MATHCOUNTS: Memorization List

  • Four Primitive Pythagorean Triples ______, ______, ______, ______
  • Area: Parallelogram A=Trapezoid A =

Triangle A =Circle A =

Cube, Edge- S.A.= Sphere, S.A.=

Rectangular Prism-S.A.= Cylinder- Lateral Area=

Cylinder-S.A.=

  • Circumference of a Circle:
  • Volume:

Cube, Edge e, V=Pyramid, V=

Any Right Prism, V=Sphere V=

Cylinder, V=

  • Diagonal of a Square, d=
  • Space Diagonal of a cube, d=
  • Space Diagonal of a Rectangular Prism, d=
  • Number of Diagonals in a n-gon=
  • Total Measures of the angles of an n-gon=
  • Measure of one angle of a regular n-gon=
  • Number of squares in an n by n grid =
  • Number of rectangles in an n by n grid =
  • Distance () to d =
  • Midpoint of AB, A=, B=, M=
  • =
  • 181925
  • 5
  • 1 mile = ______feet = ______Yards
  • 1!= 2! = 3! = 4! = 5! =
  • Prime factorization of 1001 = ______x ______x ______
  • Percents:
  • Number of subsets of an n-set =
  • Sum of the first “n” number of odd integers is ______
  • Area of an Equilateral Triangle =
  • Number of cubes in an n x n x n cube =
  • Slope through and =
  • Geometric mean of a and b =
  • Sides of a 45-45-90 triangle =
  • Sides of a 30-60-90 triangle =
  • Pascal’s Triangle to 15______
  • ______
  • Powers of 2, to 2
  • Equations of a line:Slope-intercept form

Point-Slope form

  • Quadratic Formula, x =
  • Centroid of a Triangle on a coordinate system =
  • Distance in a 3-D coordinate system =
  • Natural numbers, whole numbers, integers, …
  • Number of rectangular solids in an n x n x n cube =

MATHCOUNTS Procedures:

  • Hexidecimal notation (base sixteen)
  • Pascal’s Triangle
  • Triangular numbers
  • Fibonacci’s sequence
  • Square a number ending in 5.
  • Square one more or one less than a known number
  • Add or subtract 99, 98, 95, 999, 998, 995, …
  • Multiply by 99, 999, 98, 998, …
  • Multiply a 2-digit number by 101
  • Multiply a 3 digit number by 1001
  • 99% of_____, 98% of _____, 99 ½ % of _____, 98 ½ % of _____
  • Largest product, given sum of 2 numbers
  • Largest product, given 4 digits:

X

  • Like how many multiples of 6 from 100 to 511 [69]
  • Add a series of numbers
  • Sum of first n odd numbers
  • Number of codes from letters, some repeated
  • Fractional percent (eg. 58 )----- Fraction
  • Determine whether the decimal for a given fraction is terminating or repeating
  • Repeating decimal----- fraction
  • …------repeating decimal
  • Three methods to compare fractions
  • Probability (at least one)
  • Probability – two or more things are the same (or different)
  • How to find the mean of an arithmetic sequence
  • Given the sum of a sequence, find the numbers (Eg. Seven multiples of 3 whose sum is 189).
  • How to estimate:
  • The Triangle Inequalitiy
  • Given three sides of a triangle----- right, obtuse, acute or no triangle?
  • Number of 0’s at end of a factorial.
  • Remainder of 1 when divided by many numbers
  • Remainder 1 less than the divisor
  • Divisibility Rules 2, 3, 4, 5, 6, 8, 9, 10, 11 or any composite number (eg. 33, 36)
  • Prime factorization 2 or more umbers----- GCF and LCM
  • Two numbers: GCF x LCM
  • Number of factors of (prime)
  • Which numbers have an odd number of divisors
  • Last digit of a perfect square can only be…
  • Given product of two consecutive whole numbers, find the numbers.
  • Find how many cows or chickens, given how many animals and how many feet.
  • Method for absolute value equations
  • Method for absolute value inequalities
  • Method for higher degree inequalities
  • Simplify:
  • How many paths, A to B:
  • Units digit of
  • Simplify:
  • Probability (A to B)—mutually exclusive

---- Not mutually exclusive

  • How many factors of any number
  • How many factors of a number are perfect squares
  • How many factors of a number are odd
  • How many factors of a number are even
  • Solve a radical equation
  • Add or subtract 2 fractions on sight
  • Sum of powers of 2
  • Pascal----- coins
  • Given the products of 2 or 3 consecutive numbers….
  • Calendar----- next year
  • Multiply numbers above and below a fixed number
  • Factor a number 1, 4, or 9 below a perfect square
  • Base 2 ----- Base 4, 8, 16
  • Base 3 ----- Base 9
  • Places on a clock, 2 hands in same position
  • Multiply roots with different indices
  • Compare powers: Eg.
  • Half of
  • Nth odd number
  • Absolute value equation with number outside absolute value sign
  • How many numbers divisible by a or b
  • Check by 9’s
  • Partition of triangle into n equal areas
  • In any base, identify odd or even
  • Smallest sum, given product of two numbers
  • Sum of first n even numbers
  • Number of committees with m people, from n
  • Compare roots, like
  • How many numbers divisible by a, b, or c
  • Sum of first n natural numbers
  • 0!,
  • Probability A or B or C, not mutually exclusive
  • Odds
  • Number of m-sets in an n-set
  • Vertices, Faces, Edges
  • Orders around a round table
  • Rule of 72
  • Angle inscribed in a semi-circle
  • Number of lines of symmetry in a regular n-gon
  • Fermat’s Last Theorem
  • Heron’s Formula