3.3 Mathematical Expressions

Enduring Understanding

The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

Learning Objective

Express an algorithm that uses sequencing without using a programming language.

Essential Knowledge

An algorithm is a finite set of instructions that accomplish a specific task.

Beyond visual and textual programming languages, algorithms can be expressed in a variety of ways, such as natural language, diagrams, and pseudocode.

Algorithms executed by programs are implemented using programming languages.

Every algorithm can be constructed using combinations of sequencing, selection, and iteration.

Learning Objective

Represent a step-by-step algorithmic process using sequential code statements. 

Essential Knowledge

Sequencing is the application of each step of an algorithm in the order in which the code statements are given.

A code statement is a part of program code that expresses an action to be carried out.

An expression can consist of a value, a variable, an operator, or a procedure call that returns a value.

Expressions are evaluated to produce a single value

The evaluation of expressions follows a set order of operations defined by the programming language.

Sequential statements execute in the order they appear in the code segment.

Clarity and readability are important considerations when expressing an algorithm in a programming language.

Learning Objective

Evaluate expressions that use arithmetic operators.

Essential Knowledge

Arithmetic operators are part of most programming languages and include addition, subtraction, multiplication, division, and modulus operators.

The exam reference sheet provides a MOD b, which evaluates to the remainder when a is divided by b. Assume that a is an integer greater than or equal to 0 and b is an integer greater than 0. For example, 17 MOD 5 evaluates to 2.

The exam reference sheet provides the arithmetic operators +, -, *, /, and MOD. Text and Block:

• a + b

• a - b

• a * b

• a / b

• a MOD b

These are used to perform arithmetic on a and b. For example, 17 / 5 evaluates to 3.4.

The order of operations used in mathematics applies when evaluating expressions. The MOD operator has the same precedence as the * and / operators.