SSAT (Secondary School Admission Test) Quantitative Reasoning: Number Sense and Arithmetic Syllabus

Quantitative Reasoning: Number Sense and Arithmetic 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: Number Sense and Arithmetic in SSAT (Secondary School Admission Test), not a summary of it.

1. 1

   Integers and the Number System

   5 topics

   • Place value and number representation
     • Reading and writing whole numbers and decimals
     • Expanded and standard form
     • Rounding and estimation strategies
   • Operations with signed integers
     • Adding and subtracting negatives on a number line
     • Multiplying and dividing signed numbers
     • Absolute value and distance
   • Order of operations (PEMDAS)
     • Nested grouping symbols
     • Common error patterns and traps
   • Properties of operations
     • Commutative and associative properties
     • Distributive property
     • Identity and inverse elements
   • Factors, multiples, and primes
     • Prime factorization
     • Greatest common factor (GCF)
     • Least common multiple (LCM)
     • Divisibility rules
2. 2

   Fractions, Decimals, and Percents

   5 topics

   • Equivalent fractions and simplification
     • Building and reducing fractions
     • Comparing and ordering fractions
   • Operations with fractions
     • Adding and subtracting with unlike denominators
     • Multiplying and dividing fractions
     • Mixed numbers and improper fractions
   • Decimal operations
     • Placement of the decimal point in multiplication and division
     • Terminating versus repeating decimals
   • Converting among fractions, decimals, and percents
     • Benchmark conversions to memorize
   • Percent applications
     • Percent of a number
     • Percent increase and decrease
     • Finding the whole from a part
3. 3

   Ratios, Proportions, and Rates

   5 topics

   • Writing and simplifying ratios
     • Part-to-part versus part-to-whole
     • Three-term ratios
   • Setting up and solving proportions
     • Cross multiplication
     • Scaling recipes and quantities
   • Unit rates and unit pricing
     • Comparing best buys
   • Speed, distance, and time problems
   • Scale drawings and maps
4. 4

   Powers, Roots, and Scientific Notation

   4 topics

   • Exponent rules
     • Product and quotient of powers
     • Power of a power
     • Zero and negative exponents
   • Square roots and perfect squares
     • Estimating non-perfect square roots
   • Cube roots and higher roots
   • Scientific notation
     • Converting to and from standard form
     • Multiplying and dividing in scientific notation

Quantitative Reasoning: Number Sense and Arithmetic flashcards for SSAT (Secondary School Admission Test)

21 of 50 cards from the Quantitative Reasoning: Number Sense and Arithmetic deck — real questions with worked answers.

1. In the number $4{,}728$, what is the place value of the digit $7$?

   It is in the hundreds place, so its value is $7 \times 100 = 700$.

2. Write the number $6{,}040{,}000$ in expanded form using place values.

   $6{,}000{,}000 + 40{,}000 = (6 \times 10^{6}) + (4 \times 10^{4})$.

3. What is the rule for adding two integers that have different signs?

   Subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value. Example: $-8 + 3 = -5$.

4. What is the rule for the sign of a product or quotient of two integers?

   Same signs give a positive result; different signs give a negative result. Example: $(-6)\times(-4)=24$ and $(-6)\div 2 = -3$.

5. Compute $-7 - (-12)$.

   Subtracting a negative is adding its opposite: $-7 + 12 = 5$.

6. What does the acronym PEMDAS stand for in order of operations?

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

7. Evaluate $3 + 4 \times 2^{2} - 6 \div 3$ using PEMDAS.

   Exponent: $2^{2}=4$. Then $3 + 4\times 4 - 6\div 3 = 3 + 16 - 2 = 17$.

8. In order of operations, how do you handle multiplication and division when both appear?

   They have equal priority, so evaluate them from left to right in the order they appear, not multiplication first.

9. State the commutative, associative, and distributive properties of operations.

   Commutative: $a+b=b+a$ and $ab=ba$. Associative: $(a+b)+c=a+(b+c)$. Distributive: $a(b+c)=ab+ac$.

10. What is the identity element for addition and the identity element for multiplication?

    The additive identity is $0$ (since $a+0=a$); the multiplicative identity is $1$ (since $a\times 1 = a$).

11. What is a factor of a number, and what is a multiple of a number?

    A factor divides the number evenly with no remainder (e.g., $4$ is a factor of $12$). A multiple is the product of the number and an integer (e.g., $12$ is a multiple of $4$).

12. 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 $2$.

13. Write the prime factorization of $60$.

    $60 = 2^{2} \times 3 \times 5$.

14. 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 positive number that both divide into. For $12$ and $18$: GCF $=6$, LCM $=36$.

15. How do you create a fraction equivalent to a given fraction?

    Multiply (or divide) the numerator and denominator by the same nonzero number. Example: $\frac{2}{3} = \frac{2\times 4}{3\times 4} = \frac{8}{12}$.

16. How do you simplify a fraction to lowest terms?

    Divide the numerator and denominator by their GCF. Example: $\frac{18}{24} = \frac{18\div 6}{24\div 6} = \frac{3}{4}$.

17. What is the procedure for adding fractions with unlike denominators?

    Find a common denominator (the LCD), rewrite each fraction with it, add the numerators, and simplify. Example: $\frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{5}{12}$.

18. How do you multiply two fractions and how do you divide by a fraction?

    Multiply: numerator times numerator over denominator times denominator. Divide: multiply by the reciprocal of the second fraction. Example: $\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}=\frac{5}{6}$.

19. How do you convert the mixed number $3\frac{2}{5}$ to an improper fraction?

    Multiply the whole number by the denominator and add the numerator: $\frac{3\times 5 + 2}{5} = \frac{17}{5}$.

20. When adding or subtracting decimals, what is the key alignment rule?

    Line up the decimal points (and the place values) vertically, filling in zeros as needed, then add or subtract. Example: $2.50 + 1.07 = 3.57$.

21. How do you place the decimal point when multiplying decimals, e.g. $0.3 \times 0.04$?

    Multiply as whole numbers, then give the product the total number of decimal places from both factors. $3\times 4 = 12$ with $1+2 = 3$ decimal places, so $0.3\times 0.04 = 0.012$.

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