Math.abs, max, min, random, the Exact Methods and Java Expressions (ICSE Class 9)

Understand abs, max, min, random, the Exact Methods and Writing Java Expressions

abs, max, min, random, the Exact Methods and Writing Java Expressions: key facts

abs, max, min

Math.abs	x
Math.max	a, b
Math.min	a, b
	result type follows the arguments

Mixed types give the larger type.

Random range

• •Math.random() is in [0.0, 1.0)
• •(int)(Math.random() times n) + start
• •n values from start

Die: n = 6, start = 1.

Exact methods

• •addExact
• •subtractExact
• •multiplyExact
• •ArithmeticException on overflow

Plain + wraps around silently.

abs, max, min, random, the Exact Methods and Writing Java Expressions in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Tricks to remember abs, max, min, random, the Exact Methods and Writing Java Expressions

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Random is below one

  Math.random() is at least 0.0 and always less than 1.0.

  Use it when: Ranges.

• Multiply by how many, add where it starts

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

  Use it when: Random ranges.

• Exact stops, plus wraps

  Exact methods throw an exception; + wraps silently.

  Use it when: Overflow.

abs, max, min, random, the Exact Methods and Writing Java Expressions: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

System.out.println(Math.abs(-2.25) + " " + Math.max(3, 8) + " " + Math.min(-2, -9) + " " + Math.max(Math.abs(-9), Math.min(4, 6)));

Where students lose marks in abs, max, min, random, the Exact Methods and Writing Java Expressions

The slips examiners see most often, and what to write instead.

• ✗Mistake: Random range off by one

  The count and start are confused.

  Wrong working

  (int)(Math.random() * 6) gives 1 to 6

  Right working

  (int)(Math.random() * 6) gives 0 to 5; add 1 for 1 to 6

  ✓Do this: Multiply by count, then add start.

  Usually costs: 1 to 2 marks

• ✗Mistake: Omitting the cast on random

  A decimal is stored in an int.

  Wrong working

  int x = Math.random() * 6;

  Right working

  int x = (int) (Math.random() * 6);

  ✓Do this: Cast before storing.

  Usually costs: 1 mark

• ✗Mistake: Wrong type for max

  Types are ignored.

  Wrong working

  Math.max(3, 8.0) = 8

  Right working

  Math.max(3, 8.0) = 8.0

  ✓Do this: Mixed types give a double.

  Usually costs: 1 mark

Practice questions on abs, max, min, random, the Exact Methods and Writing Java Expressions

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   The value of Math.min(5, -3) is:
   (a) 5 (b) -3 (c) 3 (d) 2

   Hint

   Smaller of the two.

   Answer

   (b) -3

2. Q2 · 1 mark · Very short answerBoard level

   Which method returns a decimal number that is at least 0.0 and less than 1.0?

   Hint

   Think of the Math class.

   Answer

   Math.random()

3. Q3 · 2 marks · Short answerHarder board level

   Evaluate Math.abs(-6) + Math.pow(2, 3).

   Hint

   An int plus a double is a double.

   Answer

   14.0 (6 + 8.0)

4. Q4 · 3 marks · Short answerHarder board level

   Write a statement that stores a random whole number from 20 to 29 in an int variable r, and another that simulates the roll of a die.

   Hint

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

   Answer

   int r = (int) (Math.random() * 10) + 20;
   int die = (int) (Math.random() * 6) + 1;

5. Q5 · 3 marks · Short answerHOTS / competency

   A student writes int n = Math.addExact(2000000000, 2000000000); What happens? What would the plain sum 2000000000 + 2000000000 give?

   Hint

   The largest int is 2147483647.

   Answer

   The true sum 4000000000 is larger than the largest int (2147483647), so addExact throws an ArithmeticException (integer overflow). The plain sum wraps around and gives -294967296.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Math.abs(-9)?Show answer

   9

2. 2.Can Math.random() return 1.0?Show answer

   No; it is less than 1.0.

3. 3.Math.max(3, 8.0)?Show answer

   8.0

4. 4.Which exception do the exact methods throw?Show answer

   ArithmeticException

5. 5.Range of (int)(Math.random() * 6) + 1?Show answer

   1 to 6

6. 6.Write the positive difference of a and b.Show answer

   Math.abs(a - b)

abs, max, min, random, the Exact Methods and Writing Java Expressions: frequently asked questions