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CMA Foundation Mathematics Formulas

CMA Foundation Mathematics Formulas | CMAKnowledge

CMA Foundation Mathematics Formulas

Complete collection of mathematical formulas with interactive calculators and visualizations for practical applications in cost accounting and financial management

Formula Categories

Arithmetic & Ratios

Percentages, ratios, proportions, averages

Algebra

Equations, inequalities, functions

Calculus

Differentiation, integration, optimization

Probability

Probability distributions, expected values

Financial Math

Interest, annuities, present value

Statistics

Measures, correlation, regression

CMA Foundation Formulas

Percentage Change

Percentage Change = [(New Value - Old Value) / Old Value] × 100

Explanation

This formula calculates the percentage increase or decrease between two values. It's fundamental in business for analyzing growth, price changes, and performance metrics.

CMA Application

Used in financial analysis to calculate revenue growth, cost variances, and performance improvements. Essential for variance analysis in cost accounting.

Percentage Change Calculator
Result:
Percentage Change Visualization
Example:

If material costs increased from ₹500 to ₹600, the percentage change is:
[(600 - 500) / 500] × 100 = 20% increase

Ratio and Proportion

a : b = c : d ⇒ a/b = c/d

Explanation

Ratios compare two quantities, while proportions state that two ratios are equal. This is fundamental for financial analysis and cost allocation.

CMA Application

Used in financial statement analysis (current ratio, debt-equity ratio), cost allocation, and break-even analysis.

Ratio Calculator
Result:
Ratio Visualization
Example:

If the current ratio is 2:1 and current liabilities are ₹50,000, then current assets = 2 × ₹50,000 = ₹100,000

Average (Mean)

Average = (Sum of all values) / (Number of values)

Explanation

The average or arithmetic mean is the sum of all values divided by the number of values. It represents the central value of a dataset.

CMA Application

Used to calculate average cost, average revenue, and other business metrics. Essential for inventory valuation and performance analysis.

Average Calculator
Result:
Example:

If production costs for 5 days are ₹100, ₹120, ₹90, ₹110, ₹130, then average cost = (100+120+90+110+130)/5 = ₹110

Linear Equations

y = mx + c

Explanation

This represents a straight line where m is the slope and c is the y-intercept. It models relationships with constant rates of change.

CMA Application

Used in cost-volume-profit analysis, where y represents total cost, m is variable cost per unit, x is quantity, and c is fixed cost.

Linear Equation Calculator
Result:
Linear Equation Graph
Example:

If fixed costs are ₹10,000 and variable cost per unit is ₹5, then total cost = 5x + 10,000

Quadratic Equations

ax² + bx + c = 0 ⇒ x = [-b ± √(b² - 4ac)] / 2a

Explanation

Quadratic equations are polynomial equations of degree 2. The solutions are found using the quadratic formula.

CMA Application

Used in economic models, break-even analysis with nonlinear costs, and optimization problems.

Quadratic Equation Calculator
Result:
Quadratic Equation Graph
Example:

For the equation 2x² - 4x - 6 = 0, the solutions are:
x = [4 ± √(16 + 48)] / 4 = [4 ± 8] / 4 ⇒ x = 3 or x = -1

Derivative for Optimization

f'(x) = limh→0 [f(x+h) - f(x)] / h

Explanation

The derivative measures the rate of change of a function. It's used to find maximum and minimum values of functions.

CMA Application

Used in economic order quantity (EOQ) models, profit maximization, and cost minimization problems.

Derivative Calculator (Simple)
Result:
Function and Derivative Graph
Example:

To maximize profit function P(x) = -2x² + 100x - 500, find where P'(x) = 0:
P'(x) = -4x + 100 = 0 ⇒ x = 25 units for maximum profit

Basic Probability

P(A) = Number of favorable outcomes / Total number of possible outcomes

Explanation

Probability measures the likelihood of an event occurring. It ranges from 0 (impossible) to 1 (certain).

