PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Algebra Syllabus

Math: Algebra syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Math: Algebra in PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test), not a summary of it.

1. 1

   Linear Equations in One Variable

   3 topics

   • Solving Single-Variable Linear Equations
     • Equations with variables on both sides
     • Equations with fractions and parentheses
   • Creating Linear Equations from Context
     • Translating word problems into equations
   • Equations with No or Infinite Solutions
     • Conditions for identity and contradiction
2. 2

   Linear Equations in Two Variables

   3 topics

   • Slope-Intercept and Standard Form
     • Interpreting slope and intercepts in context
     • Converting between forms
   • Graphing Lines
     • Plotting from equations and tables
     • Finding equations from graphs
   • Writing Linear Models
     • Modeling real-world linear relationships
3. 3

   Systems of Linear Equations

   3 topics

   • Solving by Substitution and Elimination
     • Choosing an efficient method
   • Number of Solutions of a System
     • Parallel, intersecting, and identical lines
   • Systems from Word Problems
     • Setting up two-equation models
4. 4

   Linear Inequalities

   3 topics

   • Solving One- and Two-Variable Inequalities
     • Flipping the inequality sign
   • Graphing Inequalities and Systems
     • Identifying solution regions
   • Inequalities in Context
     • Constraints and feasible values

Math: Algebra flashcards for PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test)

24 of 50 cards from the Math: Algebra deck — real questions with worked answers.

1. What is a single-variable linear equation?

   An equation that can be written as ax + b = 0, where the variable appears only to the first power and a ≠ 0; it has exactly one solution.

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

   1) Distribute and clear parentheses, 2) combine like terms on each side, 3) move variable terms to one side and constants to the other using addition/subtraction, 4) divide by the coefficient of the variable.

3. To solve a linear equation with fractions, what is the most efficient first step?

   Multiply both sides by the least common denominator (LCD) of all fractions to clear the denominators.

4. Solve: 3(x − 4) = 2x + 5.

   3x − 12 = 2x + 5, so x = 17.

5. When solving a literal equation for one variable in terms of others, what rule governs each step?

   Apply inverse operations to both sides (treat the target variable like the unknown), isolating it just as you would a number-only equation.

6. When translating a word problem into a linear equation, what does the phrase 'per' typically indicate?

   A constant rate, which becomes the coefficient (slope) multiplying the variable.

7. In a linear model, what does a fixed one-time amount (like a flat fee or starting value) become?

   The constant term (the y-intercept) of the equation.

8. A gym charges a $25 sign-up fee plus $15 per month. Write an equation for total cost C after m months.

   C = 15m + 25.

9. How do you find when two linear cost models are equal (a break-even point)?

   Set the two expressions equal to each other and solve for the variable.

10. Translate: 'five less than twice a number is 11' into an equation.

    2x − 5 = 11.

11. How can you tell a linear equation has NO solution?

    After simplifying, the variables cancel out and you get a false statement (e.g., 3 = 7).

12. How can you tell a linear equation has INFINITELY many solutions?

    After simplifying, the variables cancel out and you get a true statement (e.g., 5 = 5), meaning both sides are identical (an identity).

13. For ax + b = cx + d, what condition gives exactly one solution?

    a ≠ c (the coefficients of x differ).

14. For ax + b = cx + d, what conditions give no solution?

    a = c but b ≠ d (same slope, different constant).

15. For ax + b = cx + d, what conditions give infinitely many solutions?

    a = c and b = d (the two sides are identical).

16. In the equation 6x + 12 = a(2x + 4), what value of a creates infinitely many solutions?

    a = 3, because then both sides equal 6x + 12.

17. What is the slope-intercept form of a line?

    y = mx + b, where m is the slope and b is the y-intercept.

18. What is the standard form of a linear equation?

    Ax + By = C, where A, B, and C are constants (commonly integers, A ≥ 0).

19. How do you find the slope from standard form Ax + By = C?

    Slope = −A/B.

20. How do you find the y-intercept from standard form Ax + By = C?

    y-intercept = C/B (set x = 0).

21. What is the point-slope form of a line?

    y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is a point on the line.

22. What is the slope formula given two points (x₁, y₁) and (x₂, y₂)?

    m = (y₂ − y₁) / (x₂ − x₁).

23. What does the slope of a line represent in a real-world context?

    The constant rate of change—how much y changes for each one-unit increase in x.

24. What is the slope of a horizontal line, and what is its equation form?

    Slope = 0; equation is y = constant.

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