1.11 Math Class

What you need to know

• Math.abs(x) — absolute value; returns int for int input, double for double.
• Math.pow(base, exp) — base raised to exp; always returns a double, even Math.pow(2, 3) is 8.0.
• Math.sqrt(x) — square root, returns a double.
• Math.random() — returns a double ≥ 0.0 and < 1.0. Never exactly 1.0.
• Random int in a range [low, high] inclusive: (int) (Math.random() * (high - low + 1)) + low. Number of possible values = high − low + 1.
• Example: die roll 1–6 is (int) (Math.random() * 6) + 1. Random 10–20: (int) (Math.random() * 11) + 10.
• All Math methods are static: always Math.method(...), never new Math().

Worked example

int a = Math.abs(-7);                          // 7
double b = Math.pow(2, 10);                     // 1024.0
double c = Math.sqrt(2.25);                     // 1.5
int roll = (int) (Math.random() * 6) + 1;       // 1..6
int r = (int) (Math.random() * 50) + 25;        // 25..74 (50 values)
int wrong = (int) Math.random() * 6 + 1;        // always 1! cast binds first

The last line is the classic error: (int) Math.random() is 0 before the multiplication happens.

Going deeper

The nuance, edge cases, and connections that turn a 3 into a 5.

• Math.abs is overloaded: abs(int) returns int, abs(double) returns double. Math.abs(-3) is 3; Math.abs(-3.0) is 3.0.
• Math.pow takes two doubles (ints widen) and always returns a double. Math.pow(2, 3) is 8.0. Assigning it to an int requires a cast: int x = (int) Math.pow(2, 3);.
• Math.sqrt returns a double. Negative input gives NaN, not an exception.
• Math.random() returns a double in [0.0, 1.0) — 0 possible, 1 impossible. Multiply by n → [0, n). Cast to int → 0 to n−1. Add low → low to low+n−1.
• The formula, fully: (int) (Math.random() * (high - low + 1)) + low. Parentheses around the multiplication are essential — the cast must apply to the product, not to Math.random() alone (which would always give 0).
• Reverse-engineering a range: for (int) (Math.random() * 7) + 3: multiplier 7 → 7 values; added 3 → starts at 3; so 3 through 9.
• Probability questions: Math.random() < 0.3 is true 30% of the time. (int) (Math.random() * 4) == 0 is true 25% of the time.
• All Math methods are static: Math.sqrt(x), never x.sqrt() or new Math().

Mistakes that cost points

• Casting Math.random() before multiplying. (int) Math.random() * 6 is always 0. The cast binds first.
• Off-by-one in the multiplier. For 1–6 you need 6 values → multiply by 6. For 5–15 you need 11 values → multiply by 11, not 10.
• Treating Math.pow's result as an int. It's a double. Math.pow(2, 3) + 1 is 9.0.
• Thinking Math.random() can return 1.0. It can't. The upper bound is exclusive.

Practice questions

Written in the style of the real exam. Try each one before revealing the answer.