GMAT (Graduate Management Admission Test) Quantitative Reasoning: Algebra Syllabus

Quantitative Reasoning: Algebra syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning: Algebra in GMAT (Graduate Management Admission Test), not a summary of it.

1. 1

   Algebraic Expressions & Manipulation

   5 topics

   • Combining like terms and the distributive law
   • Factoring techniques
     • Common factor extraction
     • Special products (difference of squares, perfect squares)
     • Factoring quadratics
   • Polynomial multiplication (FOIL)
   • Simplifying rational expressions
   • Substitution and evaluating expressions
2. 2

   Linear Equations & Inequalities

   5 topics

   • Solving single-variable linear equations
   • Systems of linear equations
     • Substitution method
     • Elimination method
     • When systems have no or infinite solutions
   • Linear inequalities and flipping the sign
   • Compound and absolute-value inequalities
   • Translating word problems into equations
3. 3

   Quadratics & Higher-Order Equations

   5 topics

   • Solving quadratics by factoring
   • The quadratic formula and discriminant
   • Completing the square
   • Roots, sum and product of roots
   • Equations reducible to quadratic form
4. 4

   Functions, Formulas & Sequences

   5 topics

   • Function notation and evaluation
   • Symbolism / made-up function problems
   • Arithmetic sequences
     • Common difference and nth term
     • Sum of an arithmetic series
   • Geometric sequences
   • Rearranging and solving formulas
5. 5

   Coordinate Geometry (Algebra-based)

   5 topics

   • The x-y plane and plotting points
   • Slope of a line
     • Positive, negative, zero, and undefined slope
     • Parallel and perpendicular slopes
   • Equations of lines (slope-intercept and point-slope)
   • Distance and midpoint formulas
   • Intercepts and intersection of lines

Quantitative Reasoning: Algebra flashcards for GMAT (Graduate Management Admission Test)

20 of 50 cards from the Quantitative Reasoning: Algebra deck — real questions with worked answers.

1. What does it mean to combine like terms, and which terms qualify as "like"?

   Combining like terms means adding/subtracting the coefficients of terms that have the exact same variable part (same variables raised to the same powers). E.g., 3x + 5x = 8x, and 2x^2 + 4x cannot be combined.

2. State the distributive law and give an example.

   a(b + c) = ab + ac. The factor outside is multiplied by every term inside the parentheses. Example: 3(x + 4) = 3x + 12.

3. What is the FOIL method for multiplying two binomials (a + b)(c + d)?

   FOIL = First, Outer, Inner, Last: (a+b)(c+d) = ac + ad + bc + bd. Multiply the first terms, outer terms, inner terms, and last terms, then combine like terms.

4. Expand (x + y)^2, (x - y)^2, and (x + y)(x - y).

   (x+y)^2 = x^2 + 2xy + y^2; (x-y)^2 = x^2 - 2xy + y^2; (x+y)(x-y) = x^2 - y^2 (difference of squares).

5. Factor the difference of squares a^2 - b^2.

   a^2 - b^2 = (a + b)(a - b).

6. How do you factor a quadratic of the form x^2 + bx + c?

   Find two numbers that multiply to c and add to b. If they are p and q, then x^2 + bx + c = (x + p)(x + q).

7. What is the first step in factoring any polynomial?

   Factor out the greatest common factor (GCF) shared by all terms. E.g., 6x^2 + 9x = 3x(2x + 3).

8. Factor x^3 + x^2 by grouping/GCF and state the technique called grouping.

   x^3 + x^2 = x^2(x + 1). Factoring by grouping pairs terms with common factors: e.g., ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y).

9. How do you simplify a rational expression?

   Factor the numerator and denominator completely, then cancel any common factors. E.g., (x^2 - 9)/(x + 3) = ((x+3)(x-3))/(x+3) = x - 3 (x ≠ -3).

10. What restriction must you keep in mind when simplifying rational expressions?

    The denominator can never equal zero, so any value making the original denominator zero is excluded from the domain even after canceling.

11. What does "substitution" / "evaluating an expression" mean?

    Replacing each variable with its given numerical value and then computing the result following order of operations (PEMDAS). E.g., for x=2, 3x^2 - 1 = 3(4) - 1 = 11.

12. List the order of operations (PEMDAS).

    Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

13. What are the steps to solve a single-variable linear equation?

    Simplify each side (distribute, combine like terms), move all variable terms to one side and constants to the other using inverse operations, then divide by the coefficient to isolate the variable.

14. How many solutions can a linear equation in one variable have?

    Exactly one solution normally; no solution if it reduces to a false statement (e.g., 0 = 5); infinitely many solutions if it reduces to a true identity (e.g., 0 = 0).

15. What are the two main algebraic methods for solving a system of two linear equations?

    Substitution (solve one equation for a variable and plug into the other) and elimination/combination (add or subtract scaled equations to cancel a variable).

16. How can you tell whether a 2x2 linear system has one, none, or infinitely many solutions?

    One solution if the lines intersect (different slopes); no solution if the lines are parallel (same slope, different intercepts); infinitely many if the equations are the same line (same slope and intercept).

17. What is the key rule when multiplying or dividing an inequality by a negative number?

    You must flip (reverse) the direction of the inequality sign. E.g., -2x < 6 becomes x > -3.

18. When does the inequality sign NOT flip while solving an inequality?

    When adding/subtracting any number to both sides, or multiplying/dividing both sides by a positive number. The sign only flips for multiplication/division by a negative.

19. How do you solve a compound inequality such as -3 < 2x + 1 ≤ 7?

    Perform the same operation on all three parts: subtract 1 to get -4 < 2x ≤ 6, then divide by 2 to get -2 < x ≤ 3.

20. How do you solve an absolute-value equation |x| = a (a > 0)?

    Split into two cases: x = a or x = -a. If a < 0 there is no solution; if a = 0 then x = 0.

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