1, 1-0, 0-2, 2-1) = 12 ...s left is simply the "negative" of the term generated by the changing side and the side to its right (i.e. 212 to 202 changes 12 to 21).
    2 KB (355 words) - 04:48, 18 April 2018
  • ...f the eleventh term of the first series to the eleventh term of the second series is: ...</math>, so the common difference of <math>S</math> is <math>3b-16a</math> and the common difference of <math>T</math> is <math>7b-62a</math>.
    3 KB (572 words) - 22:44, 3 April 2023
  • Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a f ...getting all heads. Then the next probability is all of them getting tails and then on the second try, they all get heads. The probability of that happeni
    2 KB (338 words) - 00:32, 10 November 2024
  • ...BC. AP Calculus AB is supposed to be roughly equal to the first semester and a half of a typical year-long introductory, single-variable college calculu **Trigonometric, logarithmic, and exponential limits
    5 KB (665 words) - 14:27, 3 March 2016
  • ...h day thereafter Anh read one more page than she read on the previous day, and it took her one more minute than on the previous day until she completely r ...19</math>, and <math>374</math>. The only such numbers are <math>1</math> and <math>11</math>. We know that Anh reads for at least <math>2</math> days.
    5 KB (818 words) - 00:25, 10 January 2024

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