MATHCOUNTS: Memorization List
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Four Primitive Pythagorean Triples ___________________, ____________________,
___________________, ____________________
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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:
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Volume:
Cube, Edge e, V=
Pyramid, V=
Any Right Prism, V=
Sphere V=
Cylinder, V=

Diagonal of a Square, d=
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Space Diagonal of a cube, d=
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Space Diagonal of a Rectangular Prism, d=

Number of Diagonals in a n-gon=
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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 ( x1 , y1 ) to x2 , y2  d =

Midpoint of AB, A= x1 , y1  , B= x2 , y2  , M=
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112 =
16 2 
27 2 
63 
12 3 
12 2 
17 2 
23 
73 
25 
13 2 
18 2 
33 
83 
210 
14 2 
19 2 
43 
93 
15 2 
25 2 
53
113 
1 mile = _______________________ feet = _________________ Yards
1!=
2! =
3! =
4! =
5! =
Prime factorization of 1001 = __________ x _____________ x ___________
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Percents:
1

8
3

8
5

8

1

6
5

6
1

12
1

16
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Number of subsets of an n-set =
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0.9 

Sum of the first “n” number of odd integers is _______________

Area of an Equilateral Triangle =
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Number of cubes in an n x n x n cube =
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Slope through x1 , y1  and x2 , y2  =
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Geometric mean of a and b =
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Sides of a 45-45-90 triangle =
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Sides of a 30-60-90 triangle =
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7

8
2
3
10 

Pascal’s Triangle to

112 ,113 ,114

Powers of 2, to 2 10

Equations of a line:
1
5
_____________
_____ _____ _____ _____
____________
Slope-intercept form
Point-Slope form
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Quadratic Formula, x =
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Centroid of a Triangle on a coordinate system =
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Distance in a 3-D coordinate system =
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Natural numbers, whole numbers, integers, …
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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
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Square a number ending in 5.
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Square one more or one less than a known number
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Add or subtract 99, 98, 95, 999, 998, 995, …
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Multiply by 99, 999, 98, 998, …
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Multiply a 2-digit number by 101
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Multiply a 3 digit number by 1001
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99% of_____, 98% of _____, 99 ½ % of _____, 98 ½ % of _____
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Largest product, given sum of 2 numbers
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Largest product, given 4 digits:
X

Like how many multiples of 6 from 100 to 511 [69]

Add a series of numbers
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Sum of first n odd numbers
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Number of codes from letters, some repeated

x k 

x
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34  5 2 34  5 2
vs 1
31  5
3  52
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Fractional percent (eg. 58
p
q

1
7
% )----- Fraction  
3
12 

Determine whether the decimal for a given fraction is terminating or repeating
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Repeating decimal----- fraction 0.07,0.0063

x x x x x
x
, ,
, ,
,
, …------repeating decimal
9 90 900 99 990 999
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Three methods to compare fractions
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Probability (at least one)
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Probability – two or more things are the same (or different)
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How to find the mean of an arithmetic sequence
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Given the sum of a sequence, find the numbers (Eg. Seven multiples of 3 whose sum is 189).
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cm 2  m 2 , mm3  m 3 , ft 3  in 3
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How to estimate:
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The Triangle Inequalitiy
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Given three sides of a triangle----- right, obtuse, acute or no triangle?
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Number of 0’s at end of a factorial.
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Remainder of 1 when divided by many numbers
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Remainder 1 less than the divisor
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Divisibility Rules 2, 3, 4, 5, 6, 8, 9, 10, 11 or any composite number (eg. 33, 36)
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Prime factorization 2 or more umbers----- GCF and LCM

Two numbers: GCF x LCM
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Number of factors of (prime) power
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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


decimal , 3 decimal

Method for absolute value inequalities
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Method for higher degree inequalities
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Simplify:

How many paths, A to B:
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Units digit of
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Simplify:

Probability (A to B)—mutually exclusive
a a a
,
,
b b b
 5
a b
or
a b
---- 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
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qqqq q 1

2 n  2 n ,3n  3n  3n
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Pascal----- coins

Given the products of 2 or 3 consecutive numbers….
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Calendar----- next year

Multiply numbers above and below a fixed number
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Factor a number 1, 4, or 9 below a perfect square

Base 2 ----- Base 4, 8, 16
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Base 3 ----- Base 9
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Places on a clock, 2 hands in same position

Multiply roots with different indices
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Compare powers: Eg. 2 75 ,350
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1
Half of 2 n , of 3 n
3
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Nth odd number
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Absolute value equation with number outside absolute value sign

How many numbers divisible by a or b
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Check by 9’s
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Partition of triangle into n equal areas
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In any base, identify odd or even

Smallest sum, given product of two numbers
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Sum of first n even numbers
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Number of committees with m people, from n
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Compare roots, like

How many numbers divisible by a, b, or c
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Sum of first n natural numbers
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0!, 0 0

Probability A or B or C, not mutually exclusive
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Odds
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Number of m-sets in an n-set
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Vertices, Faces, Edges
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Orders around a round table
5
5, 3 2

Rule of 72
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Angle inscribed in a semi-circle
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Number of lines of symmetry in a regular n-gon

Fermat’s Last Theorem
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Heron’s Formula