Quick Answer
An expression is a mathematical phrase combining numbers, variables, and operators without an equals sign. On the Digital SAT, expressions are fundamental to the Algebra and Advanced Math sections. Typically, approximately 20-30% of Math questions involve manipulating or simplifying expressions, appearing frequently in both multiple-choice and student-produced response formats.
An expression is a finite combination of symbols—such as numbers, variables, and operators—that represents a mathematical value. Unlike an equation, an expression like 3x² + 5x - 7 does not contain an equality or inequality sign.
Question: Which of the following is equivalent to the expression 3(x + 4) - 2(x - 1)? Solution: 1. Distribute the constants: 3x + 12 - 2x + 2. 2. Combine like terms: (3x - 2x) + (12 + 2). 3. Simplified expression: x + 14.
Confusing expressions with equations: Students often try to 'solve' for a variable by setting the expression equal to zero, which leads to incorrect conclusions.
Distribution errors: Forgetting to distribute a negative sign to every term inside parentheses, such as writing -(x - 3) as -x - 3 instead of -x + 3.
Incorrectly combining terms: Attempting to add terms with different variables or exponents, like treating x² and x as like terms.
Students targeting 750+ should know that for complex equivalent expression questions, you can often pick a small value for the variable (like x = 2) and plug it into both the original expression and the answer choices to quickly verify equivalence if algebraic manipulation becomes too time-consuming.
Equation
An equation is a mathematical statement asserting that two expressions are equal. On the Digital SAT, equations form the core of the Algebra and Advanced Math sections. Typically, linear and quadratic equations appear in approximately 30-40% of the Math modules, requiring students to solve for a specific variable or interpret constants.
Polynomial
A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents. On the Digital SAT, polynomials frequently appear in the Advanced Math section, typically requiring students to add, subtract, multiply, or factor expressions. These questions often represent approximately 10-15% of the math content across both modules.
Factoring
Factoring is the mathematical process of breaking down a polynomial into a product of simpler expressions or factors. On the Digital SAT, this technique is frequently tested in the Math modules, appearing in approximately 10-15% of algebra and advanced math questions, often requiring students to identify equivalent expressions or find the zeros of quadratic functions.
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.
Coefficient
Coefficient is the numerical factor that multiplies a variable in an algebraic expression. On the Digital SAT, coefficients are central to the Math section, appearing in approximately 20% of questions. They are most frequently tested in Heart of Algebra problems, where students must interpret their real-world meaning as rates of change.
An expression on the SAT is a collection of numbers, variables, and operations that represents a single value or relationship. Unlike equations, expressions do not have an equals sign. On the Digital SAT, you will frequently be asked to simplify these phrases or find equivalent versions. Understanding expressions is essential for navigating the Algebra and Advanced Math sections of the test.
To simplify an expression, you must use the order of operations (PEMDAS) to combine like terms and eliminate parentheses. This typically involves using the distributive property to expand products and then grouping terms with the same variable and exponent. On the SAT, simplifying is often the first step in identifying equivalent forms among the provided multiple-choice options.
The primary difference between an expression and an equation is the presence of an equals sign. An expression is a mathematical 'phrase' (like 2x + 5), while an equation is a mathematical 'sentence' stating that two expressions are equal (like 2x + 5 = 11). You simplify or evaluate an expression, but you solve an equation to find the value of a variable.
While the exact number varies, approximately 15% to 25% of the Math section involves direct or indirect manipulation of expressions. You will typically see several questions specifically asking for 'equivalent expressions' in each module. Because expressions form the building blocks of equations and functions, they are foundational to nearly every algebra-based question you will encounter on the Digital SAT.
