AP CSA Unit 2: Selection & Iteration - Complete Study Guide (2025)

📘 2.1 Unit Overview & Big Ideas

In this unit, you’ll learn how programs:

Decide what to do using boolean expressions and if statements
Repeat code using while and for loops
Combine decisions and repetition to implement algorithms

Main topics:

Relational & logical operators (>, <, ==, !=, &&, ||, !)
Boolean expressions and truth tables
if, else-if, else, and nested conditionals
De Morgan’s Law and simplifying conditions
while loops, for loops, and nested loops
Loop patterns: counting, summing, searching
Off-by-one errors and infinite loops
Tracing and debugging selection + iteration

      AP Exam Insight:  
      If you can comfortably trace if-statements and loops, most AP CSA 
      multiple-choice questions become much easier. Many FRQs are just 
      “nicer looking” loops and conditionals.
    

🧠 2.2 Boolean Expressions & Relational Operators

A boolean expression is an expression that evaluates to either true or false. You’ll use these inside if-statements and loops.

Relational Operators

Operator	Meaning	Example
`==`	equal to	`x == 5`
`!=`	not equal to	`x != 0`
`>`	greater than	`score > 90`
`<`	less than	`temp < 32`
`>=`	greater than or equal to	`age >= 16`
`<=`	less than or equal to	`count <= 10`

Examples

int x = 7;
boolean a = (x > 5);    // true
boolean b = (x == 7);   // true
boolean c = (x != 7);   // false

      Important: == compares values of primitives (like int, double).  
      For Strings, you must use equals(), not ==.
    

🔗 2.3 Logical Operators, Truth Tables & Precedence

Logical operators combine or modify boolean values:

&& (AND) – true only if both conditions are true
|| (OR) – true if at least one condition is true
! (NOT) – reverses a boolean value

Truth Table

A	B	A && B	A \|\| B
true	true	true	true
true	false	false	true
false	true	false	true
false	false	false	false

NOT Operator

boolean isRaining = true;
boolean stayInside = !isRaining;  // false

Operator Precedence (Simplified)

Relational: >, <, >=, <=, ==, !=
Logical NOT: !
Logical AND: &&
Logical OR: ||

      Use parentheses generously. They improve readability and prevent mistakes, 
      especially under exam pressure.
    

Short-Circuit Evaluation

Java uses short-circuiting:

A && B → if A is false, B is never evaluated
A || B → if A is true, B is never evaluated

if (x != 0 && 10 / x > 1) {
    // safe: 10/x only happens if x != 0
}

      AP Tip: Many MCQs rely on short-circuit logic to avoid 
      runtime errors like division by zero.
    

🧩 2.4 De Morgan’s Law & Simplifying Conditions

De Morgan’s Law lets you distribute a NOT over an AND/OR expression:

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

Example

Suppose we want to check that a value x is outside the range 1 to 10:

// x is NOT between 1 and 10 inclusive:
if (x < 1 || x > 10) {
    ...
}

// Equivalent to:
if (!(x >= 1 && x <= 10)) {
    ...
}

      De Morgan’s Law appears frequently on AP questions that ask for 
      equivalent boolean expressions.
    

🔀 2.5 if, else-if, else – Making Decisions

Selection lets your program choose between different paths of execution.

Basic if Statement

if (condition) {
    // runs only if condition is true
}

if-else

if (score >= 60) {
    System.out.println("Pass");
} else {
    System.out.println("Fail");
}

if-else-if Chain

if (score >= 90) {
    grade = "A";
} else if (score >= 80) {
    grade = "B";
} else if (score >= 70) {
    grade = "C";
} else {
    grade = "D or F";
}

      Only the first true condition in an if/else-if/else chain executes.  
      Once one block runs, the rest are skipped.
    

Example – Two Separate if Statements

int x = 12;

if (x % 2 == 0)
    System.out.println("even");

if (x % 3 == 0)
    System.out.println("divisible by 3");

Output:

even
divisible by 3

Because these are two separate if statements, both can run.

🏛 2.6 Nested Conditionals & Common Decision Patterns

You can place an if-statement inside another if or else block. This is called a nested conditional.

