Navy Sailor Test Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in Navy Sailor Test, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number System
   • Fractions and Decimals
   • HCF and LCM
   • Ratio and Proportion
2. 2

   Commercial Mathematics

   4 topics

   • Percentage
   • Profit and Loss
   • Simple and Compound Interest
   • Average
3. 3

   Algebra

   4 topics

   • Algebraic Expressions
   • Factorization
   • Linear Equations
   • Algebraic Formulas
4. 4

   Geometry and Mensuration

   4 topics

   • Lines and Angles
   • Triangles and Circles
   • Area and Perimeter
   • Volume and Surface Area
5. 5

   Quantitative Aptitude

   3 topics

   • Time and Work
   • Time, Speed and Distance
   • Unitary Method

Mathematics flashcards for Navy Sailor Test

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

1. What is a natural number, and what is the smallest natural number?

   Natural numbers are the counting numbers 1, 2, 3, 4, ... The smallest natural number is 1.

2. What are whole numbers, and how do they differ from natural numbers?

   Whole numbers are 0, 1, 2, 3, ... They include all natural numbers plus 0. The smallest whole number is 0.

3. Define a prime number and give the only even prime number.

   A prime number has exactly two distinct factors: 1 and itself (e.g., 2, 3, 5, 7, 11). The only even prime number is 2.

4. What is a composite number? Give an example.

   A composite number has more than two factors (it is divisible by numbers other than 1 and itself), e.g., 4, 6, 8, 9. The number 1 is neither prime nor composite.

5. What is the difference between rational and irrational numbers?

   A rational number can be written as p/q where p and q are integers and q is not 0 (e.g., 1/2, 0.75). An irrational number cannot be expressed as such a fraction (e.g., pi, the square root of 2).

6. State the divisibility rule for 3 and for 9.

   A number is divisible by 3 if the sum of its digits is divisible by 3. It is divisible by 9 if the sum of its digits is divisible by 9.

7. State the divisibility rules for 4 and 8.

   A number is divisible by 4 if its last two digits form a number divisible by 4. It is divisible by 8 if its last three digits form a number divisible by 8.

8. State the divisibility rule for 11.

   A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

9. What is a proper fraction versus an improper fraction?

   A proper fraction has a numerator smaller than its denominator (e.g., 3/5). An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4).

10. How do you convert a fraction to a decimal, and what is a recurring decimal?

    Divide the numerator by the denominator. A recurring (repeating) decimal has one or more digits that repeat endlessly, e.g., 1/3 = 0.333... = 0.3 with a bar.

11. How do you add or subtract two fractions with different denominators?

    Find the LCM of the denominators to get a common denominator, convert both fractions to equivalent fractions with that denominator, then add or subtract the numerators.

12. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second. For example, (a/b) divided by (c/d) = (a/b) x (d/c).

13. Define HCF (Highest Common Factor).

    The HCF (also called GCD) of two or more numbers is the largest number that divides each of them exactly without leaving a remainder.

14. Define LCM (Least Common Multiple).

    The LCM of two or more numbers is the smallest number that is a multiple of each of them (the smallest number exactly divisible by all of them).

15. State the relationship between HCF and LCM of two numbers.

    For two numbers, HCF x LCM = product of the two numbers. So LCM = (a x b) / HCF.

16. How do you find HCF using the prime factorization method?

    Express each number as a product of prime factors, then multiply the common prime factors taken with their lowest (smallest) powers.

17. How do you find LCM using the prime factorization method?

    Express each number as a product of prime factors, then multiply all prime factors taken with their highest (greatest) powers.

18. What is a ratio, and how is the ratio a:b expressed as a fraction?

    A ratio compares two quantities of the same kind by division. The ratio a:b is expressed as the fraction a/b, where a is the antecedent and b is the consequent.

19. What is a proportion, and what is the rule of cross-multiplication?

    A proportion states two ratios are equal: a:b = c:d. By cross-multiplication, a x d = b x c (product of extremes equals product of means).

20. In the proportion a:b = c:d, what are the means and extremes?

    The extremes are the outer terms a and d; the means are the inner terms b and c.

21. What is the difference between direct proportion and inverse proportion?

    In direct proportion, as one quantity increases the other increases (x/y is constant). In inverse proportion, as one increases the other decreases (x times y is constant).

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