Math Class: Practice Questions (Computer Science A 1.11)

These are original Marlbridge practice questions, not past exam questions. All code is invented for these questions and was compiled and run before publication. The rubrics are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. No calculator is allowed on the exam, so work everything by hand. Code fragments are assumed to be inside a main method. Math.random() returns a double greater than or equal to 0.0 and less than 1.0.

Question 1 (multiple choice · foundation)

Which statement about the Math class is true?

• (A) It must be imported with import java.util.Math; before it is used
• (B) You must write Math m = new Math(); before calling m.sqrt(16)
• (C) It is in java.lang, so it is available by default, and its methods are class methods
• (D) It contains only instance methods

Question 2 (multiple choice · foundation)

What is printed by System.out.println(Math.abs(-7) + Math.abs(-2.5));?

• (A) 9
• (B) 9.5
• (C) -9.5
• (D) 4.5

Question 3 (multiple choice · core)

What are the value and type of Math.pow(2, 5)?

• (A) 32, an int
• (B) 10, an int
• (C) 25, an int
• (D) 32.0, a double

Question 4 (multiple choice · core)

What is printed by the following statement?

System.out.println(Math.sqrt(Math.pow(6, 2) + Math.pow(8, 2)));

• (A) 10.0
• (B) 14.0
• (C) 10
• (D) 100.0

Question 5 (multiple choice · core)

Which expression produces a random int from 1 to 6, both inclusive?

• (A) (int) (Math.random() * 6) + 1
• (B) (int) (Math.random() * 6)
• (C) (int) (Math.random() * 7)
• (D) (int) Math.random() * 6 + 1

Question 6 (multiple choice · core)

What is the range of possible values of the following expression?

int n = (int) (Math.random() * 10 + 5);

• (A) 0 to 9
• (B) 5 to 15, both inclusive
• (C) 5 to 14, both inclusive
• (D) 5 to 10, both inclusive

Question 7 (multiple choice · stretch)

What value is stored in roll by the following statement?

int roll = (int) Math.random() * 6 + 1;

• (A) A random integer from 1 to 6
• (B) A random integer from 0 to 5
• (C) The expression does not compile
• (D) Always 1

Question 8 (writing expressions · core)

Write an expression for each of the following, and test it using the smallest and largest possible values of Math.random() (0.0 and just under 1.0).

(a) a random int from 20 to 30, both inclusive

(b) a random double that is at least 0.5 and less than 2.5

Question 9 (a class method · core)

(a) Write a class method distance that takes four int parameters x1, y1, x2, y2 and returns the distance between the points (x1, y1) and (x2, y2) as a double, using Math.pow and Math.sqrt.

(b) Write a call to it for the points (1, 2) and (4, 6), and state the value.

public class Points {
    public static double distance(int x1, int y1, int x2, int y2) {
        return Math.sqrt(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2));
    }

    public static void main(String[] args) {
        System.out.println(distance(1, 2, 4, 6));
    }
}

5.0

Question 10 (tracing with chosen values · stretch)

The following helper turns a value r (standing in for Math.random()) into an integer from low to high inclusive.

public class Scaler {
    public static int scale(double r, int low, int high) {
        return (int) (r * (high - low + 1)) + low;
    }

    public static void main(String[] args) {
        System.out.println(scale(0.0, 3, 8));
        System.out.println(scale(0.34, 3, 8));
        System.out.println(scale(0.5, 3, 8));
        System.out.println(scale(0.84, 3, 8));
        System.out.println(scale(0.999, 3, 8));
    }
}

(a) State the five values printed.

(b) Explain why no value of r from 0.0 up to but not including 1.0 can make scale(r, 3, 8) return 9.

3
5
6
8
8

How did you do?

• Questions 1 to 4: re-read “A toolbox of mathematical class methods” in the study guide and the table of return types.
• Questions 5 to 8: re-read “The general recipe”, and always test the smallest and largest possible values.
• Question 7: mark exactly how far each cast reaches with brackets.
• Questions 9 and 10: trace each call line by line.

Then try the checklist.