Algorithms & Programming

Name: AP Computer Science Principles Unit 3: Algorithms & Programming
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30–35% of the exam4 lessons · 53 min

What this unit covers

The topics below follow the published CS Principles course framework for Unit 3. This unit is worth 30–35% of the exam, so budget your time against that rather than against how long the unit takes to teach.

VariablesProceduresListsSimulation

Lessons in this unit

Variables, Assignment & Expressions13 min · 3 objectivesExplain what a variable is and how assignment stores a value · Trace how variable values change as statements execute · Evaluate arithmetic expressions including MOD
Procedures & Abstraction14 min · 3 objectivesDefine a procedure with parameters and call it with arguments · Explain how procedures use abstraction to manage complexity · Trace a program that returns and uses a value from a procedure
Lists & Iteration14 min · 3 objectivesAccess and modify list elements using 1-based indexing · Use FOR EACH and indexed loops to process every element · Trace list operations such as APPEND, INSERT, and REMOVE
Simulation & Randomness12 min · 3 objectivesExplain what a simulation is and why simulations are useful · Describe the trade-offs between a simulation and the real experiment · Use RANDOM to model chance in a program

Formulas in Unit 3

The MOD operator

a MOD b = the remainder when a is divided by b

Example: 23 MOD 10 = 3. A number n is even exactly when n MOD 2 = 0, and n MOD b = 0 means b divides n evenly.

Defining and calling a procedure

PROCEDURE square(n) { RETURN(n * n) } → result ← square(6) // result = 36

The parameter n receives the argument 6; RETURN sends back 36, which the call stores in result.

AP pseudocode list operations

APPEND(L, v) · INSERT(L, i, v) · REMOVE(L, i) · LENGTH(L) · L[i] (1-indexed)

INSERT and REMOVE shift the positions of later elements. LENGTH gives the current element count. The first element is always L[1].

RANDOM in AP pseudocode

RANDOM(a, b) → a random integer from a to b, inclusive

Every integer in the range is equally likely. RANDOM(1, 6) yields 1, 2, 3, 4, 5, or 6, each with probability 1/6.

What examiners penalize here

`MOD` returns the *remainder*, not the quotient. Keep the classic uses ready: `n MOD 2 = 0` tests even, and `n MOD b = 0` tests whether b divides n evenly.
The exam frames procedures around **abstraction** and **reuse** (managing complexity), not speed. Know the vocabulary precisely: a *parameter* is in the definition, an *argument* is the value you pass in the call.
On list-tracing questions, redraw the list after **every** INSERT or REMOVE, because those operations shift the positions of all later elements. Track indices carefully — the exam builds traps out of these shifts.
`RANDOM(a, b)` is **inclusive** of both endpoints. To model n equally likely outcomes numbered 1 to n, use `RANDOM(1, n)`. Off-by-one endpoints are a favorite exam distractor.

Practice CS Principles

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

30 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric CS Principles study guideAll units, weights and score data in one place All 5 CS Principles unitsThe full course

Questions about this unit

How much of the AP Computer Science Principles exam is Unit 3?

Unit 3, Algorithms & Programming, is worth 30–35% of the CS Principles multiple-choice section according to the published course framework. Across all 5 units that makes it one of the heaviest units on the exam, and worth front-loading.

What topics are covered in CS Principles Unit 3?

Algorithms & Programming covers Variables, Procedures, Lists and Simulation.

How should I study CS Principles Unit 3?

Read the 4 lessons below first — about 55 minutes — then work practice questions on these topics. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 5 units of AP Computer Science Principles

Unit names, topics and exam weights follow the published College Board course framework for AP Computer Science Principles. AP® is a trademark registered by the College Board, which does not endorse this site.