Maths Properties/Tricks Flashcards
Triangle Inequality
The sum of any two sides of a triangle must be bigger than the third side
30-60-90 triangles
Also called the 1-2-squ(3) triangle
30-60-90 triangles
Special nature of these right triangles is their abililty to yield exact answers instead of decimal approximations when dealing with trigo functions
Circle property I
If two inscribed angles in the same circle intercept the same arc/chord, then the two inscribed angles are equal
Finding out about Prime numbers
If a number less than 100 is not divisible by 2, 3 or 5 or 7, then it is prime (NB: sun the digits to check for divisibility)
Generalized Pythagorean Theorem
- a2 + b2 = c2 then the angle opposite c is a right triangle
- a2 + b2 90•)
- a2 + b2
Sum of a sequence
Sum = (n*(n-1))/2
remainder/dividend rule
If dividend
2/3
0.6666
4/3
1.3333
3/4
0.75
4/5
0.8
5/6
0.8333
9/8
1.125
30-60-90 triangle’s sides
Hypothenus: x * square root of 3
Side I: 1
Side II: 2
Area of an equilateral triangle
(Square root of 3)/4 * (side^2)
2/3
0.6666
4/3
1.3333
3/4
0.75
4/5
0.8
5/6
0.8333
9/8
1.125
30-60-90 triangle’s sides
Hypothenus: x * square root of 3
Side I: 1
Side II: 2
Area of an equilateral triangle
(Square root of 3)/4 * (side^2)
Solve by elimination
Multiply both sides of the equation by chosen nbs, then add them to cancel one of the two variables
Solve by substitution
Solve one of the two equations for one of the variables, then we replace y in the other equation with this expression for y, finally we solve for x
Permutation vs. Combination
Permutation: order of the selection matters
Combination: only the result matters, not the order of selection
Fundamental Counting Principle
If task #1 can happen inm ways, task #2 can happen in n ways, and task #3 can happen in p ways, and if all three tasks are independent, then the nb of outcome is nmp
In how many ways can 5 books be ordered on a shelf
Permutation! 5! = 5x4x3x2x1 = 120
nCr
The nb of combination of r things that can be selected from a pool of n things
p is a factor of q
p and q are positive integers and there’s another positive integer k such that p*k=q.
You can multiply p by some positive integer and get q
Divisibility rule
A number is divisible by k iif the sum of the digits is also a nb divisible by k
Inclusive counting
(End) - (Start) + 1
Multiple of every positive integer
0
Factor pairs
The pairs of factors that, when multiplied together, yield the integer (eg. 1&60 2&30…)
Large nb divisible by 4
If the last two digits are divisible by 4 then the whole nb is divisible by 4
Order of Operations
PEMDAS Parentheses Exponents Multiplication&Division Addition&Substraction
Greatest Common Factor
Found by finding the common factor in the prime factorisations of the nbs
Rounding Rule
We look only at the single digit in the next smallest place (if 4 or less -> round down, if 4 or more -> round up)
LCM
Useful in adding two fractions bc the LCM is identical to the LCD
Percent change
((New) - (Original)) / (Original) * 100
Percent change
((New) - (Original)) / (Original) * 100
1/6
0.16666
Ratio vs. Proportion
Ratio: single fraction
Proportion: an equation of the form fraction equal fraction
Mixed numeral
One way of writing a fraction greater than 1 (eg. 6 (3/5) )
Area of a trapeze
(b1 + b2)/2 * h
Slope of perpendicular lines in the x-y plane
They are opposite (+-) reciprocals (x/ 1/x)
Rhombus
A quadrilateral with four equal sides. The angle of tilt can be anything.
Three different sets of three lengths that satisfy the Pythagorean Theorem
- (3, 4, 5)
- (5, 12, 13)
- (8, 15, 17)
Length of a circular arc
Arc length/2pir =. Arc angle/360
Moribund
At the point of death OR in terminal decline; lacking vitality or vigour
Keen
Sharp or penetrating
Uncanny
Strange and mysterious
Volume of a cube
s^3
Nb of positive factors a particular integer has
- Find the prime factorisation of N
- Collect the set of exponents of the prime factors
- Add one to every member of this set
- Find the product of every nb in the set
nCr (shortcut)
n(n-1) / r
Normal distribution; mean; standard deviation
- between mean and 1d: 34.1%
- between 1d and 2d: 13.6%
Volume of a cylinder
pi * r^2 * h
Reflecting a point over y=-x
Reversing the coordinates and giving each thr opposite sign
Find two numberd’ LCM
- Find the prime factorisation of the two numbers
- Multiply the multiples
(E.g. 9 and 15 => 335=45)
Prime factorisation
Expresses the number as a product of prime numbers
Cylinder lateral area
2 * pi * r * h
Cylinder: total area
2pirh + 2pi*r^2
Amount of solute =
(Concentration)*(Volume of Solution)
Doubling and halving trick
88*25
44*50
22*100 = 2200
