PMA Graduate Course 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 PMA Graduate Course, not a summary of it.

1. 1

   Arithmetic

   4 topics

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

   Percentages and Averages

   2 topics

   • Percentage Calculations
   • Averages
3. 3

   Profit, Loss and Interest

   3 topics

   • Profit and Loss
   • Simple Interest
   • Compound Interest
4. 4

   Algebra

   3 topics

   • Linear Equations
   • Algebraic Expressions
   • Factorization
5. 5

   Geometry and Mensuration

   3 topics

   • Angles and Triangles
   • Area and Perimeter
   • Volume of Solids
6. 6

   Time, Speed and Work

   2 topics

   • Time and Distance
   • Time and Work

Mathematics flashcards for PMA Graduate Course

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

1. What is the difference between a natural number and a whole number?

   Natural numbers are the counting numbers starting from 1 (1, 2, 3, ...). Whole numbers include all natural numbers plus 0 (0, 1, 2, 3, ...).

2. Define a prime number and give the smallest prime.

   A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. The smallest prime number is 2 (also the only even prime).

3. What is a composite number?

   A composite number is a natural number greater than 1 that has more than two factors, i.e., it is divisible by numbers other than 1 and itself (e.g., 4, 6, 9).

4. How do rational numbers differ from irrational numbers?

   A rational number can be written as a fraction p/q where q is not 0 (e.g., 1/2, 0.75). An irrational number cannot be expressed as such a fraction and has a non-terminating, non-repeating decimal (e.g., pi, sqrt(2)).

5. State the divisibility rule for 3.

   A number is divisible by 3 if the sum of its digits is divisible by 3 (e.g., 123: 1+2+3=6, divisible by 3).

6. State the divisibility rule for 9.

   A number is divisible by 9 if the sum of its digits is divisible by 9 (e.g., 729: 7+2+9=18, divisible by 9).

7. 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.

8. Define the HCF (Highest Common Factor) of two numbers.

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

9. Define the LCM (Least Common Multiple) of two numbers.

   The LCM is the smallest number that is exactly divisible by each of the given numbers (the smallest common multiple).

10. What is the relationship between the HCF and LCM of two numbers?

    For two numbers a and b: HCF x LCM = a x b. Thus the product of two numbers equals the product of their HCF and LCM.

11. How do you find the LCM of fractions?

    LCM of fractions = LCM of the numerators / HCF of the denominators.

12. How do you find the HCF of fractions?

    HCF of fractions = HCF of the numerators / LCM of the denominators.

13. What is the difference between a proper and an improper fraction?

    In a proper fraction the numerator is less than the denominator (value < 1, e.g., 3/5). In an improper fraction the numerator is greater than or equal to the denominator (value >= 1, e.g., 7/4).

14. How do you convert an improper fraction to a mixed number?

    Divide the numerator by the denominator; the quotient is the whole part, the remainder becomes the new numerator, and the denominator stays the same (e.g., 7/4 = 1 3/4).

15. How do you multiply two fractions?

    Multiply the numerators together and the denominators together: (a/b) x (c/d) = (a x c)/(b x d), then simplify.

16. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second: (a/b) / (c/d) = (a/b) x (d/c).

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

    Divide the numerator by the denominator (e.g., 3/4 = 3 divided by 4 = 0.75).

18. How do you convert the recurring decimal 0.333... to a fraction?

    0.333... (repeating 3) equals 1/3. A single repeating digit over 9: 0.bar(d) = d/9.

19. Define a ratio.

    A ratio is a comparison of two quantities of the same kind by division, written as a:b or a/b, showing how many times one quantity contains the other.

20. What does it mean for four quantities to be in proportion?

    Four quantities a, b, c, d are in proportion (a:b :: c:d) when a/b = c/d, i.e., the two ratios are equal.

21. State the rule of cross-multiplication in a proportion a:b = c:d.

    The product of the means equals the product of the extremes: a x d = b x c.

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