Properties

Question 1

Sum of interior angles = ?

Answer 1

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

Question 2

Area of an equilateral triangle

Answer 2

s^2*sqrt(3)/4

Question 3

Height of an equilateral triangle

Answer 3

s*sqrt(3)/2

Question 4

Sides of 30-60-90 triangles

Answer 4

1 : sqrt(3) : 2

Question 5

Sides of 45-45-90 triangles

Answer 5

1 : 1 : sqrt(2)

Question 6

Obtuse triangle rule

Answer 6

c^2 > a^2 + b^2

Question 7

Common right triangles

Answer 7

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

Question 8

Properties of a rectangle

Answer 8

• All angles are 90 degrees
• Opposite sides are equal
• Opposite sides are parallel
• Diagonals bisect each other

Question 9

Properties of a square

Answer 9

• All angles are 90 degrees
• All sides are equal
• Opposite sides are parallel
• Diagonals bisect PERPENDICULARLY

Question 10

Properties of a parallelogram

Answer 10

• Opposite angles are equal
• Opposite sides are equal
• Opposite sides are parallel
• Diagonals bisect each other
• Sum of adjacent angles is 180 degrees

Question 11

Properties of a rhombus

Answer 11

• 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

Question 12

Properties of a trapezium

Answer 12

• Only one pair of opposite sides are parallel

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

Question 13

Properties of a regular hexagon

Answer 13

• Longest diagonal = 2*side

Question 14

Properties of a cuboid

Answer 14

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

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

Question 15

Volume of a cone

Answer 15

• Volume = 1/3 * pi * r^2 * h

Question 16

Properties of a sphere

Answer 16

• Volume = 4/3 * pi * r^3

- Surface = 4 * pi * r^2

Question 17

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

Answer 17

2a^2 + 2b^2

Question 18

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

Answer 18

4ab

Question 19

Average speed (ONLY IF SAME DISTANCE)

Answer 19

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

Question 20

Last n digit(s) of a product = ?

Answer 20

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

Question 21

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

Answer 21

0, 1 , 5, 6

Question 22

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

Answer 22

• 4 (4^2 = 6; 4^3= 4; 4^4 = 6)

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

Question 23

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

Answer 23

2, 3, 7, 8

Question 24

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

Answer 24

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

Question 25

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

Answer 25

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

Question 26

Sum of n consecutive integers

Answer 26

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

Question 27

Arithmetic mean general formula

Answer 27

an = a1 + (n-1)*d ; d is the difference | Reminder: Sum of first n integers is n*(a1*an)/2 as it is an evenly spaced sequence

Question 28

Geometric mean general formula

Answer 28

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

Question 29

Which fractions are not terminating

Answer 29

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

Question 30

How to check if a number is divisible by 3?

Answer 30

The sum of digits should be divisible by 3

Question 31

How to check if a number is divisible by 4?

Answer 31

The LAST TWO digits should be divisible by 4

Question 32

How to check if a number is divisible by 9?

Answer 32

The sum of digits should be divisible by 9