Properties Flashcards
Sum of interior angles = ?
180(n-2) - Each interior angle is 180(n-2)/n
Area of an equilateral triangle
s^2*sqrt(3)/4
Height of an equilateral triangle
s*sqrt(3)/2
Sides of 30-60-90 triangles
1 : sqrt(3) : 2
Sides of 45-45-90 triangles
1 : 1 : sqrt(2)
Obtuse triangle rule
c^2 > a^2 + b^2
Common right triangles
3:4:5 / 5:12:13 / 8:15:17 / 7:24:25 / 9:40:41
Properties of a rectangle
- All angles are 90 degrees
- Opposite sides are equal
- Opposite sides are parallel
- Diagonals bisect each other
Properties of a square
- All angles are 90 degrees
- All sides are equal
- Opposite sides are parallel
- Diagonals bisect PERPENDICULARLY
Properties of a parallelogram
- Opposite angles are equal
- Opposite sides are equal
- Opposite sides are parallel
- Diagonals bisect each other
- Sum of adjacent angles is 180 degrees
Properties of a rhombus
- Opposite angles are equal
- All sides are equal (only difference from parallelograms)
- Opposite sides are parallel
- Diagonals bisect PERPENDICULARLY
- Sum of adjacent angles is 180 degrees
- Area = b*h OR (diagonal 1 * diagonal 2)/2
Properties of a trapezium
- Only one pair of opposite sides are parallel
- Area = 0.5 (AB + CD)*h (AB and CD are parallel)
Properties of a regular hexagon
- Longest diagonal = 2*side
Properties of a cuboid
- Surface = 2(ab + bc + ca) ; 6a^2 for a cube
- Diagonal = sqrt(a^2 + b^2 + c^2) ; sqrt(3)*a for a cube
Volume of a cone
- Volume = 1/3 * pi * r^2 * h
Properties of a sphere
- Volume = 4/3 * pi * r^3
- Surface = 4 * pi * r^2
(a+b)^2 + (a-b)^2
2a^2 + 2b^2
(a+b)^2 - (a-b)^2
4ab
Average speed (ONLY IF SAME DISTANCE)
(2* speed 1 * speed 2)/ (speed 1 + speed 2)
Last n digit(s) of a product = ?
Product of last n digits of each number (e.g. Last 2 digits of 84594929292 = 454992)
Which one-digit numbers have their powers end in the same digit
0, 1 , 5, 6
Which one-digit numbers have their even powers end in the same digit, and odd power in another digit
- 4 (4^2 = 6; 4^3= 4; 4^4 = 6)
- 9 (9^2 = 1; 9^3 =9; 9^4 = 1)
Which one digit-numbers have their power end in a 4 by 4 pattern
2, 3, 7, 8
Sum of all numbers which can be formed using n digits (WITHOUT repetition)
= (n-1)!(sum of digits)(1111… n times)
How do you find general formula given two divisions/ remainders?
- Find LCM of divisors 2. Find first common value between two equations
Example: x = 5q +3 and x = 7q + 4
1. LCM(5,7) = 35
2. First common value of both equations is 18
Result: x = 35q + 18
Sum of n consecutive integers
n*(first term + last term)/2 (applies for all evenly spaced sequences)
Arithmetic mean general formula
an = a1 + (n-1)*d ; d is the difference
Reminder: Sum of first n integers is n(a1an)/2 as it is an evenly spaced sequence
Geometric mean general formula
an = a1r^(n-1)
Sum of first n terms = a1(1-r^n)/(1-r)
Sum of all terms = a1/(1-r)
Which fractions are not terminating
Once fully reduced, if denominator has any PRIME factor other than 2 or 5, then it is not a terminating number
How to check if a number is divisible by 3?
The sum of digits should be divisible by 3
How to check if a number is divisible by 4?
The LAST TWO digits should be divisible by 4
How to check if a number is divisible by 9?
The sum of digits should be divisible by 9
