Essential formulas for Math Kangaroo: Geometry, Algebra, Number Theory, and Probability.
| Name | Formula | Note |
|---|---|---|
| Triangle Area | S = ½ × b × h | base × height ÷ 2 |
| Circle Area | S = πr² | π × radius squared |
| Circumference | C = 2πr | 2 × π × radius |
| Trapezoid Area | S = ½(a+b)h | (sum of parallel sides) × height ÷ 2 |
| Pythagorean Theorem | a² + b² = c² | right triangle side relationship |
| Cuboid Volume | V = l × w × h | length × width × height |
| Name | Formula | Note |
|---|---|---|
| Arithmetic Series Sum | S = n(a₁+aₙ)/2 | number of terms × (first + last) ÷ 2 |
| Perfect Square | (a±b)² = a²±2ab+b² | expansion formula |
| Difference of Squares | a²-b² = (a+b)(a-b) | factoring formula |
| Quadratic Formula | x = (-b±√(b²-4ac))/2a | solutions of ax²+bx+c=0 |
| Name | Formula | Note |
|---|---|---|
| Divisibility by 3 | sum of digits divisible by 3 | if digit sum ÷ 3 = 0, the number is divisible |
| GCD × LCM | GCD(a,b) × LCM(a,b) = a × b | product relationship for two numbers |
| Euler's Totient | φ(n) = n−1-1/p) | count of integers ≤ n coprime to n |
| Name | Formula | Note |
|---|---|---|
| Classical Probability | P = favorable / total | equally likely outcomes |
| Combinations | C(n,k) = n!/(k!(n-k)!) | choose k from n |
| Permutations | P(n,k) = n!/(n-k)! | arrange k from n |
