SSAT (Secondary School Admission Test) Quantitative Reasoning: Algebra and Functions Syllabus

Quantitative Reasoning: Algebra and Functions 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 and Functions in SSAT (Secondary School Admission Test), not a summary of it.

1. 1

   Algebraic Expressions

   4 topics

   • Variables and translating words into expressions
     • Keyword-to-operation mapping
   • Evaluating expressions by substitution
   • Combining like terms
   • The distributive property in expressions
     • Factoring out a common factor
2. 2

   Linear Equations and Inequalities

   4 topics

   • Solving one-step and two-step equations
   • Multi-step equations with variables on both sides
   • Solving and graphing inequalities
     • Reversing the sign when multiplying or dividing by a negative
     • Number-line representation
   • Setting up equations from word problems
     • Age, money, and mixture problems
3. 3

   Coordinate Geometry and Graphs

   5 topics

   • The coordinate plane and plotting points
     • Quadrants and axes
   • Slope of a line
     • Rise over run
     • Positive, negative, zero, and undefined slope
   • Slope-intercept form and graphing lines
   • Distance and midpoint between points
   • Interpreting graphs and trends
4. 4

   Patterns, Sequences, and Functions

   4 topics

   • Arithmetic sequences and common difference
   • Geometric sequences and common ratio
   • Identifying and extending number patterns
   • Function tables and input-output rules

Quantitative Reasoning: Algebra and Functions flashcards for SSAT (Secondary School Admission Test)

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

1. What is a variable in algebra?

   A variable is a letter or symbol (like $x$ or $n$) that represents an unknown or changing number.

2. Translate into an algebraic expression: "7 more than a number $n$."

   $n + 7$

3. Translate into an algebraic expression: "5 less than twice a number $x$."

   $2x - 5$

4. What operation do the words "product," "times," and "of" usually signal when translating words to expressions?

   Multiplication.

5. What operation do the words "difference," "less than," and "decreased by" signal?

   Subtraction. (Note: "$5$ less than $x$" reverses order to $x - 5$.)

6. Evaluate $3x + 4$ when $x = 5$.

   $3(5) + 4 = 15 + 4 = 19$

7. Evaluate $x^{2} - 2x$ when $x = 4$.

   $4^{2} - 2(4) = 16 - 8 = 8$

8. What does it mean to evaluate an expression by substitution?

   Replace each variable with its given numerical value, then simplify using the order of operations (PEMDAS).

9. What are "like terms"?

   Terms that have the exact same variable(s) raised to the exact same power(s), such as $3x$ and $7x$, or $2y^{2}$ and $-5y^{2}$.

10. Combine like terms: $4x + 7 + 2x - 3$.

    $6x + 4$

11. Can $5x$ and $5x^{2}$ be combined as like terms?

    No. They have different powers of $x$, so they are not like terms.

12. State the distributive property.

    $a(b + c) = ab + ac$

13. Use the distributive property to expand $3(x + 4)$.

    $3x + 12$

14. Expand $-2(3x - 5)$.

    $-6x + 10$

15. What is the goal when solving an equation?

    To isolate the variable on one side, finding the value that makes the equation true, by applying inverse operations to both sides.

16. Solve the one-step equation $x + 9 = 15$.

    $x = 6$ (subtract $9$ from both sides).

17. Solve the one-step equation $\frac{x}{4} = 7$.

    $x = 28$ (multiply both sides by $4$).

18. Solve the two-step equation $2x + 5 = 17$.

    $2x = 12$, so $x = 6$.

19. What is the general process for solving a two-step equation?

    First undo addition/subtraction, then undo multiplication/division, applying inverse operations to both sides.

20. Solve the multi-step equation $5x - 3 = 2x + 9$ (variables on both sides).

    $3x = 12$, so $x = 4$ (subtract $2x$, add $3$, divide by $3$).

21. When solving equations with variables on both sides, what is the first strategic step?

    Move all variable terms to one side and all constant terms to the other side by adding/subtracting equal amounts.

22. What are the four inequality symbols and their meanings?

    $<$ less than, $>$ greater than, $\leq$ less than or equal to, $\geq$ greater than or equal to.

23. What special rule applies when solving inequalities?

    When you multiply or divide both sides by a negative number, you must reverse (flip) the inequality sign.

24. Solve the inequality $-3x < 12$.

    $x > -4$ (divide by $-3$ and flip the sign).

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