AP CSA Unit 5 | Arrays

What Arrays Are For

An array stores many values of the same type in one fixed-size object. Instead of making score1, score2, and score3, an array lets you use one name and an index.

Key Vocabulary

arrayelementindexlength

Indexes start at 0. The last valid index is arr.length - 1.

AP Exam Focus

Expect to trace loops, find off-by-one errors, write accumulator algorithms, and modify arrays using indexes.

Physics Connection

Arrays are perfect for storing repeated measurements: launch angles, ranges, time values, positions, velocities, or accelerations.

Exam habit: before tracing an array loop, write the indexes above the values. Most mistakes come from forgetting that index 0 is first and arr.length is not valid.

Array Syntax

Create an empty array

int[] scores = new int[5];
// values start as 0
scores[0] = 92;
scores[1] = 85;

Create with values

double[] times = {12.4, 12.1, 11.9, 12.0};
System.out.println(times[2]); // 11.9
System.out.println(times.length); // 4

Why is arr[arr.length] always an error?

If an array has length 5, its valid indexes are 0, 1, 2, 3, and 4. The expression arr.length is 5, which is one past the last valid index.

Common AP Array Algorithms

These patterns show up constantly in AP CSA multiple choice and free-response questions.

Sum and Average

int total = 0;
for (int i = 0; i < nums.length; i++) {
    total += nums[i];
}
double avg = (double) total / nums.length;

Maximum

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

Count Matching Values

int count = 0;
for (int n : nums) {
    if (n % 2 == 0) {
        count++;
    }
}

Linear Search

int index = -1;
for (int i = 0; i < names.length; i++) {
    if (names[i].equals(target)) {
        index = i;
    }
}

Reverse In Place

for (int i = 0; i < nums.length / 2; i++) {
    int j = nums.length - 1 - i;
    int temp = nums[i];
    nums[i] = nums[j];
    nums[j] = temp;
}

Shift Left

for (int i = 0; i < nums.length - 1; i++) {
    nums[i] = nums[i + 1];
}
nums[nums.length - 1] = 0;

Interactive IDE Examples

Students can paste the examples below into the embedded Java IDE, run them, then modify the array values or algorithm.

Example 1: Average Score

public class Main {
    public static void main(String[] args) {
        int[] scores = {85, 92, 77, 100, 88};
        int total = 0;
        for (int i = 0; i < scores.length; i++) {
            total += scores[i];
        }
        double average = (double) total / scores.length;
        System.out.println("Average = " + average);
    }
}

Example 2: Projectile Range Analyzer

public class Main {
    public static void main(String[] args) {
        double[] ranges = {18.4, 24.9, 29.8, 31.2, 30.7, 27.1};
        int bestIndex = 0;
        for (int i = 1; i < ranges.length; i++) {
            if (ranges[i] > ranges[bestIndex]) {
                bestIndex = i;
            }
        }
        System.out.println("Best trial index = " + bestIndex);
        System.out.println("Best range = " + ranges[bestIndex]);
    }
}

Code Tracing Practice

1. What is printed?

int[] a = {3, 5, 7, 9};
System.out.println(a[0] + a[2]);

Answer: 10

2. What is printed?

int[] a = {2, 4, 6, 8};
for (int i = 0; i < a.length; i++) {
    a[i] += i;
}
System.out.println(a[3]);

Answer: 11. The array becomes {2, 5, 8, 11}.

3. What is printed?

int[] nums = {1, 3, 5, 7};
int total = 0;
for (int n : nums) {
    total += n;
}
System.out.println(total);

Answer: 16

4. What is printed?

int[] x = {10, 20, 30};
int[] y = x;
y[1] = 99;
System.out.println(x[1]);

Answer: 99. Both variables refer to the same array object.

5. What is printed?

int[] a = {4, 1, 9, 2};
int m = a[0];
for (int i = 1; i < a.length; i++) {
    if (a[i] < m) {
        m = a[i];
    }
}
System.out.println(m);

Answer: 1. This finds the minimum value.

6. What is printed?

int[] a = {5, 10, 15};
for (int item : a) {
    item = item + 100;
}
System.out.println(a[0]);

Answer: 5. Enhanced for-loop variables do not replace primitive array elements.

Debugging: Common Array Mistakes

Off-by-one

for (int i = 0; i <= arr.length; i++)

Fix: use i < arr.length.

Wrong last index

arr[arr.length] = 0;

Fix: use arr[arr.length - 1].

Integer division

double avg = total / arr.length;

Fix: cast before division: (double) total / arr.length.

Changing enhanced loop variable

for (int n : arr) { n = 0; }

Fix: use an index loop when changing array values.

Find the bug: why does this crash?

int[] a = {2, 4, 6};
for (int i = 1; i <= a.length; i++) {
    System.out.println(a[i]);
}

The loop starts at 1, skipping index 0, and continues through i == 3. Index 3 is invalid. Use for (int i = 0; i < a.length; i++).

AP-Style Multiple Choice

1. Which creates an array of 10 integers?

Answer: int[] values = new int[10];

2. What is the last valid index of data if data.length is 12?

Answer: 11

3. What value is printed?

int[] a = {4, 8, 12};
System.out.println(a.length);

Answer: 3

4. Which loop correctly traverses every element?

Answer: for (int i = 0; i < arr.length; i++)

5. Which statement is true about arrays?

Answer: Once an array is created, its length cannot be changed.

