Big Idea 3: Algorithms and Programming

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

1. Question 1Foundational

   In College Board pseudocode, the list numbers contains the values 4, 8, 15, and 16 in that order. What value does numbers[2] represent?

   1. A8
   2. B4
   3. C15
   4. DNothing, because the index is out of range

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   Answer: A. 8

   AP pseudocode lists are indexed starting at 1, so numbers[1] is 4 and numbers[2] is 8. Answering 15 assumes indexing starts at 0, which is the convention in many programming languages but not on this exam.

   Key insight: In AP Computer Science Principles pseudocode the first element of a list is at index 1.

2. Question 2Foundational

   What must be true about a list before a binary search can be used on it?

   1. AThe list must be sorted
   2. BThe list must contain only numbers
   3. CThe list must contain no duplicate values
   4. DThe list must have an even number of elements

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   Answer: A. The list must be sorted

   Binary search works by discarding half the remaining list at each step, which is only valid if order guarantees where the target can be. Duplicates, data type, and list length do not affect correctness; an unsorted list does, because the halving decision becomes meaningless.

   Key insight: Binary search buys speed with an assumption: the data must already be in order.

3. Question 3Intermediate

   In College Board pseudocode the following statements are executed: sum ← 0; REPEAT 4 TIMES { sum ← sum + 3 }; DISPLAY(sum). What value is displayed?

   1. A12
   2. B7
   3. C4
   4. D3

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   Answer: A. 12

   The loop body runs four times and each pass adds 3 to sum, so the final value is 4 times 3 = 12. Answering 7 adds 3 and 4 rather than repeating the addition, and answering 3 reports the value after a single pass.

   Key insight: Trace a loop with a table of values; a repeated addition is multiplication in disguise.

4. Question 4Intermediate

   In College Board pseudocode, what is the value of the expression (a > 5) AND (NOT (b = 3)) when a = 7 and b = 4?

   1. Atrue
   2. Bfalse
   3. CAn error occurs, because = is the assignment operator
   4. DIt cannot be determined from the information given

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   Answer: A. true

   The first condition is true because 7 > 5, and b = 3 is false because b holds 4, so NOT (b = 3) is true. An AND expression is true only when both operands are true, which they both are here. Assignment in AP pseudocode uses ←, which leaves = free as the comparison operator.

   Key insight: Evaluate the innermost condition first, apply NOT, and only then combine with AND.

5. Question 5Advanced

   An algorithm requires about 2^n steps for an input of size n. How is that running time classified in AP Computer Science Principles?

   1. AUnreasonable, because the number of steps grows exponentially
   2. BReasonable, because the steps grow as a polynomial
   3. CReasonable, because the number of steps is constant
   4. DUndecidable, because no algorithm can solve the problem

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   Answer: A. Unreasonable, because the number of steps grows exponentially

   The course calls a running time reasonable when it grows no faster than a polynomial in the input size, so exponential growth such as 2^n is unreasonable. Unreasonable is not the same as undecidable: a solution exists here, it simply becomes impractical as n grows, which is why heuristics are used instead.

   Key insight: Reasonable time means polynomial growth; exponential growth is unreasonable but still solvable in principle.