CMA Application

Used in risk assessment, decision making under uncertainty, and forecasting business outcomes.

Basic Probability Calculator
Result:
Probability Visualization
Example:

If a company has 5 profitable projects out of 20 total projects, the probability of selecting a profitable project is:
P(Profitable) = 5/20 = 0.25 or 25%

Conditional Probability

P(A|B) = P(A ∩ B) / P(B)

Explanation

Conditional probability measures the probability of event A occurring given that event B has already occurred.

CMA Application

Used in risk analysis, quality control, and decision trees for business strategy.

Conditional Probability Calculator
Result:
Conditional Probability Visualization
Example:

If 30% of products are defective and 10% are both defective and from Supplier X, the probability a product is from Supplier X given it's defective is:
P(Supplier X | Defective) = 0.10 / 0.30 = 0.333 or 33.3%

Expected Value

E(X) = Σ [x × P(x)]

Explanation

The expected value is the weighted average of all possible values of a random variable, with weights being their respective probabilities.

CMA Application

Used in decision making under uncertainty, risk analysis, and calculating expected returns in investment appraisal.

Expected Value Calculator
Result:
Expected Value Visualization
Example:

If a project has 30% chance of ₹100,000 profit, 50% chance of ₹20,000 profit, and 20% chance of ₹10,000 loss:
Expected value = (0.3 × 100,000) + (0.5 × 20,000) + (0.2 × -10,000) = ₹38,000

Binomial Distribution

P(X = k) = C(n, k) × pk × (1-p)n-k

Explanation

The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success.

CMA Application

Used in quality control, risk assessment, and forecasting the likelihood of a certain number of successes in business processes.

Binomial Distribution Calculator
Result:
Binomial Distribution
Example:

If a production process has a 5% defect rate, the probability of exactly 2 defects in a batch of 20 items is:
P(X=2) = C(20, 2) × 0.05² × 0.95¹⁸ ≈ 0.1887 or 18.87%

Normal Distribution

f(x) = (1 / (σ√(2π))) × e-(x-μ)²/(2σ²)

Explanation

The normal distribution is a continuous probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

CMA Application

Used in quality control, risk management, financial modeling, and forecasting business metrics that follow a bell-shaped distribution.

Normal Distribution Calculator
Result:
Normal Distribution Curve
Example:

If product weights are normally distributed with mean 500g and standard deviation 20g, the probability of a product weighing less than 480g is found using the Z-score:
Z = (480 - 500) / 20 = -1 → P(X<480) ≈ 0.1587 or 15.87%

Compound Interest

A = P (1 + r/n)nt

Explanation

This calculates the future value of an investment where interest is compounded over multiple periods.

CMA Application

Fundamental in time value of money calculations, investment appraisal, and financial planning.

Compound Interest Calculator
Result:
Compound Interest Growth
Example:

₹10,000 invested at 8% annual interest compounded quarterly for 5 years:
A = 10,000 (1 + 0.08/4)4×5 = 10,000 (1.02)20 ≈ ₹14,859

Present Value

PV = FV / (1 + r)n

Explanation

This calculates the current worth of a future sum of money, given a specified rate of return.

CMA Application

Essential for capital budgeting, investment decisions, and valuing future cash flows.

Present Value Calculator
Result:
Example:

Present value of ₹50,000 to be received in 3 years at 10% discount rate:
PV = 50,000 / (1.10)3 ≈ ₹37,565

Correlation Coefficient

r = [nΣxy - (Σx)(Σy)] / √{[nΣx² - (Σx)²][nΣy² - (Σy)²]}

Explanation

The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.

CMA Application

Used to analyze relationships between business variables like advertising expenditure and sales, or production volume and costs.

Correlation Calculator
Result:
Correlation Scatter Plot
Example:

If advertising expenditure (x) and sales (y) have a correlation coefficient of 0.85, this indicates a strong positive relationship between advertising and sales.

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