6. What does this algorithm compute?

int c = 0;
for (int n : nums) {
    if (n > 0) c++;
}

Answer: It counts positive values.

7. Why might int max = 0; be a bad initialization?

Answer: If all values are negative, the algorithm may incorrectly return 0 even though 0 is not in the array. Use arr[0] for initialization.

8. What is printed?

int[] a = {1, 2, 3};
a[0] = a[2];
System.out.println(a[0]);

Answer: 3

9. Which loop is best if you need to modify array elements?

Answer: A standard index loop, because it lets you assign values back into arr[i].

10. What runtime error is most likely from accessing arr[arr.length]?

Answer: ArrayIndexOutOfBoundsException

FRQ Practice

FRQ 1: Practice Log

A PracticeLog class stores the number of problems a student solved each day.

public class PracticeLog {
    private int[] problems;

    public PracticeLog(int[] p) {
        problems = p;
    }

    /** Returns the total number of problems solved. */
    public int totalProblems() { /* to be implemented */ }

    /** Returns the number of days with at least target problems. */
    public int countDaysAtLeast(int target) { /* to be implemented */ }

    /** Replaces any negative values with 0. */
    public void removeInvalidData() { /* to be implemented */ }
}

Sample solution

public int totalProblems() {
    int total = 0;
    for (int n : problems) {
        total += n;
    }
    return total;
}

public int countDaysAtLeast(int target) {
    int count = 0;
    for (int n : problems) {
        if (n >= target) {
            count++;
        }
    }
    return count;
}

public void removeInvalidData() {
    for (int i = 0; i < problems.length; i++) {
        if (problems[i] < 0) {
            problems[i] = 0;
        }
    }
}

FRQ 2: Projectile Trial Analyzer

A ProjectileData class stores launch angles and measured ranges from an experiment.

public class ProjectileData {
    private double[] angles;
    private double[] ranges;

    public ProjectileData(double[] a, double[] r) {
        angles = a;
        ranges = r;
    }

    /** Returns the index of the trial with the greatest range. */
    public int bestTrialIndex() { /* to be implemented */ }

    /** Returns the angle for the trial with the greatest range. */
    public double bestAngle() { /* to be implemented */ }

    /** Returns the average range. */
    public double averageRange() { /* to be implemented */ }
}

Sample solution and rubric

public int bestTrialIndex() {
    int best = 0;
    for (int i = 1; i < ranges.length; i++) {
        if (ranges[i] > ranges[best]) {
            best = i;
        }
    }
    return best;
}

public double bestAngle() {
    return angles[bestTrialIndex()];
}

public double averageRange() {
    double total = 0.0;
    for (double r : ranges) {
        total += r;
    }
    return total / ranges.length;
}

Correct traversal and index bounds: 2 pts
Correct maximum-index algorithm: 2 pts
Correct use of helper method in bestAngle: 1 pt
Correct accumulator and average calculation: 2 pts
Clear return types and no unnecessary printing: 1 pt

Mini-Project: Projectile Data Analyzer

Students create a Java program that stores projectile experiment data in arrays, analyzes the data, and makes a conclusion about the launch angle that produced the greatest range.

Requirement	Description
Data	Use one `double[]` for launch angles and one `double[]` for measured ranges.
Methods	Write methods for average range, best range, best angle, and count of trials above a target range.
Output	Print a clear summary explaining the strongest trial and the overall pattern.
Extension	Calculate theoretical range using `R = v² sin(2θ) / g` and compare experimental error.

Starter Code

public class Main {
    public static void main(String[] args) {
        double[] angles = {15, 25, 35, 45, 55, 65, 75};
        double[] ranges = {12.1, 20.4, 27.8, 31.2, 29.5, 22.0, 13.6};

        ProjectileAnalyzer analyzer = new ProjectileAnalyzer(angles, ranges);
        System.out.println(analyzer.summary());
    }
}

class ProjectileAnalyzer {
    private double[] angles;
    private double[] ranges;

    public ProjectileAnalyzer(double[] a, double[] r) {
        angles = a;
        ranges = r;
    }

    public int bestIndex() {
        int best = 0;
        for (int i = 1; i < ranges.length; i++) {
            if (ranges[i] > ranges[best]) {
                best = i;
            }
        }
        return best;
    }

    public String summary() {
        int best = bestIndex();
        return "Best angle: " + angles[best] + " degrees, range: " + ranges[best] + " m";
    }
}

Teacher note: This mini-project is intentionally smaller than the final physics simulation PBL. It builds AP array fluency first, then gives students a bridge into full object-oriented simulation work.

Teacher Implementation Notes

Suggested pacing: one 75-minute block for syntax and tracing, one block for algorithms and debugging, one block for FRQ/project work.

Skill	Evidence of Mastery
Traversal	Student can write a loop that visits every element once without an index error.
Accumulator	Student can correctly initialize, update, and return a total/count/average.
Index reasoning	Student can explain why `length - 1` is the last index.
FRQ readiness	Student writes methods that return values rather than printing unless asked.