CMA Foundation Mathematics Tool
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CMA Foundation Mathematics Tool
Comprehensive resource for formulas, explanations, and interactive calculators
Topics Overview
Algebra & Quadratics
- Quadratic Equations
- Polynomials
- Linear Equations
- Inequalities
Sequences & Series
- Arithmetic Progression
- Geometric Progression
- Harmonic Progression
- Special Series
Geometry & Mensuration
- Lines and Angles
- Triangles and Circles
- Area and Volume
- Coordinate Geometry
Finance (Interest)
- Simple Interest
- Compound Interest
- Annuities
- Present Value
Counting Principles
- Permutations
- Combinations
- Probability
- Set Theory
Statistics
- Measures of Central Tendency
- Dispersion
- Correlation
- Regression
Key Formulas
Algebra & Quadratics
Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a
Example: Solve 2x² + 5x - 3 = 0
Solution: a=2, b=5, c=-3 → x = [-5 ± √(25 + 24)]/4 = [-5 ± 7]/4 → x = 0.5 or x = -3
Solution: a=2, b=5, c=-3 → x = [-5 ± √(25 + 24)]/4 = [-5 ± 7]/4 → x = 0.5 or x = -3
Sequences & Series
Arithmetic Progression: aₙ = a₁ + (n-1)d, Sₙ = n/2 [2a₁ + (n-1)d]
Geometric Progression: aₙ = a₁ × rⁿ⁻¹, Sₙ = a₁(1 - rⁿ)/(1 - r) for r≠1
Finance
Compound Interest: A = P(1 + r/n)ⁿᵗ
Example: ₹10,000 at 8% compounded quarterly for 2 years
A = 10000(1 + 0.08/4)⁴ˣ² = 10000(1.02)⁸ ≈ ₹11,716.59
A = 10000(1 + 0.08/4)⁴ˣ² = 10000(1.02)⁸ ≈ ₹11,716.59
Interactive Calculators
Quadratic Equation Solver
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Compound Interest Calculator
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Arithmetic Progression Calculator
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Worked Examples
Algebra: Solving Quadratic Equations
Solve the equation: 3x² - 7x + 2 = 0
Solution:
Using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a
Here, a = 3, b = -7, c = 2
Discriminant D = b² - 4ac = (-7)² - 4(3)(2) = 49 - 24 = 25
x = [7 ± √25] / 6 = [7 ± 5] / 6
So, x = (7+5)/6 = 12/6 = 2 or x = (7-5)/6 = 2/6 = 1/3
Finance: Compound Interest Calculation
Calculate the maturity amount for ₹15,000 invested at 6% per annum compounded semi-annually for 3 years.
Solution:
Principal P = ₹15,000, Rate r = 6% = 0.06, Time t = 3 years, Compounds per year n = 2
Amount A = P(1 + r/n)ⁿᵗ = 15000(1 + 0.06/2)²ˣ³ = 15000(1 + 0.03)⁶
= 15000(1.03)⁶ = 15000 × 1.19405 ≈ ₹17,910.75