← Computer Science Principles syllabus

United StatesComputer Science Principles

Big Idea 3: Algorithms and Programming

11 dot points across 11 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How does binary search beat linear search, and how do we compare the efficiency of algorithms?

Topic 3.11/3.17/3.18 Binary Search and Efficiency: binary search finds a value in a sorted list far faster than linear search, and algorithms are compared by efficiency, with some problems being unsolvable or only approximable.
A focused answer to AP CSP Topics 3.11, 3.17 and 3.18, covering linear versus binary search, why binary search needs a sorted list, reasonable versus unreasonable running time, polynomial versus exponential growth, heuristics, and undecidable problems.
11 min answer →

How do conditionals let a program make decisions, and how do nested conditionals handle several cases?

Topic 3.6/3.7 Conditionals and Nested Conditionals: conditional (IF/ELSE) statements select which code runs based on a Boolean condition, and nested conditionals handle multiple decision paths.
A focused answer to AP CSP Topics 3.6 and 3.7, covering IF and IF/ELSE selection, the role of the Boolean condition, nested conditionals for multiple paths, tracing which branch runs, and writing decision logic in AP CSP pseudocode.
10 min answer →

How does data abstraction, especially the use of lists, let programmers manage and reuse data?

Topic 3.2 Data Abstraction: data abstraction manages complexity by giving a collection of data a single name, most commonly using a list to represent many values as one variable.
A focused answer to AP CSP Topic 3.2, covering what data abstraction is, how a list represents many values under one name, the benefits for managing and modifying programs, the link to procedural abstraction, and why abstraction manages complexity.
9 min answer →

What is an algorithm, and how are sequencing, selection and iteration combined to solve problems?

Topic 3.9 Developing Algorithms: an algorithm is a finite set of instructions that accomplishes a task, built by combining sequencing, selection and iteration, and different algorithms can solve the same problem.
A focused answer to AP CSP Topic 3.9, covering what an algorithm is, the three building blocks (sequencing, selection, iteration), expressing algorithms in pseudocode and language, that different algorithms can solve the same problem, and standard list algorithms.
10 min answer →

How do procedures and libraries let programmers reuse code and manage complexity through abstraction?

Topic 3.12-3.14 Procedures and Libraries: procedures are named, reusable blocks with parameters and return values, and libraries and APIs package procedures so programmers reuse code through abstraction.
A focused answer to AP CSP Topics 3.12 to 3.14, covering defining and calling procedures, parameters and return values, procedural abstraction, modularity, libraries and APIs, and how reusing procedures manages complexity, with worked pseudocode.
11 min answer →

How do loops repeat instructions, and how do you avoid infinite loops and off-by-one errors?

Topic 3.8 Iteration: iteration (REPEAT n TIMES and REPEAT UNTIL) repeats a block of code, with the number of repetitions controlled by a count or a condition.
A focused answer to AP CSP Topic 3.8, covering REPEAT n TIMES and REPEAT UNTIL loops in AP CSP pseudocode, counting iterations, accumulating values, infinite loops and off-by-one errors, and tracing loop execution.
10 min answer →

How do lists store collections of data, and how do you access, traverse and modify their elements?

Topic 3.10 Lists: a list is an ordered collection of elements accessed by index; AP CSP lists are 1-indexed and support traversal and modification with APPEND, INSERT and REMOVE.
A focused answer to AP CSP Topic 3.10, covering lists as ordered collections, 1-based indexing in AP CSP pseudocode, accessing elements, traversing with FOR EACH and REPEAT, list operations (APPEND, INSERT, REMOVE, LENGTH), and why lists scale data processing.
11 min answer →

How do programs evaluate arithmetic, MOD and Boolean expressions, and how do logical operators combine conditions?

Topic 3.3/3.5 Mathematical and Boolean Expressions: programs evaluate arithmetic (including MOD) and Boolean expressions using relational and logical operators (AND, OR, NOT) that produce true or false.
A focused answer to AP CSP Topics 3.3 and 3.5, covering arithmetic operators and the MOD operator, relational operators, the Boolean operators AND, OR and NOT with truth tables, evaluating compound conditions, and the common uses of MOD such as testing even or odd.
10 min answer →

How do simulations model real phenomena, and how are random values used to add variability?

Topic 3.15/3.16 Random Values and Simulations: simulations are simplified, abstract models of real phenomena that often use random values to represent variability, trading detail for speed, safety and repeatability.
A focused answer to AP CSP Topics 3.15 and 3.16, covering the RANDOM procedure and generating random values, what a simulation is, why simulations are abstractions, their advantages and limitations, and using randomness to model variability, with worked pseudocode.
10 min answer →

What are the limits of computation, and what does it mean for a problem to be undecidable?

Topic 3.18 Undecidable Problems: some problems cannot be solved by any algorithm for all inputs (undecidable problems), and some solvable problems take unreasonable time, so heuristics give approximate answers.
A focused answer to AP CSP Topic 3.18, covering decidable versus undecidable problems, the limits of computation, the difference between unsolvable and merely slow problems, reasonable versus unreasonable running time, and the role of heuristics.
9 min answer →

How do variables store and update values, and how does the assignment operator work?

Topic 3.1 Variables and Assignments: a variable is a named reference to a stored value, and the assignment operator stores the value of an expression into a variable.
A focused answer to AP CSP Topics 3.1 to 3.3, covering variables as named storage, the assignment operator (the arrow) in AP CSP pseudocode, evaluating the right side first, updating variables, data types, and tracing assignment statements.
10 min answer →