SAT (Scholastic Assessment 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 SAT (Scholastic Assessment Test), not a summary of it.

1. 1

   Linear Equations in One Variable

   4 topics

   • Solving multi-step linear equations
     • Distributing and combining like terms
     • Variables on both sides
   • Equations with no solution or infinite solutions
     • Identifying contradictions
     • Identifying identities
   • Solving for a variable in a formula
     • Literal equations
   • Translating word problems into equations
2. 2

   Linear Functions and Graphs

   4 topics

   • Slope and rate of change
     • Slope formula
     • Interpreting slope in context
   • Forms of linear equations
     • Slope-intercept form
     • Standard and point-slope form
   • Interpreting intercepts in context
     • Meaning of x- and y-intercepts
   • Writing equations from points or graphs
3. 3

   Systems of Linear Equations

   4 topics

   • Solving by substitution
   • Solving by elimination
   • Number of solutions of a system
     • Parallel lines, no solution
     • Coincident lines, infinite solutions
   • Systems from word problems
4. 4

   Linear Inequalities

   4 topics

   • Solving one-variable inequalities
     • Flipping the sign when multiplying by negatives
   • Graphing inequalities in two variables
     • Boundary lines and shading
   • Systems of inequalities
     • Feasible region
   • Modeling constraints with inequalities

Math: Algebra flashcards for SAT (Scholastic Assessment Test)

24 of 49 cards from the Math: Algebra deck — real questions with worked answers.

1. What is the first goal when solving a multi-step linear equation?

   Isolate the variable: simplify each side (distribute, combine like terms), then use inverse operations to undo addition/subtraction, then multiplication/division.

2. To solve a linear equation with the variable on both sides, what is the key step?

   Move all variable terms to one side and all constants to the other (by adding/subtracting), then divide by the variable's coefficient.

3. How do you handle fractions in a multi-step linear equation?

   Multiply every term on both sides by the least common denominator (LCD) to clear the fractions, then solve normally.

4. Solve: 3(x - 4) = 2x + 5

   3x - 12 = 2x + 5, so x = 17.

5. When does a linear equation have NO solution?

   When the variables cancel and you are left with a false statement (e.g., 0 = 5). The lines are parallel (same slope, different intercepts).

6. When does a linear equation have INFINITELY many solutions?

   When the variables cancel and you are left with a true statement (e.g., 0 = 0). Both sides are identical (same line).

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

   a ≠ c (the coefficients of x are different).

8. In c(x + m) = dx + n, what makes it have infinitely many solutions?

   The equations must be identical after simplifying: the x-coefficients are equal AND the constants are equal (c = d and cm = n).

9. What does 'solving for a variable in a formula' (literal equation) mean?

   Isolating one specified variable in terms of all the others, treating the other letters as constants.

10. Solve the formula A = (1/2)bh for h.

    h = 2A/b.

11. Solve d = rt for the rate r.

    r = d/t.

12. Solve F = (9/5)C + 32 for C.

    C = (5/9)(F - 32).

13. When translating word problems, how is 'is/equals' represented, and 'of'?

    'Is/are/equals' becomes the = sign; 'of' usually means multiplication.

14. How do you translate 'a number increased by 7' and '5 less than a number'?

    Increased by 7: x + 7. Five less than a number: x - 5 (the order is reversed).

15. Translate: 'Twice a number decreased by 9 equals 15.'

    2x - 9 = 15.

16. How do you model a total-cost word problem with a flat fee plus a per-unit rate?

    Total = (rate per unit)(number of units) + flat fee, i.e., y = mx + b where b is the fixed fee and m is the per-unit cost.

17. What is the definition of slope?

    The rate of change of y with respect to x: slope = rise/run = change in y divided by change in x.

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

    m = (y2 - y1)/(x2 - x1).

19. What is the slope of a horizontal line and of a vertical line?

    Horizontal line: slope = 0. Vertical line: slope is undefined.

20. In a real-world linear model, what does the slope represent?

    The rate of change — the amount y changes for each one-unit increase in x (e.g., dollars per hour).

21. What are the slopes of parallel lines and of perpendicular lines?

    Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (product = -1).

22. State slope-intercept form and what each letter means.

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

23. State point-slope form of a line.

    y - y1 = m(x - x1), using slope m and a point (x1, y1) on the line.

24. State standard form of a linear equation.

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

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