APCSA Class Notes – 1.11 The Math Class

Overview

The Math class in Java is a built-in utility class that provides common mathematical functions. It is part of java.lang, so it does not require an import statement. All methods in the Math class are static, meaning you call them using the class name:

Math.methodName(parameters);

You never create a Math object.

1. Static Methods in the Math Class

A. Square Root – `Math.sqrt()`

Returns the square root of a number.

double result = Math.sqrt(25); // result = 5.0

Parameter must be non-negative (otherwise the result is NaN).
Returns a double.

B. Powers – `Math.pow()`

Raises a number to a specific power.

double result = Math.pow(3, 4); // result = 81.0

Always returns a double.
Used frequently in geometry, physics, growth models, and algorithms.

C. Random Values – `Math.random()`

Generates a value from 0.0 up to 1.0 (but not including 1.0).

double r = Math.random(); // r is between 0.0 and 1.0

Creating Random Integers

General formula:

(int)(Math.random() * range + start)

Examples:

// Random int 0–9
int num = (int)(Math.random() * 10);

// Random int 1–6 (dice)
int roll = (int)(Math.random() * 6 + 1);

// Random int 5–15
int n = (int)(Math.random() * 11 + 5);

2. Other Important Math Methods

Absolute Value – `Math.abs()`

int x = Math.abs(-12); // 12

Rounding Methods

Math.round(x) – nearest whole number
Math.floor(x) – rounds down
Math.ceil(x) – rounds up

Math.round(3.6); // 4
Math.floor(3.6); // 3.0
Math.ceil(3.1);  // 4.0

3. Why APCS A Uses the Math Class

The Math class is used frequently in:

FRQs
Array algorithms
Distance and geometry calculations
Simulations and randomization
Searching and sorting
Conditional logic

4. Summary Table

Method	Purpose	Returns	Example
`Math.sqrt(x)`	Square root	double	`Math.sqrt(16)` → 4.0
`Math.pow(a, b)`	a to the power of b	double	`Math.pow(2, 3)` → 8.0
`Math.random()`	Random number 0.0–1.0	double	`Math.random()`
`Math.abs(x)`	Absolute value	int/double	`Math.abs(-5)`
`Math.round(x)`	Rounds to nearest	long/int	`Math.round(2.7)`
`Math.floor(x)`	Rounds down	double	`Math.floor(2.7)`
`Math.ceil(x)`	Rounds up	double	`Math.ceil(2.1)`

5. Practice Examples

A. Write the Java expression for:

Square root of 89
Math.sqrt(89);

7 to the 3rd power
Math.pow(7, 3);

Random integer from 1 to 100
(int)(Math.random() * 100 + 1);

Absolute value of (x − y)
Math.abs(x - y);