PIPFA Quantitative Methods Syllabus

Quantitative Methods syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Methods in PIPFA, not a summary of it.

1. 1

   Basic Mathematics

   4 topics

   • Number Systems and Operations
   • Ratios, Proportions and Percentages
   • Equations and Inequalities
   • Sequences and Series
2. 2

   Financial Mathematics

   3 topics

   • Simple and Compound Interest
   • Annuities
   • Present Value and Discounting
3. 3

   Descriptive Statistics

   3 topics

   • Presentation of Data
   • Measures of Central Tendency
   • Measures of Dispersion
4. 4

   Probability and Distributions

   3 topics

   • Basic Probability Concepts
   • Normal Distribution
   • Binomial Distribution
5. 5

   Index Numbers and Time Series

   3 topics

   • Price and Quantity Index Numbers
   • Time Series Components
   • Trend Analysis and Forecasting
6. 6

   Correlation and Regression

   2 topics

   • Correlation Analysis
   • Simple Linear Regression

Quantitative Methods flashcards for PIPFA

19 of 60 cards from the Quantitative Methods deck — real questions with worked answers.

1. In number systems, how do you classify real numbers into rational and irrational?

   Rational numbers can be expressed as a fraction p/q (q ≠ 0) and have terminating or repeating decimals (e.g. 1/2, 0.75, 3). Irrational numbers cannot be written as a fraction and have non-terminating, non-repeating decimals (e.g. √2, π).

2. What is the BODMAS/order of operations rule for arithmetic expressions?

   Evaluate in order: Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

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

   a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n); (a^m)^n = a^(mn). Also a^0 = 1 and a^(−n) = 1/a^n.

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

   A ratio compares two quantities of the same kind (a : b). A proportion is a statement that two ratios are equal (a : b = c : d), meaning a/b = c/d, so a×d = b×c.

5. How do you convert a fraction or decimal to a percentage, and a percentage back to a decimal?

   Multiply the fraction/decimal by 100 to get a percentage (0.25 → 25%). Divide a percentage by 100 to get a decimal (25% → 0.25).

6. How do you calculate percentage change between an old value and a new value?

   Percentage change = [(New value − Old value) / Old value] × 100. A positive result is an increase; a negative result is a decrease.

7. How do you divide an amount in a given ratio a : b : c?

   Add the parts (a + b + c) to get total parts, divide the amount by total parts to find the value of one part, then multiply each ratio number by that value.

8. How do you solve a quadratic equation ax² + bx + c = 0 using the quadratic formula?

   x = [−b ± √(b² − 4ac)] / (2a). The term b² − 4ac is the discriminant: >0 gives two real roots, =0 gives one repeated root, <0 gives no real roots.

9. When solving an inequality, what rule applies when multiplying or dividing by a negative number?

   The direction of the inequality sign must be reversed. For example, if −2x < 6 then x > −3 (the < becomes >).

10. How do you solve a pair of simultaneous linear equations by elimination?

    Multiply one or both equations so a variable has equal coefficients, add or subtract the equations to eliminate that variable, solve for the remaining variable, then substitute back to find the other.

11. What is the difference between an arithmetic sequence and a geometric sequence?

    An arithmetic sequence has a constant common difference d between terms (add d each time). A geometric sequence has a constant common ratio r between terms (multiply by r each time).

12. State the formula for the nth term of an arithmetic progression.

    aₙ = a + (n − 1)d, where a is the first term, d is the common difference, and n is the term number.

13. State the formula for the sum of the first n terms of an arithmetic progression.

    Sₙ = n/2 × [2a + (n − 1)d], or equivalently Sₙ = n/2 × (a + l), where l is the last term.

14. State the formula for the nth term and the sum of n terms of a geometric progression.

    nth term: aₙ = a·r^(n−1). Sum: Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1. For |r| < 1, the sum to infinity = a/(1 − r).

15. What is the formula for simple interest, and on what is it calculated?

    Simple Interest = P × r × t, where P = principal, r = interest rate per period (decimal), t = number of periods. It is always calculated on the original principal only.

16. What is the compound interest (future value) formula for annual compounding?

    A = P(1 + r)ⁿ, where A = accumulated amount, P = principal, r = interest rate per period, n = number of periods. Compound interest = A − P.

17. How is the compound interest formula adjusted for m compounding periods per year over t years?

    A = P(1 + r/m)^(mt), where r is the nominal annual rate, m is the number of compounding periods per year, and t is the number of years.

18. What is the Effective Annual Rate (EAR) and its formula?

    EAR is the actual annual interest earned after accounting for compounding. EAR = (1 + r/m)^m − 1, where r is the nominal annual rate and m is the number of compounding periods per year.

19. What is the key difference between simple interest and compound interest?

    Simple interest is earned only on the original principal each period, giving linear growth. Compound interest is earned on principal plus accumulated interest, giving exponential growth, so it always exceeds simple interest over more than one period.

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