Nested Example

if (age >= 16) {
    if (hasPermit) {
        System.out.println("You can drive.");
    } else {
        System.out.println("Get your permit first.");
    }
} else {
    System.out.println("Too young to drive.");
}

Range Checking Pattern

if (score < 0 || score > 100) {
    System.out.println("Invalid score");
} else if (score >= 90) {
    grade = 'A';
} else if (score >= 80) {
    grade = 'B';
} else if (score >= 70) {
    grade = 'C';
} else {
    grade = 'D';
}

Multi-Condition Decisions

if (gpa >= 3.5 && communityServiceHours >= 50) {
    eligibleForScholarship = true;
}

      When tracing nested conditions, write down the values of variables 
      and follow the structure step by step. Don’t try to “eyeball” complex logic.
    

🧪 2.7 Selection Practice – Predict the Output

Example 1

int x = 5;
if (x > 10)
    System.out.println("big");
else if (x > 3)
    System.out.println("medium");
else
    System.out.println("small");

Output: medium

Example 2

int a = 4;
int b = 7;

if (a > b || b % 2 == 1)
    System.out.println("A");
else if (a % 2 == 0 && b % 2 == 0)
    System.out.println("B");
else
    System.out.println("C");

Output: A (because b % 2 == 1 is true)

Example 3

boolean hot = true;
boolean sunny = false;

if (!hot && sunny)
    System.out.println("Cool day");
else if (hot && !sunny)
    System.out.println("Humid");
else
    System.out.println("Mixed");

Output: Humid

      When you see selection-heavy MCQs, treat them like these small exercises:  
      copy the values mentally, then follow each branch carefully.
    

🔁 2.8 Introduction to Iteration (Loops)

Iteration means repeating a block of code multiple times. In Java, the main loop constructs are:

while loops – repeat while a condition is true
for loops – repeat a specific number of times
nested loops – loops inside loops

while (condition) { // repeated code } for (initialization; condition; update) { // repeated code }

      Almost every algorithm you write in AP CSA will use some combination of if-statements and loops.
    

🔂 2.9 while Loops – Condition-Controlled Repetition

A while loop repeats as long as its condition evaluates to true.

while (condition) {
    // body runs repeatedly
}

Counting Example

int i = 0;
while (i < 5) {
    System.out.println(i);
    i++;
}

Output: 0 1 2 3 4

Key Points

The condition is checked before each iteration.
The loop body may run zero times if the condition starts false.
You must change something inside the loop so the condition eventually becomes false.

Common Mistake – Infinite Loop

int n = 10;
while (n > 0) {
    System.out.println(n);
    // n never changes → infinite loop
}

      Always identify the loop variable and verify it changes every iteration in the direction that makes the condition false.
    

🔁 2.10 for Loops – Counting-Controlled Iteration

A for loop is ideal when you know in advance how many times the loop should run.

for (initialization; condition; update) {
    // repeated code
}

Typical Example

for (int i = 0; i < 5; i++) {
    System.out.println(i);
}

Output: 0 1 2 3 4

For Loop Anatomy

initialization: runs once before the loop starts
condition: checked before each iteration
update: runs at the end of each iteration

Counting Down

for (int k = 10; k > 0; k--) {
    System.out.println(k);
}

Skipping Values

for (int i = 0; i < 20; i += 2) {
    System.out.println(i);   // even numbers
}

      Rule to remember: 

      A for-loop is just a while-loop rewritten more compactly.  
      AP MCQs often show equivalence between the two.
    

🏗 2.11 Nested Loops

A nested loop is a loop inside another loop. These are common in algorithms that deal with grids, tables, and repeated comparisons.

Example: 2D Pattern

for (int r = 0; r < 3; r++) {
    for (int c = 0; c < 5; c++) {
        System.out.print("*");
    }
    System.out.println();
}

Output:

*****
*****
*****

How to Trace Nested Loops

Use this mental model:

Outer runs: 0 → 1 → 2 For each outer value: Inner runs: 0 → 1 → 2 → 3 → 4 Total iterations = outerCount × innerCount = 3 × 5 = 15

      AP Tip: When a nested loop MCQ asks “How many times does this print?”,  
      multiply the loop counts—unless a break/condition interrupts flow.
    

🧮 2.12 Common Loop Patterns

Almost every FRQ and MCQ relies on one of these patterns.

