CAMS Level I

Fundamentals of Business Mathematics flashcards

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What is the difference between mark-up and margin?

Both start from the same profit (selling price - cost price). Mark-up = profit / cost price x 100. Margin = profit / selling price x 100. Cost KES 2,000, price KES 2,500: profit 500, mark-up 25%, margin 20%. The two are never equal except when profit is zero.

What is the difference between a ratio, a rate and a proportion?

Ratio: compares quantities of the same kind, written a:b (cement to sand 2:3). Rate: compares quantities in different units as a single value (80 km per hour, KES per US dollar). Proportion: a statement that two ratios are equal, a:b = c:d, used to find a missing value.

What does BODMAS stand for, and why does it matter?

Brackets, Orders, Division and Multiplication, Addition and Subtraction. It fixes the order operations run in, so an expression always has one unambiguous value. Example: 5 + 3 x (7 - 4)² = 5 + 3 x 9 = 5 + 27 = 32.

How do simple interest and compound interest differ, and what are their formulas?

Simple interest is earned on the original principal only: I = PRT, A = P(1 + RT). Compound interest is also earned on interest already added: A = P(1 + r/m)^(mt), where m is the number of compounding periods per year.

How are the mean, the median and the mode found?

Mean: the sum of the values divided by their number, x̄ = Σx / n. Median: the middle value once the data is arranged in order. Mode: the value that occurs most often.

State the additive rule of probability, and how it simplifies for mutually exclusive events.

General form: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Mutually exclusive events share no outcome, so P(A ∩ B) = 0 and the rule becomes P(A ∪ B) = P(A) + P(B).

How are the determinant and the inverse of a 2×2 matrix [[a, b], [c, d]] found?

Determinant = ad - bc. Where the determinant is non-zero, inverse = (1/determinant) x [[d, -b], [-c, a]]: swap the leading diagonal and negate the other two entries. Example: [[4, 3], [2, 5]] has determinant 20 - 6 = 14.

What are the three steps of a profit-maximisation question?

1. Form the profit function: π = TR - TC. 2. Differentiate it. 3. Set the derivative to zero and solve for Q. This is the point where marginal revenue equals marginal cost.

What are the variance and the standard deviation?

Variance: the average of the squared differences between each value and the mean, σ² = Σ(x - x̄)² / n. Standard deviation: the square root of the variance, σ = √σ², which brings the measure back into the data's own units.

How is expected monetary value (EMV) calculated?

Weight each possible outcome's payoff by its probability and add the results. Example: 70% chance of a KES 420,000 profit, 30% chance of a KES 150,000 loss. EMV = (0.7 x 420,000) + (0.3 x -150,000) = 294,000 - 45,000 = KES 249,000.

How is a missing value found from a proportion?