things you must know (1)

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Things you must know for competitive math!!!  ____ All fraction/decimal/percent equivalencies for denominators up to 12.  ____ All square numbers from 1 2 to 25 2 (You must also be able to recognize them and know the )  ____ All cubic numbers from 1 3 to 10 3 ( Same as above with the cube roots 3 )  ____ Powers of 2 from 2 0 to 2 12 (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096)  ____ Powers of 3 from 3 0 to 3 6 (1, 3, 9, 27, 81, 243, 729)  ____ Powers of 5 from 5 0 to 5 5 (1, 5, 25, 125, 625, 3125)  ____ You must al so be able to recognize those powers the other way Ex. 243 = ????? (3 5 )  ____ Triangular numbers : 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120 These numbers are the sums of the consecutive counting numbers starting at 1. Ex. 1=1; 3=1+2; 6=1+2+3; 10=1+2+3+4; 15=1+2+3+4+5; 21=1+2+3+4+5+6 and so on  ____ Sum of the first n odd numbers n 2   ____ Sum of the first n square numbers  ____ Sum of the first n cubic numbers  ____ Sum of the first n triangular numbers  ____ Factorials from 1! to 8! (1!=1 2!=1x2=2 3!=1x2x3=6 4!=24 5!=120 6!=720 7!=5040)  ____ Pythagorean Triples: 3-4-5 ; 5-12-13; 8-15-17; 7-24-25; 9-40-41 and recognize mult iples like 6-8-10{2x(3-4-5)} 15-36-39{3x(5-12-13)}  ____ You must be able to create Pascal’s Triangle and use for probability especially! Formulas for area, Surface Area, and Volume Area: ____ square = s 2 or d 2 /2 (d = diagonal)  ____ rectangle and parallelogram = bh  ____ Triangle = bh/2  ____ Trapezoid = (b 1 +b 2 )h/2  ____ Rhombus = (d 1 d 2 )/2 (d = diagonal)  ____ Circle = π  r 2  ____ Equilateral Triangle : 4 s 3 2  ____ Hexagon = 2 3 3 2  s  Surface Area : ____ Con e = π  r 2 + π  rs or π  r(r + s) (s = slant height)  ____ Cylinder = 2 π  r 2 + 2 π  rh ( 2 bases + circumference x height)  ____ Sphere = 4 π  r 2 Vol ume : __ pr is m and cyli nde r : BH (B= area of base, H = hei ght of pr is m)  ____ Cones and pyramids : 1/3 BH  ____ Sphere 4/3 π  r 3 Special area formulas  ___Heron’s formula ) ) ( ) ( ( c  s b  s a  s  s  A =

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Page 1: Things You Must Know (1)

8/3/2019 Things You Must Know (1)

http://slidepdf.com/reader/full/things-you-must-know-1 1/2

Things you must know for competitive math!!!

 ____ All fraction/decimal/percent equivalencies for denominators up to 12.

 ____ All square numbers from 12 to 252(You must also be able to recognize them and know the )

 ____ All cubic numbers from 13 to 103 ( Same as above with the cube roots 3 )

 ____ Powers of 2 from 2

0

to 2

12

(1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096) ____ Powers of 3 from 30 to 36 (1, 3, 9, 27, 81, 243, 729) ____ Powers of 5 from 50 to 55 (1, 5, 25, 125, 625, 3125)

 ____ You must also be able to recognize those powers the other way Ex. 243 = ????? (35)

 ____ Triangular numbers : 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120

These numbers are the sums of the consecutive counting numbers starting at 1.

Ex. 1=1; 3=1+2; 6=1+2+3; 10=1+2+3+4; 15=1+2+3+4+5; 21=1+2+3+4+5+6 and so on

 ____ Sum of the first n odd numbers n2 

 ____ Sum of the first n square numbers

 ____ Sum of the first n cubic numbers ____ Sum of the first n triangular numbers

  ____ Factorials from 1! to 8! (1!=1 2!=1x2=2 3!=1x2x3=6 4!=24 5!=120 6!=720 7!=5040)

 ____ Pythagorean Triples: 3-4-5 ; 5-12-13; 8-15-17; 7-24-25; 9-40-41 and recognize multiples like

6-8-10{2x(3-4-5)} 15-36-39{3x(5-12-13)}

 ____ You must be able to create Pascal’s Triangle and use for probability especially!

Formulas for area, Surface Area, and Volume

Area: ____ square = s2 or d2/2 (d = diagonal)

 ____ rectangle and parallelogram = bh

 ____ Triangle = bh/2 ____ Trapezoid = (b1+b2)h/2

 ____ Rhombus = (d1d2)/2 (d = diagonal)

 ____ Circle = π  r 2

 ____ Equilateral Triangle :4

s3 2

 ____ Hexagon =2

332

 s 

Surface Area : ____ Cone =π  

r 2

+π  

rs or π  

r(r + s) (s = slant height) ____ Cylinder = 2π  r 2 + 2π  rh ( 2 bases + circumference x height)

 ____ Sphere = 4π  r 2

Volume : ____ prism and cylinder : BH (B= area of base, H = height of prism)

 ____ Cones and pyramids : 1/3 BH

 ____ Sphere 4/3 π  r 3

Special area formulas

 ___Heron’s formula ))()(( c sb sa s s A −−−=

Page 2: Things You Must Know (1)

8/3/2019 Things You Must Know (1)

http://slidepdf.com/reader/full/things-you-must-know-1 2/2

 ___Pick’s Law / formula 12

−+= I  B

 A

 ___Finding area from the coordinates (shoestring method)

 ___How to find the number of factors for a number (using prime factorization)

 ___How to find the sum of the factors of a number (using prime factorization)

Radicals

 ___Simplifying ___Rationalizing denominators

 ___Multiplying and Dividing (squaring and cubing)

Special right triangles

 ___30-60-90 ___45-45-90

How to find the number of arrangements

 ____ Permutations (order does matter) ____ Combinations (order does not matter)

Finding figurate numbers

 ___Triangular n(n+1)/2

 ___Square n2

 ___Pentagonal(3n2-n)/2 or (the house method)

 ___Hexagonal 2n2-n

 ___ n-gonal -- all from the triangular #s

 ___ Know all primes up to 144(only need to check #s that end in 1,3,7,9 and for divisibility by 3,7,11)

Polygons ____ How to find the number of diagonals in a polygon (n(n-3))/2

 ____ How to find the number of degrees in each angle of a regular polygon ____ How to find the exterior angle of a regular polygon

 ____ How to find the sum of degrees in angles of a polygon

 ____ Finding all angles when two parallel lines are crossed by a transversal

 ____ How to change repeating decimals into fractions, and all other Fraction-Decimal-Percent conversions

How to find slope ____ From an equation

 ____ From a pair of coordinates

 ____ Finding parallel and perpendicular slopes

 ____ Mr Frost's Tips and Tricks