Topic 1.11 — Math Class

Goal: use common Math class methods (as class/static methods), understand their return types, and trace code that uses them.

The big idea

Math is a Java library class that provides useful methods for calculations. These are class (static) methods, so you call them using Math.

Pattern: Math.methodName(...)

You don’t need to memorize every method—focus on how to use them and how to trace them.

Method call	What it does	Returns
`Math.abs(x)`	Absolute value (distance from 0)	`int` or `double` (matches type of `x`)
`Math.pow(a, b)`	`a` raised to the power `b`	`double`
`Math.sqrt(x)`	Square root of `x`	`double`
`Math.random()`	Random number in the range `[0.0, 1.0)`	`double`
`Math.min(a, b)`	Smaller of two values	`int` or `double`
`Math.max(a, b)`	Larger of two values	`int` or `double`

int a = Math.abs(-12);      // 12
double b = Math.pow(2, 3);  // 8.0
double c = Math.sqrt(81);   // 9.0

Notice how pow and sqrt return double, even if inputs look like ints.

Math.random() returns a double from 0.0 up to (but not including) 1.0. To make a random integer in a range, you scale and cast.

int r = (int) (Math.random() * 10);  // 0 to 9

Multiply first, then cast. The cast truncates.

These two are NOT the same:

(int) (Math.random() * 10)   // 0..9 ✅

// WRONG:
(int) Math.random() * 10     // always 0 ❌

Why? (int) Math.random() becomes 0 most of the time (since random is < 1), then 0 * 10 = 0.

int low = Math.min(4, 9);   // 4
int high = Math.max(4, 9);  // 9