ISEE (Independent School Entrance Examination) Quantitative Reasoning Syllabus

Quantitative Reasoning 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 in ISEE (Independent School Entrance Examination), not a summary of it.

1. 1

   Word Problems and Logical Reasoning

   4 topics

   • Translating Words into Math
     • Keyword-to-operation mapping
     • Setting up equations from situations
   • Multi-Step Reasoning Problems
     • Ordering steps efficiently
     • Working backward from answer choices
   • Patterns and Sequences
     • Arithmetic and visual patterns
     • Finding rules and next terms
   • Logic Without Computation
     • Reasoning about relationships and inequalities
     • Estimating to eliminate answers
2. 2

   Quantitative Comparisons (Middle and Upper Levels)

   3 topics

   • Quantitative Comparison Format
     • Column A versus Column B structure
     • The four fixed answer choices (greater, less, equal, cannot be determined)
   • Comparison Strategies
     • Manipulating both columns equally
     • Plugging in numbers including 0, 1, negatives, and fractions
   • Cannot-Be-Determined Recognition
     • Detecting variable ranges that change the result
     • Avoiding assumptions about figures
3. 3

   Data Interpretation and Probability

   5 topics

   • Reading bar graphs, line graphs, and pie charts
   • Tables, pictographs, and frequency data
   • Mean, median, mode, and range
   • Basic probability and likelihood
   • Drawing conclusions from data sets
4. 4

   Estimation and Number Sense

   3 topics

   • Rounding and approximation strategies
   • Reasonableness of answers
   • Mental math for speed

Quantitative Reasoning flashcards for ISEE (Independent School Entrance Examination)

25 of 71 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. In word problems, which words signal addition?

   Sum, total, plus, increased by, more than, combined, and together all signal addition.

2. In word problems, which words signal subtraction?

   Difference, less than, decreased by, fewer, minus, reduced by, and 'take away' signal subtraction.

3. When translating 'less than' or 'fewer than' into math, what order trap must you avoid?

   You must reverse the order: '5 less than x' means x - 5, NOT 5 - x.

4. Which words signal multiplication in word problems?

   Product, times, of, twice, double, triple, and 'per' (in rate setups) signal multiplication.

5. Which words signal division in word problems?

   Quotient, per, divided by, ratio, split equally, and 'out of' signal division.

6. How do you translate 'the product of a number and 7 is 42' into an equation?

   7n = 42.

7. What does the word 'is' usually translate to in a word problem?

   'Is' translates to an equals sign (=).

8. How do you translate '8 more than twice a number' into an expression?

   2n + 8.

9. What is the recommended first step for a multi-step word problem?

   Identify exactly what is being asked and define a variable for the unknown before doing any computation.

10. In a multi-step problem, why should you 'work in stages'?

    Each intermediate result becomes the input for the next step; solving one piece at a time prevents errors and keeps the logic clear.

11. A shirt costs $20 and is marked up 25%, then put on sale for 20% off. What is the final price?

    $20 x 1.25 = $25, then $25 x 0.80 = $20.

12. What is a common multi-step trap with 'how many are left' problems?

    You must complete all the in-between operations (additions and removals) before subtracting, not just the last number given.

13. In an arithmetic sequence, how do you find the next term?

    Add the common difference (the constant amount each term increases or decreases by) to the previous term.

14. In a geometric sequence, how do you find the next term?

    Multiply the previous term by the common ratio (the constant multiplier).

15. What are the next two terms: 3, 6, 12, 24, ...?

    48 and 96 (each term is multiplied by 2; it is geometric with ratio 2).

16. What are the next two terms: 2, 5, 8, 11, ...?

    14 and 17 (arithmetic with common difference 3).

17. How do you find the common difference of an arithmetic sequence?

    Subtract any term from the term that follows it (later term minus earlier term).

18. What kind of pattern is 1, 4, 9, 16, 25, ...?

    Perfect squares (1², 2², 3², 4², 5²); the next term is 36.

19. What is the strategy for a repeating-pattern problem like 'the 50th shape in ABCABC...'?

    Divide the position number by the cycle length and use the remainder to find which item in the cycle it is.

20. In the repeating pattern ABCABC..., what is the 50th letter?

    50 divided by 3 leaves remainder 2, so it is the 2nd letter, B.

21. What does 'logic without computation' mean on the ISEE?

    Using reasoning about size, sign, or relationships to reach an answer without performing the full arithmetic.

22. Without computing, is the product of two numbers each greater than 1 larger or smaller than either factor?

    Larger than either factor.

23. Without calculating, what happens to a positive number when you multiply it by a fraction between 0 and 1?

    The result gets smaller than the original number.

24. Without calculating, what happens to a number when you divide it by a fraction between 0 and 1?

    The result gets larger than the original number.

25. What two quantities are compared in the ISEE Quantitative Comparison format?

    Column A and Column B; you decide which is greater, if they are equal, or if it cannot be determined.

See more Quantitative Reasoning flashcards →

Planning Quantitative Reasoning for ISEE (Independent School Entrance Examination)

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