Quick Answer
An integer is a whole number that can be positive, negative, or zero. On the Digital SAT, integers appear frequently across both Math modules, particularly in student-produced response questions where answers must often be non-decimal. Mastering integers is essential for solving approximately 15-20% of algebraic and data analysis problems.
An integer is any member of the set {..., -3, -2, -1, 0, 1, 2, 3, ...}, representing a number without a fractional or decimal component. In mathematical notation, the set of all integers is often denoted by the symbol Z.
Question: If 4x + 9 < 22 and x is a positive integer, what is the greatest possible value of x? Solution: Subtract 9 from both sides: 4x < 13. Divide by 4: x < 3.25. Since x must be an integer, the greatest value is 3.
Mistake 1: Forgetting that zero is an integer and is neither positive nor negative.
Mistake 2: Assuming 'integer' only refers to positive numbers, thereby ignoring negative whole numbers in algebraic solutions.
Mistake 3: Rounding to the nearest integer incorrectly in word problems when the context (like 'minimum' or 'maximum') requires a specific floor or ceiling value.
Students targeting 750+ should know that the SAT frequently uses the 'integer' constraint in quadratic equations and systems of equations to limit potential solutions, often requiring the use of the discriminant or factorability rules to ensure the roots are integers.
Composite Number
A composite number is a positive integer greater than 1 that has more than two distinct factors. On the Digital SAT, these appear typically in Math Module 1 or 2 within number theory or factoring questions. Understanding them is crucial for identifying prime versus non-prime options in multiple-choice questions about integer properties.
Factor (Number)
A factor is an integer that divides another integer perfectly without leaving a remainder. On the Digital SAT, factors appear frequently in Math Modules 1 and 2, often within algebraic simplification or polynomial questions. Typically, students must identify factors to find roots or simplify expressions, making this concept vital for a high score.
Multiple
A multiple is the product of any integer and another integer. On the Digital SAT, multiples appear frequently in Math Modules 1 and 2, often within word problems involving cycles or sequences. Typically, students must calculate the Least Common Multiple (LCM) to solve problems concerning synchronized events or common denominators.
Prime Number
A prime number is a positive integer greater than 1 with exactly two distinct factors: 1 and itself. On the Digital SAT, prime numbers frequently appear in Math Module 1 and 2 within Number Properties or Algebra questions. Students typically encounter at least one question involving prime factorization or integer constraints per test.
Variable
A variable is a symbol, usually a letter, representing an unknown or changing numerical value. On the Digital SAT, variables are foundational to the Math section, appearing in approximately 70% of questions. They are most prevalent in algebra problems where students must solve for a specific unknown or model real-world relationships.
An integer on the SAT is any whole number, including positive numbers, negative numbers, and zero, without any fractional or decimal parts. It appears across various question types in the Math section, often as a constraint in algebraic equations or inequalities. Understanding this term is vital because it dictates whether a solution like 2.5 is valid or if it must be rounded to a whole value.
You can identify an integer by checking if a number has a decimal or fractional remainder; if it is a whole value like -5, 0, or 12, it is an integer. On the Digital SAT, look for the specific word 'integer' in the problem stem, which indicates that your final answer or the variables involved cannot be fractions like 1/2 or decimals like 0.75.
The primary difference is that integers are a subset of real numbers that do not include fractions or decimals. While real numbers encompass everything from pi to 2.75, integers are strictly restricted to whole values like -1, 0, and 1. On the SAT, 'real number' allows for any value on the number line, whereas 'integer' limits your choices to specific points.
While the exact number varies, approximately 10 to 15 questions per test typically involve integers either as the primary subject or as a necessary constraint for solving the problem. They are most common in the Heart of Algebra and Passport to Advanced Math sections, appearing in both multiple-choice and student-produced response formats where precise numerical entry is required.
