MATHCOUNTS: Memorization List



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 ([pic]) to [pic] d =

• Midpoint of AB, A=[pic], B=[pic], M=

• [pic][pic][pic]= [pic] [pic] [pic] [pic]

• [pic] [pic] 18[pic] 19[pic] 25[pic]

• [pic] [pic] [pic] [pic] 5[pic]

• [pic] [pic] [pic] [pic] [pic]

• [pic] [pic] [pic]

• 1 mile = _______________________ feet = _________________ Yards

• [pic]1!= 2! = 3! = 4! = 5! =

• Prime factorization of 1001 = __________ x _____________ x ___________

• Percents: [pic] [pic] [pic] [pic]

• [pic] [pic] [pic] [pic]

• Number of subsets of an n-set =

• [pic]

• 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 [pic] and [pic]=

• Geometric mean of a and b =

• Sides of a 45-45-90 triangle =

• Sides of a 30-60-90 triangle =

• [pic]

• [pic]

• [pic]

• Pascal’s Triangle to 1 5 _____ _____ _____ _____

• [pic] _____________ ____________ _____________

• Powers of 2, to 2[pic]

• 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

• [pic]

• [pic]

• [pic]

• Fractional percent (eg. 58 [pic])----- Fraction [pic]

• Determine whether the decimal for a given fraction is terminating or repeating

• Repeating decimal----- fraction [pic]

• [pic]…------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).

• [pic]

• How to estimate: [pic]

• 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)[pic]

• 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: [pic]

| | | | | |

| | | | | |

| | | | | |

• How many paths, A to B:

• Units digit of [pic]

• Simplify: [pic]

• 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

• [pic]

• [pic]

• 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. [pic]

• Half of [pic]

• 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 [pic]

• How many numbers divisible by a, b, or c

• Sum of first n natural numbers

• 0!, [pic]

• 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

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