Mathematical Expressions Chapter Notes | AP Computer Science Principles - Grade 9 PDF Download

Introduction

This chapter covers mathematical expressions and algorithms, key concepts in the AP Computer Science Principles course. It introduces algorithms, their relationship to programs, sequencing as a core algorithmic concept, and how expressions are used with arithmetic operators. Understanding these concepts is essential for creating and implementing algorithms in programming for the AP CSP exam.

Algorithms

• An algorithm is a set of instructions designed to accomplish a specific task or solve a problem.
• Algorithms differ from programs: an algorithm represents the problem-solving logic, while a program is the implementation of that logic for execution.
• Analogy: An algorithm is like the steps to bake a cake, while a program is the written recipe a computer (or baker) follows.
• Algorithms can be expressed in:
  • Programming languages (e.g., C++, Java, Scratch).
  • Pseudocode or natural language (e.g., English).
  • Diagrams.
• Computers execute exactly what is specified, so algorithms must be clear and detailed to avoid errors.

Sequencing in Algorithms

Algorithms are built using three core concepts: sequencing, selection, and iteration. These are expressed through code statements, which are instructions for actions to be executed.
Sequencing refers to executing steps in the exact order they are written. For example:

first_number = 7
second_number = 5
sum_value = first_number + second_number
print(sum_value)

Expressions

An expression is a statement that evaluates to a single value. It may include:

• A literal value
• A variable
• An operator
• A procedure call that returns a value

Programs use arithmetic operators for calculations, including addition (+), subtraction (-), multiplication (*), and division (/).

Operators in College Board Pseudocode

The operators in College Board’s Pseudocode align with Python, except for the MOD operator, which is represented as % in Python. The Modulo (MOD) operator returns the remainder of a division operation. For example:

• 13 MOD 3 returns 1 (since 13 ÷ 3 = 4 with a remainder of 1).

Order of Operations

• Expressions are evaluated using the programming language’s order of operations, typically following PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). 
• In College Board Pseudocode, the MOD operator shares the same precedence as multiplication and division, making it more like PEMMDAS.

Key Terms