Properties Flashcards

1
Q

Sum of interior angles = ?

A

180(n-2) - Each interior angle is 180(n-2)/n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Area of an equilateral triangle

A

s^2*sqrt(3)/4

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Height of an equilateral triangle

A

s*sqrt(3)/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Sides of 30-60-90 triangles

A

1 : sqrt(3) : 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Sides of 45-45-90 triangles

A

1 : 1 : sqrt(2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Obtuse triangle rule

A

c^2 > a^2 + b^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Common right triangles

A

3:4:5 / 5:12:13 / 8:15:17 / 7:24:25 / 9:40:41

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Properties of a rectangle

A
  • All angles are 90 degrees
  • Opposite sides are equal
  • Opposite sides are parallel
  • Diagonals bisect each other
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Properties of a square

A
  • All angles are 90 degrees
  • All sides are equal
  • Opposite sides are parallel
  • Diagonals bisect PERPENDICULARLY
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Properties of a parallelogram

A
  • Opposite angles are equal
  • Opposite sides are equal
  • Opposite sides are parallel
  • Diagonals bisect each other
  • Sum of adjacent angles is 180 degrees
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Properties of a rhombus

A
  • 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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Properties of a trapezium

A
  • Only one pair of opposite sides are parallel

- Area = 0.5 (AB + CD)*h (AB and CD are parallel)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Properties of a regular hexagon

A
  • Longest diagonal = 2*side
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Properties of a cuboid

A
  • Surface = 2(ab + bc + ca) ; 6a^2 for a cube

- Diagonal = sqrt(a^2 + b^2 + c^2) ; sqrt(3)*a for a cube

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Volume of a cone

A
  • Volume = 1/3 * pi * r^2 * h
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Properties of a sphere

A
  • Volume = 4/3 * pi * r^3

- Surface = 4 * pi * r^2

17
Q

(a+b)^2 + (a-b)^2

A

2a^2 + 2b^2

18
Q

(a+b)^2 - (a-b)^2

A

4ab

19
Q

Average speed (ONLY IF SAME DISTANCE)

A

(2* speed 1 * speed 2)/ (speed 1 + speed 2)

20
Q

Last n digit(s) of a product = ?

A

Product of last n digits of each number (e.g. Last 2 digits of 84594929292 = 454992)

21
Q

Which one-digit numbers have their powers end in the same digit

A

0, 1 , 5, 6

22
Q

Which one-digit numbers have their even powers end in the same digit, and odd power in another digit

A
  • 4 (4^2 = 6; 4^3= 4; 4^4 = 6)

- 9 (9^2 = 1; 9^3 =9; 9^4 = 1)

23
Q

Which one digit-numbers have their power end in a 4 by 4 pattern

A

2, 3, 7, 8

24
Q

Sum of all numbers which can be formed using n digits (WITHOUT repetition)

A

= (n-1)!(sum of digits)(1111… n times)

25
Q

How do you find general formula given two divisions/ remainders?

A
  1. 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

26
Q

Sum of n consecutive integers

A

n*(first term + last term)/2 (applies for all evenly spaced sequences)

27
Q

Arithmetic mean general formula

A

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

28
Q

Geometric mean general formula

A

an = a1r^(n-1)
Sum of first n terms = a1
(1-r^n)/(1-r)
Sum of all terms = a1/(1-r)

29
Q

Which fractions are not terminating

A

Once fully reduced, if denominator has any PRIME factor other than 2 or 5, then it is not a terminating number

30
Q

How to check if a number is divisible by 3?

A

The sum of digits should be divisible by 3

31
Q

How to check if a number is divisible by 4?

A

The LAST TWO digits should be divisible by 4

32
Q

How to check if a number is divisible by 9?

A

The sum of digits should be divisible by 9