⚡ Must Memorize
1
First 10 odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. Their sum = 10² = 100
2
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
3
Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
4
Divisibility: by 3 → digit sum divisible by 3; by 9 → digit sum divisible by 9
5
Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...
6
Percent formula: Part = (Percent/100) × Whole
7
Distance = Rate × Time (D = R × T)
8
Triangle inequality: sum of any 2 sides > third side
Example 1 · Arithmetic
What is the sum of the first 10 positive odd numbers?
The first 10 positive odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
Key fact: The sum of the first n odd numbers = n²
So the sum = 10² = 100
Answer: 100
Example 2 · Geometry
A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
Using the Pythagorean theorem: a² + b² = c²
3² + 4² = c² → 9 + 16 = 25 → c = √25 = 5
Answer: 5
Example 3 · Probability
A fair die is rolled. What is the probability of rolling an even number?
Even numbers on a die: 2, 4, 6 → 3 favorable outcomes
Total outcomes: 6
P(even) = 3/6 = 1/2
Answer: 1/2