ISEE (Independent School Entrance Examination) Mathematics Achievement Syllabus

Mathematics Achievement syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics Achievement in ISEE (Independent School Entrance Examination), not a summary of it.

1. 1

   Numbers and Operations

   5 topics

   • Whole Numbers and Integers
     • Place value and number lines
     • Operations with positive and negative integers
   • Fractions and Decimals
     • Equivalence, comparison, and ordering
     • Four operations with fractions and decimals
     • Converting among fractions, decimals, and percents
   • Ratios, Proportions, and Percents
     • Setting up and solving proportions
     • Percent increase, decrease, and of-a-number
   • Factors, Multiples, and Primes
     • GCF and LCM
     • Prime factorization
     • Divisibility rules
   • Exponents and Roots
     • Powers and exponent rules
     • Square roots and perfect squares
     • Scientific notation (Upper Level)
2. 2

   Algebraic Concepts

   4 topics

   • Expressions and Variables
     • Evaluating and simplifying expressions
     • Combining like terms and the distributive property
   • Equations and Inequalities
     • Solving one- and two-step equations
     • Solving and graphing inequalities
   • Linear Relationships (Upper Level)
     • Slope and intercepts
     • Graphing lines and interpreting equations
   • Polynomials and Factoring (Upper Level)
     • Multiplying binomials
     • Basic factoring techniques
3. 3

   Geometry

   4 topics

   • Plane Figures and Angles
     • Lines, rays, and angle relationships
     • Triangles, quadrilaterals, and polygons
   • Perimeter, Area, and Volume
     • Area and perimeter of 2D shapes
     • Surface area and volume of solids
     • Circumference and area of circles
   • Coordinate Geometry
     • Plotting points and quadrants
     • Distance and reflections on the grid
   • The Pythagorean Theorem (Upper Level)
     • Finding missing side lengths
     • Recognizing right-triangle applications
4. 4

   Measurement

   4 topics

   • Customary and metric units
   • Unit conversion within and between systems
   • Time, money, temperature, and rate problems
   • Reading scales and measurement tools
5. 5

   Data Analysis, Statistics, and Probability

   4 topics

   • Interpreting charts, graphs, and tables
   • Measures of central tendency and range
   • Simple and compound probability
   • Counting principles and basic combinations

Mathematics Achievement flashcards for ISEE (Independent School Entrance Examination)

19 of 50 cards from the Mathematics Achievement deck — real questions with worked answers.

1. What is the order of operations (PEMDAS) for evaluating an arithmetic expression?

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

2. What is an integer, and what numbers does the set of integers include?

   An integer is a whole number with no fractional part. The set includes all positive whole numbers, all negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...).

3. What are the rules for the sign of a product or quotient of two nonzero numbers?

   Same signs give a positive result; different signs give a negative result. (e.g., negative times negative = positive; negative times positive = negative.)

4. How do you add two integers with different signs?

   Subtract the smaller absolute value from the larger absolute value, then keep the sign of the number with the larger absolute value.

5. What is the absolute value of a number?

   Its distance from zero on the number line, always nonnegative. For example, |-7| = 7 and |7| = 7.

6. How do you add or subtract fractions that have different denominators?

   Find a common denominator (often the least common denominator), rewrite each fraction with that denominator, then add or subtract the numerators and keep the denominator.

7. How do you multiply two fractions, and how do you divide one fraction by another?

   To multiply, multiply numerators together and denominators together. To divide, multiply the first fraction by the reciprocal of the second (flip the divisor).

8. How do you convert a fraction to a decimal?

   Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.

9. How do you convert a terminating decimal to a fraction?

   Write the decimal over a power of 10 matching the number of decimal places, then simplify. For example, 0.35 = 35/100 = 7/20.

10. What is a ratio, and what does the proportion a/b = c/d allow you to do?

    A ratio is a comparison of two quantities by division. A proportion states two ratios are equal; you can solve it by cross-multiplying: a·d = b·c.

11. How do you convert a percent to a decimal and a decimal to a percent?

    To convert a percent to a decimal, divide by 100 (move the decimal two places left). To convert a decimal to a percent, multiply by 100 (move two places right).

12. How do you find a given percent of a number?

    Convert the percent to a decimal and multiply by the number. For example, 20% of 50 = 0.20 × 50 = 10.

13. How do you calculate percent increase or percent decrease?

    Percent change = (change in amount ÷ original amount) × 100. Use the difference between new and original values as the change.

14. What is the difference between a factor and a multiple of a number?

    A factor divides the number evenly (e.g., factors of 12: 1,2,3,4,6,12). A multiple is the number times an integer (e.g., multiples of 12: 12,24,36,...).

15. What is a prime number, and what is the only even prime?

    A prime number has exactly two distinct factors: 1 and itself. The only even prime number is 2.

16. What is the prime factorization of a number?

    Expressing the number as a product of prime numbers. For example, 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.

17. What is the difference between the GCF and the LCM of two numbers?

    The GCF (greatest common factor) is the largest number that divides both. The LCM (least common multiple) is the smallest number that both divide into.

18. What does a positive exponent mean, as in a^n?

    It means multiply the base a by itself n times. For example, 2^4 = 2 × 2 × 2 × 2 = 16.

19. What are the product and quotient rules for exponents with the same base?

    Product rule: a^m × a^n = a^(m+n). Quotient rule: a^m ÷ a^n = a^(m−n).

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