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Chapter 8

Mathematical Library Methods

Class 9 - Logix Kips ICSE Computer Applications with BlueJ


Multiple Choice Questions

Question 1

Which Java package includes the Math class?

  1. java.io
  2. java.lang ✓
  3. java.util
  4. java.sys

Question 2

Give the output of Math.sqrt(x); when x = 9.0

  1. 3
  2. 3.0 ✓
  3. 3.00
  4. All of these

Question 3

Give the output of Math.ceil(46.6).

  1. 46.6
  2. 46.5
  3. 47.0 ✓
  4. 46.0

Question 4

Give the output of Math.abs(x); when x = -9.99

  1. -9.99
  2. 9.99 ✓
  3. 0.99
  4. None of these

Question 5

Which of the following is a method to find the square root of a number?

  1. FindSquareroot(x)
  2. Sqrt(x)
  3. Math.Square(x)
  4. Math.sqrt(x) ✓

Question 6

What will be the output of Math.pow(2, 0)?

  1. 0.0
  2. 1.0 ✓
  3. 2.0
  4. -1.0

Question 7

Math.random() returns a double value r such that

  1. 0.0 <= r < 1.0 ✓
  2. 0.0 <= r <= 1.0
  3. 0.0 < r <= 1.0
  4. 0.0 < r < 1.0

Question 8

Give the output of Math.floor(46.6)?

  1. 46.5
  2. 47.0
  3. -46.0
  4. 46.0 ✓

Assignment Questions

Question 1

Distinguish between Math.ceil() and Math.floor() methods.

Answer

Math.ceil( )Math.floor( )
Returns the smallest double value that is greater than or equal to the argument and is equal to a mathematical integerReturns the largest double value that is less than or equal to the argument and is equal to a mathematical integer.
double a = Math.ceil(65.5);
In this example, a will be assigned the value of 66.0 as it is the smallest integer greater than 65.5.
double b = Math.floor(65.5);
In this example, b will be assigned the value of 65.0 as it is the largest integer smaller than 65.5.

Question 2

Explain the following Math functions in Java:

i. Math.sqrt()

Answer

Returns the square root of its argument as a double value. For example, Math.sqrt(25) will return 5.0.

ii. Math.cbrt()

Answer

Returns the cube root of its argument as a double value. For example, Math.cbrt(27) will return 3.0.

iii. Math.random()

Answer

Returns a positive double value, greater than or equal to 0.0 and less than 1.0.

iv. Math.round()

Answer

Rounds off its argument to the nearest mathematical integer and returns its value as an int or long type. If argument is float, return type is int, if argument is double, return type is long. At mid-point, it returns the higher integer. For example, Math.round(2.5) will return 3.

Question 3

Write the following as Java expressions:

i. x3y22xy\lvert x^3 - y^2 -2xy\rvert

Answer

Math.abs(Math.pow(x, 3) - Math.pow(y, 2) - 2*x*y)

ii. π6(z42π)\dfrac{\pi}{6}(z^4 - 2\pi)

Answer

Math.PI / 6*(Math.pow(z, 4) - 2*Math.PI)

iii. z2π3\sqrt[3]{z^2 - \pi}

Answer

Math.cbrt(z*z - Math.PI)

iv. x3y34\sqrt[4]{x^3 - y^3}

Answer

Math.pow(x*x*x - y*y*y, 1/4)

v. amountrate11(1+rate)n\cfrac{amount*rate}{1 - \cfrac{1}{(1 + rate)^n}}

Answer

(amount*rate) / (1 - (1 / Math.pow(1+rate, n)))

Question 4

Write valid statements for the following in Java:

i. Print the rounded off value of 234.49

Answer

System.out.println(Math.round(234.49));

ii. Print the absolute value of -9.99

Answer

System.out.println(Math.abs(-9.99));

iii. Print the largest of -45 and -50

Answer

System.out.println(Math.max(-45, -50));

iv. Print the smallest of -56 and -57.4

Answer

System.out.println(Math.min(-56, -57.4));

v. Print a random integer between 50 and 70

Answer

int range = 70 - 50 + 1;
int num = (int)(range * Math.random() + 50);
System.out.println(num);

vi. Print 10.5 raised to the power 3.8

Answer

System.out.println(Math.pow(10.5, 3.8));

Question 5

Write a program in Java to find the minimum of three numbers using Math.min() method.

Answer

import java.util.Scanner;

public class KboatSmallestNumber
{
    public static void main(String args[]) {
        
        Scanner in = new Scanner(System.in);
        
        System.out.print("Enter First Number: ");
        int a = in.nextInt();
        System.out.print("Enter Second Number: ");
        int b = in.nextInt();
        System.out.print("Enter Third Number: ");
        int c = in.nextInt();
        
        int s = Math.min(a, b);
        s = Math.min(s, c);
        
        System.out.println("Smallest Number = " + s);
    }
}
Output
BlueJ output of KboatSmallestNumber.java

Question 6

Write a program to print:

i. p to the power q
ii. the square root of p

The values of p and q are 64 and 2 respectively.

Answer

public class KboatNumber
{
    public static void main(String args[]) {
        int p = 64;
        int q = 2;
        
        double r1 = Math.pow(p, q);
        System.out.println("p to the power of q = " + r1);
        
        double r2 = Math.sqrt(p);
        System.out.println("Square root of p = " + r2);
    }
}
Output
BlueJ output of KboatNumber.java

Question 7

Write a program to generate random integers in the range 10 to 20.

Answer

public class KboatRandom
{
    public static void main(String args[]) {
        int min = 10, max = 20;
        int range = max - min + 1;
        int num = (int)(range * Math.random() + min);
        System.out.println("Random number in the range 10 to 20: " + num);
    }
}
Output
BlueJ output of KboatRandom.java

Question 8

Write the equivalent Java statements for the following, only using the mathematical functions:

i. Print the positive value of -101.

Answer

System.out.println(Math.abs(-101));

ii. Store the value -125 in a variable and print its cube root.

Answer

int a = -125;
System.out.println(Math.cbrt(a));

iii. Store the value 89.99 in a variable and convert it into its closest integer that is greater than or equal to 89.99.

Answer

double a = 89.99;
System.out.println(Math.round(a));
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