CMA Foundation Fundamentals of Business Mathematics and Statistics Syllabus

Fundamentals of Business Mathematics and Statistics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Fundamentals of Business Mathematics and Statistics in CMA Foundation, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Ratio and Proportion
   • Percentage
   • Simple and Compound Interest
   • Profit and Loss
2. 2

   Algebra

   3 topics

   • Indices
   • Logarithms
   • Linear and Quadratic Equations
3. 3

   Mensuration

   2 topics

   • Area and Perimeter of Plane Figures
   • Volume and Surface Area of Solid Figures
4. 4

   Statistics

   6 topics

   • Introduction to Statistics
   • Collection and Presentation of Data
   • Measures of Central Tendency
   • Measures of Dispersion
   • Correlation and Regression
   • Index Numbers
5. 5

   Probability

   2 topics

   • Basic Concepts of Probability
   • Probability Distributions

Fundamentals of Business Mathematics and Statistics flashcards for CMA Foundation

25 of 55 cards from the Fundamentals of Business Mathematics and Statistics deck — real questions with worked answers.

1. What is a ratio, and what is the difference between a ratio and a proportion?

   A ratio is a comparison of two quantities of the same kind by division, written a:b. A proportion is a statement that two ratios are equal, written a:b = c:d (or a:b::c:d).

2. In the proportion a:b = c:d, what is the rule for the product of means and extremes?

   Product of extremes = product of means, i.e., a x d = b x c (the cross-product rule).

3. Define duplicate ratio, sub-duplicate ratio, and inverse ratio of a:b.

   Duplicate ratio = a^2:b^2. Sub-duplicate ratio = sqrt(a):sqrt(b). Inverse (reciprocal) ratio = b:a.

4. What does the percentage 'per cent' mean, and how do you convert a fraction to a percentage?

   Per cent means 'per hundred'. To convert a fraction to a percentage, multiply it by 100, e.g., 3/4 = (3/4) x 100 = 75%.

5. How do you calculate percentage increase and percentage decrease?

   Percentage change = (Change in value / Original value) x 100. It is an increase if the new value is higher and a decrease if lower.

6. What is the formula for Simple Interest, and what does each symbol represent?

   SI = (P x R x T) / 100, where P = principal, R = rate of interest per annum (%), and T = time in years.

7. What is the formula for the amount under compound interest (interest compounded annually)?

   A = P(1 + R/100)^n, where P = principal, R = annual rate (%), n = number of years. Compound Interest = A - P.

8. How is the compound interest formula adjusted when interest is compounded k times per year?

   A = P(1 + R/(100k))^(kn), where k is the number of compounding periods per year (e.g., k=2 half-yearly, k=4 quarterly) and n is years.

9. Define Profit, Loss, and the base on which their percentages are calculated.

   Profit = Selling Price - Cost Price (when SP > CP); Loss = Cost Price - Selling Price (when CP > SP). Profit% and Loss% are calculated on the Cost Price.

10. State the formulas for Profit% and for finding SP from CP and Profit%.

    Profit% = (Profit/CP) x 100. SP = CP x (100 + Profit%)/100. For a loss, SP = CP x (100 - Loss%)/100.

11. In trading terms, what is 'marked price' and how does discount relate to it?

    Marked price (list price) is the price labelled before discount. Discount is a reduction on the marked price; Selling Price = Marked Price - Discount, and Discount% is calculated on the marked price.

12. State the basic laws of indices for multiplication, division, and power of a power.

    a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn).

13. What are the values of a^0 and a^(-n) (for a not equal to 0)?

    a^0 = 1, and a^(-n) = 1/a^n.

14. What does a fractional index a^(m/n) represent?

    a^(m/n) = the n-th root of a^m = (n-th root of a)^m, i.e., a^(m/n) = (a^m)^(1/n).

15. Define a logarithm: if a^x = N, how is x written in logarithmic form?

    x = log_a N (the logarithm of N to base a). The logarithm is the exponent to which the base must be raised to give the number.

16. State the three fundamental laws of logarithms (product, quotient, power).

    log(MN) = log M + log N; log(M/N) = log M - log N; log(M^p) = p log M (all to the same base).

17. What is the change of base formula for logarithms, and the values of log_a 1 and log_a a?

    Change of base: log_a N = log_b N / log_b a. Also log_a 1 = 0 and log_a a = 1.

18. What is the difference between common logarithms and natural logarithms?

    Common logarithms use base 10 (written log). Natural logarithms use base e (approximately 2.718), written ln or log_e.

19. What is the general form of a linear equation in one variable and a quadratic equation?

    Linear equation in one variable: ax + b = 0 (a not 0). Quadratic equation: ax^2 + bx + c = 0 (a not 0).

20. State the quadratic formula for solving ax^2 + bx + c = 0.

    x = [-b plus or minus sqrt(b^2 - 4ac)] / (2a).

21. What is the discriminant of a quadratic, and what does its sign tell about the roots?

    Discriminant D = b^2 - 4ac. If D > 0 roots are real and distinct; if D = 0 roots are real and equal; if D < 0 roots are imaginary (complex).

22. For ax^2 + bx + c = 0, what are the sum and product of the roots?

    Sum of roots = -b/a; Product of roots = c/a.

23. What are the formulas for the area and perimeter of a rectangle and a square?

    Rectangle: Area = length x breadth; Perimeter = 2(length + breadth). Square: Area = side^2; Perimeter = 4 x side.

24. State the formulas for the area of a triangle (base-height) and the circumference and area of a circle.

    Triangle area = (1/2) x base x height. Circle: Circumference = 2(pi)r; Area = (pi)r^2, where r is the radius.

25. What is Heron's formula for the area of a triangle with sides a, b, c?

    Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a + b + c)/2 is the semi-perimeter.

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