Class 9 Mathematical Library Methods Mock Test (ICSE)

Topics in Mathematical Library Methods

• Math.pow and Math.sqrt
• Math.abs, Math.max and Math.min
• Math.round, Math.ceil and Math.floor
• Math.random
• Using Math methods in expressions

Mathematical Library Methods practice questions with answers

1. Q1Multiple choice·1 mark
   What is the output of the expression `int x = (int)Math.max(Math.min(10, 15), Math.abs(-12));`?

   1. (a)$12$
   2. (b)$10$
   3. (c)$15$
   4. (d)$-12$
   Show answer and step marks

   1. Correct option: (a) $12$+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   A square sports ground has an area of 144 m². Which Java expression gives the length of one side in metres?

   1. (a)$Math.sqrt(144)$
   2. (b)$Math.pow(144, 2)$
   3. (c)$Math.sqrt(144 * 2)$
   4. (d)$Math.round(144 / 2)$
   Show answer and step marks

   1. Correct option: (a) $Math.sqrt(144)$+1

   Answer: (a)
3. Q3Short answer·3 marks
   An orchard packs fruit into boxes that each hold 10 fruit. A program stores the number of boxes needed as shown below. int fruit = 43; double boxes = fruit / 10.0; (a) Find the value of Math.floor(boxes). [1] (b) Find the value of Math.ceil(boxes). [1] (c) Find the value of Math.round(boxes). [1]
   Show answer and step marks

   1. boxes = 43 / 10.0 = 4.3, so Math.floor(4.3) gives the largest integer not greater than 4.3, which is 4.+1
   2. Math.ceil(4.3) gives the smallest integer not less than 4.3, which is 5.+1
   3. Math.round(4.3) rounds to the nearest integer, and 0.3 is less than 0.5, so the value is 4.+1

   Answer: (a) 4; (b) 5; (c) 4
4. Q4Short answer·3 marks
   A dice game program contains the statement int r = (int)(Math.random()*6)+1; to simulate the throw of a dice. (a) State the range of values that Math.random() returns. [1] (b) State the set of values that the variable r can take. [1] (c) State the value of r when Math.random() returns 0.99. [1]
   Show answer and step marks

   1. Math.random() returns a double x with $0.0 \le x < 1.0$+1
   2. Math.random()*6 lies between 0.0 and less than 6.0; the cast keeps the integer part 0 to 5, and adding 1 gives r from 1 to 6+1
   3. $0.99 \times 6 = 5.94$; cast gives 5; adding 1 gives r = 6+1

   Answer: (a) $0.0 \le x < 1.0$ (0.0 included, 1.0 excluded); (b) 1, 2, 3, 4, 5, 6; (c) 6
5. Q5Long answer·4 marks
   Write a Java program to accept the lengths of the three sides of a triangle ($a$, $b$, and $c$) as double values using the Scanner class. Calculate and display the area of the triangle using Heron's formula: $\text{Area} = \sqrt{s(s - a)(s - b)(s - c)}$ where $s = \frac{a + b + c}{2}$. Use the appropriate Math library method in your expression.
   Show answer and step marks

   1. Correct import statement (`import java.util.Scanner;`), class declaration, and `main` method setup with `Scanner` initialization.+1
   2. Correctly reading three double values for sides and computing the semi-perimeter $s = (a + b + c) / 2.0$.+1
   3. Using `Math.$\sqrt{}$` to evaluate the Heron's formula expression `Math.$\sqrt{s × (s - a) × (s - b) × (s - c)}$`.+1
   4. Printing the computed area cleanly using `System.out.println()`.+1

   Answer: import java.util.Scanner; public class HeronArea { public static void main(String[] args) { Scanner sc = new Scanner(System.in); System.out.print("Enter the three sides: "); double a = sc.nextDouble(); double b = sc.nextDouble(); double c = sc.nextDouble(); double s = (a + b + c) / 2.0; double area = Math.$\sqrt{s × (s - a) × (s - b) × (s - c)}$; System.out.println("Area of the triangle = " + area); } } (The sides are assumed to form a valid triangle.)
6. Q6Long answer·4 marks
   Write a program in Java using the `Scanner` class to accept the coordinates of a point $(x, y)$ as `double` values. Calculate and display its distance from the origin using the formula: $\text{Distance} = \sqrt{\text{Math.pow}(x, 2) + \text{Math.pow}(y, 2)}$ Use appropriate `Math` library methods for your calculations.
   Show answer and step marks

   1. Importing java.util.Scanner and setting up the class and main method structure.+1
   2. Accepting input for x and y coordinates correctly as double values using Scanner.+1
   3. Applying the mathematical expression using Math.pow() and Math.$\sqrt{}$ methods.+1
   4. Displaying the calculated distance with an appropriate output message.+1

   Answer: import java.util.Scanner; public class Distance { public static void main(String[] args) { Scanner sc = new Scanner(System.in); System.out.print("Enter x and y: "); double x = sc.nextDouble(); double y = sc.nextDouble(); double d = Math.$\sqrt{Math.pow(x, 2) + Math.pow(y, 2)}$; System.out.println("Distance from the origin = " + d); } }

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