Math Class

Java has a Math class with multiple methods. You can call a method with the following format:

Math.(method  goes here)

Absolute Value

The absolute value just returns the positive value of the number. If you input an int the method returns an int. If you input a double, it returns a double.

System.out.println(Math.abs(-4));//prints out 4

System.out.println(Math.abs(-4.0)); //prints out 4.0

Power

Java can also do exponents. The method takes in two parameters: the base and the exponent values. The method returns base raised to the value of the exponent. So Math.pow(2,3) returns 8.0 (this method returns a double always) as 2 * 2 * 2 = 8.

Square Root

The square root method takes in a parameter and returns the square root of that number in a form of a double.

Math.sqrt(4); //returns 2.0

Random Number Generator

The method Math.random() takes in no parameters but returns a double between 0.0 and .999999 (inclusive). Here is a sample question that commonly shows up on the AP exam.

What is the minimum and maximum value of x returned by the following code?

int x = (int) (Math.random()*9 - 10);

A) Min: 0 Max: 2

B) Min: -10 Max: -2

C) Min: -10 Max: - 1

D) Min: -10 Max: 0

E) Min: -2 Max: -10

When you cast a double using (int), it just removes everything after the decimal, but it doesn't round.

Let's break this down. We will calculate the smallest value possible. Math.random() returns 0 as its smallest value so 0 * 9 -10 = -10.

We can eliminate A and E as their minimum value is wrong. This leaves the max. Maximum is .99999999(repeating 9) * 9 = 8.999 (largest case). 8.999 -10 = -1.001. Remove the decimal and it leaves -1. So the answer is C.

Logic

There are other Boolean expressions. When comparing two Strings you use the .equals method : stringA.equals(stringB).

For numbers, you would use == : intA == intB

For NOT, you would use !: A != B; !stringA.equals(stringB).

You can distribute the ! when simplifying expressions (known as DeMorgan's Law).

For example:

!(A || B) = !A && !B

The opposite of AND is OR.

Evaluating Large Boolean Expressions

You evaluate expression in the parentheses first, then evaluate AND, then OR - sort of like PEMDAS but for boolean expressions.

If, else-if, and else

If- statements are code that checks a certain condition, then run the code inside the if-statement if the condition is met. else-if is used when you have multiple conditions can be met. Code in an else statement is run if all the other if and else-if statements are not met. If is used first, followed by else-if, and then else.

if(condition1){

//runs if condition1 is true and then exits the entire if-else structure

}

else if(condition2){

//runs if condition2 is true and then exits the entire if-else structure

}

else{

//runs only condition1 and condition2 are both false 

}

Note that, if condition1 is true and condition2 are both true, only the code in condition1 is run. Java breaks out of the if-else structure. However, if you had two separate if-statements that were true then both codes would run.

if(condition1){...}//runs if condition1 is true

if(condition2){...}//runs if condition2 is true, regardless of condition1

Comparing

For comparing doubles or ints use these signs:

boolean a = (5 == 5);//a = true; == checks to see if both values are equal

boolean b = (5 != 5); //b = false; != checks to see if both values are NOT equal

boolean c = (5 >= 6);//c = false; >= checks to see if first value is greater than or equal to //second value

boolean d = (5 > 6);//d = false; > checks to see if first value is greater than second value

boolean e = (5 <= 6);//e = true; >= checks to see if first value is less than or equal to second //value

boolean f = (5 < 6);//f = true; > checks to see if first value is less than second value

Lab1

https://github.com/aceAPCS/lab1

Download it by clicking clone or download button and then click on download as zip. The README.MD file has instructions in it. Extract the zipped folder, and in Dr. Java click on file -> open folder. Select lab1.

Exercises