AP CSA 2.11 FRQ Practice: Rows and Columns

Unit 2: Selection and Iteration · Lesson 2.11 · FRQ Practice

Rows and Columns

A free response question in the shape the exam uses: a stated contract, four rubric parts, and no main method handed to you. Worth 4 points.

Back to the Lesson 2.11 pageAll Unit 2 lessons

Why this question is worth four points

A nested loop multiplies. The outer loop body runs once per row, the inner one runs fully inside each of those, and the counter that belongs to the outer loop must not be reset by the inner one. Every rectangle here is deliberately NOT square, because a square hides a swapped pair of bounds completely.

What you are given

Nothing is given. Write a class named Grid containing exactly the four static methods described below. Assume rows and cols are each at least 1. Do not write a main method.

The question

  1. (a) public static int cells(int rows, int cols) returns how many cells a rows by cols rectangle has.
  2. (b) public static int sumProducts(int rows, int cols) returns the sum of r times c over every r from 1 to rows and every c from 1 to cols.
  3. (c) public static int countPairs(int n) returns how many ordered pairs (i, j) with 1 <= i < j <= n exist.
  4. (d) public static String rowLabel(int row, int cols) returns the numbers 1 through cols each multiplied by row, separated by single spaces, with no space at the start.

What the reader is looking for

  1. Write class Grid with the four static methods exactly as described. No main method.
  2. Part (a) and part (b) both use a nested loop. Count the cells rather than assuming the shape is square.
  3. Part (d) separates the numbers with single spaces and must not begin with one. Adding the separator BEFORE each item except the first is the usual way.

Worked examples

These show what a correct answer prints. There are more cases you cannot see, and they use different values, so an answer built around just these numbers will fail.

Example 1 input
2 5
Example 1 output
10
45
1
2 4 6 8 10
Example 2 input
3 2
Example 2 output
6
18
3
3 6

Your answer

Main.java

Input for the Run button

How this is scored: your answer runs against every test case, and the fraction it passes becomes your score out of 4. That is not how a human AP reader marks a rubric, so treat the score as a check on whether your code works, and the rubric above as the thing you are actually practising.


  

  
Stuck?

    
Hint 1
The accumulator belongs OUTSIDE both loops. Declaring it inside the outer loop resets it on every row and reports only the last row.

    
Hint 2
Part (c) starts its inner loop at i + 1, which is what makes each pair count once rather than twice.

    
Hint 3
Part (d) adds the space before each item after the first. Dropping the c > 1 guard puts a space at the very start of the line, which the driver does compare.



  
Before you submit

  
4 mistake(s) that lose points on this question
    
Each of these is a real error the grader catches. Check your answer against them before you submit, not instead of trying.

    
    
      
  • part (b) resets its accumulator inside the outer loop
    • 
      
  • part (a) swaps the two bounds, which only matters on a non square grid
    • 
      
  • part (c) starts the inner loop at i, counting each element with itself
    • 
      
  • part (d) puts the separator before every item, including the first
    • 
    

  


  
Where to go next

  

    Rework the Lesson 2.11 page
    Try the from-scratch exercise for this lesson
    Try the debugging exercise for this lesson
  


  
  






  

















  
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