I.Com (Intermediate in Commerce) Principles of Business Mathematics Syllabus

Principles of Business Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Principles of Business Mathematics in I.Com (Intermediate in Commerce), not a summary of it.

1. 1

   Fundamental Operations

   3 topics

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

   Percentage, Profit and Loss

   3 topics

   • Percentage Calculations
   • Profit, Loss and Discount
   • Commission and Brokerage
3. 3

   Interest

   3 topics

   • Simple Interest
   • Compound Interest
   • Present and Future Value
4. 4

   Equations

   3 topics

   • Linear Equations
   • Quadratic Equations
   • Simultaneous Equations
5. 5

   Matrices and Determinants

   3 topics

   • Types of Matrices
   • Operations on Matrices
   • Determinants and Their Applications
6. 6

   Sequences and Series

   2 topics

   • Arithmetic Progression
   • Geometric Progression
7. 7

   Mathematics of Finance

   2 topics

   • Annuities
   • Depreciation Methods
8. 8

   Sets and Logarithms

   2 topics

   • Sets and Set Operations
   • Logarithms and Their Use in Calculations

Principles of Business Mathematics flashcards for I.Com (Intermediate in Commerce)

18 of 50 cards from the Principles of Business Mathematics deck — real questions with worked answers.

1. What are natural numbers, 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 differ from natural numbers by including 0.

3. Define a rational number and give the form it can be written in.

   A rational number is any number expressible as p/q where p and q are integers and q is not equal to 0. Examples: 3/4, -5, 0.25.

4. What is an irrational number? Give two examples.

   An irrational number cannot be written as p/q; its decimal expansion is non-terminating and non-repeating. Examples: square root of 2, and pi.

5. Distinguish between prime numbers and composite numbers.

   A prime number has exactly two factors: 1 and itself (e.g., 2, 3, 5, 7). A composite number has more than two factors (e.g., 4, 6, 8, 9). Note: 1 is neither prime nor composite.

6. State the commutative, associative, and distributive laws of real numbers.

   Commutative: a+b=b+a, ab=ba. Associative: (a+b)+c=a+(b+c), (ab)c=a(bc). Distributive: a(b+c)=ab+ac.

7. What is the order of operations (BODMAS/PEMDAS) for evaluating expressions?

   Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

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

   Divide the numerator by the denominator. Example: 3/4 = 3 divided by 4 = 0.75.

9. What is the procedure to add or subtract fractions with unlike denominators?

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

10. How do you multiply and divide two fractions?

    Multiply: multiply numerators together and denominators together (a/b x c/d = ac/bd). Divide: multiply the first fraction by the reciprocal of the second (a/b divided by c/d = a/b x d/c).

11. What is the difference between a proper fraction, an improper fraction, and a mixed number?

    Proper fraction: numerator less than denominator (3/5). Improper fraction: numerator greater than or equal to denominator (7/4). Mixed number: a whole number plus a proper fraction (1 3/4).

12. How do you convert a recurring decimal such as 0.333... into a fraction?

    Let x = 0.333..., then 10x = 3.333...; subtract to get 9x = 3, so x = 3/9 = 1/3.

13. Define a ratio and state how the ratio a:b is written as a fraction.

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

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

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

15. How do you find the fourth proportional to three numbers a, b, c?

    In a:b = c:x, the fourth proportional x = (b x c)/a.

16. What is the mean proportional (geometric mean) between two numbers a and b?

    The mean proportional between a and b is the square root of (a x b), since a:x = x:b gives x squared = ab.

17. Distinguish between direct proportion and inverse proportion.

    Direct proportion: as one quantity increases, the other increases in the same ratio (y = kx). Inverse proportion: as one increases, the other decreases (xy = k, or y = k/x).

18. What is a percentage, and how do you convert a fraction to a percentage?

    A percentage is a fraction or ratio expressed out of 100. To convert a fraction to a percentage, multiply it by 100. Example: 3/4 x 100 = 75%.

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