things you must know (1)
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8/3/2019 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 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 −−−=
8/3/2019 Things You Must Know (1)
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___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