CA Foundation PAPER 3: QUANTITATIVE APTITUDE Syllabus

PAPER 3: QUANTITATIVE APTITUDE syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for PAPER 3: QUANTITATIVE APTITUDE in CA Foundation, not a summary of it.

1. 1

   BUSINESS MATHEMATICS

   8 topics

   • Ratio and proportion, Indices and Logarithms
     • Ratio and proportion and Time and work-related problems
     • Laws of Indices, Exponents and Logarithms and Anti Logarithms
   • Equations
     • Linear Simultaneous linear equations up to three variables
     • Quadratic and Cubic equations in one variable
     • Applications in Business related problems
   • Linear Inequalities
     • Linear Inequalities in one and two variables and the solution space
   • Mathematics of Finance
     • Simple Interest
     • Compound interest
     • Nominal and Effective Rate of Interest
     • Present Value
     • Net Present Value
     • Future Value
     • Perpetuity
     • Annuities
     • Sinking Funds
     • Calculating of EMI
     • Calculations of Returns: Nominal and Effective rate of Return
     • Compound Annual growth rate (CAGR)
   • Permutations and Combinations
     • Factorial
     • Permutations
     • Circular permutations
     • Permutations with restrictions
     • Combinations with standard results
   • Sequence and Series
     • Introduction Sequences, Series
     • Arithmetic and Geometric progression
     • Relationship between AM and GM and Sum of n terms of special series and Business Applications
   • Sets, Relations, and Functions
     • Basics of Limits and Continuity functions
   • Basic applications of Differential and Integral calculus in Business and Economics (Excluding the trigonometric applications)
2. 2

   LOGICAL REASONING

   4 topics

   • Number series coding and Decoding and odd man out
   • Direction Tests
   • Seating Arrangements
   • Blood Relations
3. 3

   STATISTICS

   6 topics

   • Unit 1: Statistical Representation of Data
     • Diagrammatic representation of data
     • Frequency distribution
     • Graphical representation of Frequency Distribution – Histogram, Frequency Polygon, Ogive, Pie-chart
   • Unit 2: Sampling
     • Basic principles of sampling theory
     • Comparison between sample survey and complete enumeration
     • Some important terms associated sampling types of sampling, sampling and non-sampling errors
   • Measures of Central tendency and Dispersion
     • Mean Median, Mode
     • Mean Deviation, Quartiles and Quartile Deviation
     • Standard Deviation, Co-efficient of Variation, Coefficient of Quartile Deviation
   • Probability
     • Independent and dependent events; mutually exclusive events
     • Total and Compound Probability and Bayes’ theorem
   • Theoretical Distributions
     • Random variables, Discrete and Continuous Random variables
     • Expectation of a discrete random variable
     • Theoretical Distributions: Binomial Distribution, Poisson distribution – basic application
     • Normal Distribution – basic applications
   • Correlation and Regression
     • Scatter diagram
     • Karl Pearson’s Coefficient of Correlation Rank Correlation
     • Regression lines
     • Regression equations,
     • Regression coefficients

PAPER 3: QUANTITATIVE APTITUDE flashcards for CA Foundation

18 of 69 cards from the PAPER 3: QUANTITATIVE APTITUDE deck — real questions with worked answers.

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

   A ratio compares two quantities of the same kind (a:b = a/b). A proportion is an equality of two ratios (a:b = c:d, i.e., a/b = c/d), where the product of extremes equals the product of means (ad = bc).

2. In the proportion a:b = c:d, what are the mean proportional and the third/fourth proportional?

   In a:b = c:d, a and d are extremes, b and c are means. The fourth proportional to a, b, c is d = bc/a. The third proportional to a, b is b²/a. The mean proportional between a and b is √(ab).

3. State the laws of indices for a^m × a^n, a^m ÷ a^n, (a^m)^n, a^0 and a^(-n).

   a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n); (a^m)^n = a^(mn); a^0 = 1 (a≠0); a^(−n) = 1/a^n; a^(1/n) = n-th root of a.

4. 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^n) = n·log m. Also log_a a = 1 and log_a 1 = 0.

5. State the change of base formula for logarithms and the value of log_b a × log_a b.

   Change of base: log_a m = log_b m / log_b a. Consequence: log_b a × log_a b = 1 (they are reciprocals).

6. How many roots does a quadratic equation ax² + bx + c = 0 have, and what is the quadratic formula?

   It has exactly two roots. x = [−b ± √(b² − 4ac)] / (2a).

7. For ax² + bx + c = 0, what are the sum and product of the roots?

   Sum of roots = −b/a. Product of roots = c/a.

8. What does the discriminant (b² − 4ac) of a quadratic tell you about the nature of its roots?

   If b²−4ac > 0: real and distinct roots. If = 0: real and equal roots. If < 0: imaginary (complex conjugate) roots. If it is a perfect square (and >0): roots are rational.

9. How is a cubic equation different from a quadratic, and how many roots does it have?

   A cubic equation has the highest power 3 (ax³+bx²+cx+d=0) and has exactly three roots. For roots α, β, γ: sum = −b/a, sum of products taken two at a time = c/a, product = −d/a.

10. What happens to an inequality when both sides are multiplied or divided by a negative number?

    The direction of the inequality sign is reversed. E.g., if x > y, then −x < −y, and multiplying by −2 gives −2x < −2y.

11. In linear programming, what is the feasible region and where does the optimal solution occur?

    The feasible region is the set of all points satisfying all the constraints (intersection of half-planes). The optimal value of the objective function occurs at a corner (vertex/extreme) point of the feasible region.

12. State the formula for Simple Interest and the Amount.

    Simple Interest = P × R × T / 100, where P = principal, R = rate % per annum, T = time in years. Amount = P + SI = P(1 + RT/100).

13. State the Compound Interest formula for the amount when compounded annually.

    A = P(1 + r/100)^n, where P = principal, r = rate % per period, n = number of periods. Compound Interest = A − P.

14. How is the compound amount formula adjusted when interest is compounded m times per year?

    A = P(1 + r/(100m))^(mn), where r = annual rate %, m = compounding frequency per year, n = number of years.

15. What is the formula for the effective rate of interest given nominal rate i compounded m times a year?

    Effective rate E = (1 + i/m)^m − 1, expressed as a percentage. It is the equivalent annual rate of return accounting for compounding.

16. State the formula for the Future Value of an ordinary annuity.

    FV = A × [((1 + i)^n − 1) / i], where A = periodic payment, i = interest rate per period, n = number of periods (payments made at the end of each period).

17. State the formula for the Present Value of an ordinary annuity.

    PV = A × [(1 − (1 + i)^(−n)) / i], where A = periodic payment, i = rate per period, n = number of periods.

18. What is the formula for the Present Value of a perpetuity?

    PV = A / i, where A = periodic payment and i = interest rate per period. A perpetuity is an annuity that continues forever.

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