Math Class: Revision Notes (Computer Science A 1.11)

Short on time? This page is the recap. For explanations and worked examples, use the full study guide.

Recap

• The Math class is part of the java.lang package, so it is available by default. It contains only class methods.
• The methods in the Java Quick Reference: static int abs(int x), static double abs(double x), static double pow(double base, double exponent), static double sqrt(double x) and static double random().
• Math.random() returns a double that is greater than or equal to 0.0 and less than 1.0.
• Arithmetic and casting operators turn Math.random() into a random int or double in a defined range. Each end of a range can be inclusive (the value can occur) or exclusive (it cannot).

Key relationships

Call	Value	Type
Math.abs(-7)	7	int
Math.abs(-2.5)	2.5	double
Math.pow(2, 5)	32.0	double
Math.pow(5, 0)	1.0	double
Math.sqrt(144)	12.0	double
(int) Math.pow(2, 10)	1024	int

Want	Expression
double in [0.0, 1.0)	Math.random()
int 0 to n - 1	(int) (Math.random() * n)
int low to high, both inclusive	(int) (Math.random() * (high - low + 1)) + low
double low up to, not including, high	Math.random() * (high - low) + low
int 1 to 6	(int) (Math.random() * 6) + 1

Four questions for any random-number problem

1. How many different values are wanted? That is the multiplier.
2. What is the smallest value wanted? That is the shift added at the end.
3. Is the result an int (cast the whole product, then add the shift) or a double (no cast)?
4. Test the extremes: Math.random() equal to 0.0, and just under 1.0.

Assumptions and conventions

• Arguments of type int are converted automatically to double parameters.
• The Java Quick Reference is provided on the exam; you need to read and use it correctly.
• For a random expression you cannot say the output, only the possible range, so test the smallest (0.0) and largest (just under 1.0) values.
• Use Math.sqrt on non-negative values only; results for negative values are outside the course.

Mistakes to avoid

1. Writing (int) Math.random() * n. The cast truncates Math.random() to 0 first, so the result is always 0.
2. Multiplying by high instead of by the number of values (high - low + 1).
3. Expecting 1.0 from Math.random().
4. Forgetting that pow, sqrt and random return double. Storing the result in an int needs a cast.
5. Importing Math or creating a Math object.
6. Thinking abs always returns double.
7. Adding the shift in the wrong place without checking the range.

Quick self-check

1. What does Math.sqrt(49) return, and what type? (7.0, a double)
2. How many values are in the range 5 to 12 inclusive? (8)
3. Write an expression for a random int from 1 to 100 inclusive. ((int) (Math.random() * 100) + 1)
4. What is the range of (int) (Math.random() * 10 + 5)? (5 to 14 inclusive)
5. What does (int) Math.random() * 6 + 1 always equal? (1)

Next: practice questions.