1. Accumulator Pattern (Summing Values)

int sum = 0;
for (int i = 1; i <= 100; i++) {
    sum += i;
}

2. Counting Occurrences

int count = 0;
for (int i = 0; i < list.length; i++) {
    if (list[i] % 2 == 0)
        count++;
}

3. Linear Search

boolean found = false;
for (int i = 0; i < arr.length; i++) {
    if (arr[i] == target) {
        found = true;
        break;
    }
}

4. Finding Min/Max

int max = arr[0];
for (int i = 1; i < arr.length; i++) {
    if (arr[i] > max)
        max = arr[i];
}

      These patterns reappear in Unit 4 with arrays and ArrayLists.  
      Mastering them now makes later FRQs far easier.
    

🔀 2.13 Combining Selection and Iteration

Most real algorithms mix conditionals and loops. AP exam questions assume you can follow these combinations confidently.

Example: Count How Many Numbers Are Positive

int count = 0;
for (int i = 0; i < nums.length; i++) {
    if (nums[i] > 0)
        count++;
}

Example: Find First Number Divisible by 7

int index = -1;
for (int i = 0; i < nums.length; i++) {
    if (nums[i] % 7 == 0) {
        index = i;
        break;
    }
}

Example: Validate Input Using a Loop

while (age < 0 || age > 120) {
    System.out.println("Enter a valid age:");
    age = input.nextInt();
}

      Any FRQ requiring traversal (arrays, ArrayLists, strings)  
      is really testing your Unit 2 foundations.
    

⚠️ 2.14 Common Loop & Selection Mistakes

Forgetting to update the loop variable (infinite loops)
Using == instead of equals() for Strings
Using && when || was intended (and vice versa)
Misunderstanding inclusive vs. exclusive ranges
Placing break in the wrong place inside nested loops
Off-by-one errors: using < when <= is needed
Tracing loops incorrectly (especially nested loops)

      Best Study Technique:  
      Trace 20–30 loops by hand.  
      This instantly improves your MCQ score more than memorizing syntax.
    

📝 Unit 2 Quiz – Selection & Iteration (10 Questions)

Question 1

What is the output?

int x = 5;
if (x > 10)
    System.out.println("big");
else
    System.out.println("small");

A. big
B. small
C. big small
D. no output

Question 2

What is the value of y after the loop?

int y = 0;
for (int i = 1; i <= 3; i++) {
    y += i;
}

A. 3
B. 6
C. 4
D. 1

Question 3

What does the following code print?

int n = 7;
if (n % 2 == 0)
    System.out.println("even");
else if (n % 3 == 0)
    System.out.println("divisible by 3");
else
    System.out.println("other");

A. even
B. divisible by 3
C. other
D. no output

Question 4

How many times will System.out.println() run?

for (int i = 2; i < 10; i += 2) {
    System.out.println(i);
}

A. 3 times
B. 4 times
C. 5 times
D. 6 times

Question 5

What does the loop print?

for (int i = 3; i > 0; i--) {
    System.out.print(i + " ");
}

A. 1 2 3
B. 3 2 1
C. 0 1 2 3
D. infinite loop

Question 6

What is printed?

int a = 4;
int b = 9;

if (a < b && b % 3 == 0)
    System.out.println("X");
else
    System.out.println("Y");

A. X
B. Y
C. XY
D. no output

Question 7

What is the final value of x?

int x = 1;
int i = 1;

while (i <= 3) {
    x *= i;
    i++;
}

A. 6
B. 3
C. 0
D. 1

Question 8

Which loop prints the even numbers from 2 to 10?

A. for (int i=2; i<10; i++)
B. for (int i=2; i<=10; i+=2)
C. for (int i=1; i<=10; i++)
D. for (int i=10; i>0; i-=3)

Question 9

What value is printed last?

for (int i = 0; i <= 4; i++) {
    System.out.println(i);
}

A. 3
B. 4
C. 5
D. none

Question 10

How many times does the inner loop execute?

for (int r = 0; r < 4; r++) {
    for (int c = 0; c < 3; c++) {
        System.out.println(r + "," + c);
    }
}

A. 4
B. 3
C. 7
D. 12

🚀 Next Steps: Move on to Unit 3 – Class Creation

Now that you’ve mastered selection and iteration, you’re ready for Unit 3: Class Creation, where you’ll learn how to create your own classes, constructors, and methods—skills essential for both FRQs and real-world Java programming.

Add your internal link here:
Continue to AP CSA Unit 3: Class Creation →