CMA (Cost & Management Accountancy) Foundation: Fundamentals of Business Mathematics and Statistics Syllabus

Foundation: Fundamentals of Business Mathematics and Statistics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Foundation: Fundamentals of Business Mathematics and Statistics in CMA (Cost & Management Accountancy), not a summary of it.

1. 1

   Arithmetic and Algebra

   4 topics

   • Ratio, Proportion and Indices
   • Simple and Compound Interest
     • Annuities and present value
     • Effective rate of interest
   • Arithmetic and Geometric Progressions
   • Set Theory and Logarithms
2. 2

   Calculus and Equations

   3 topics

   • Linear and Quadratic Equations
   • Simultaneous Equations
   • Basics of Differentiation and Integration
     • Maxima and minima applications
3. 3

   Statistical Representation and Measures

   3 topics

   • Collection, Tabulation and Presentation of Data
   • Measures of Central Tendency
     • Mean, median and mode
   • Measures of Dispersion
     • Range, quartile deviation and standard deviation
4. 4

   Probability and Correlation

   3 topics

   • Theory of Probability
     • Addition and multiplication theorems
     • Bayes' theorem basics
   • Correlation and Regression
     • Karl Pearson's coefficient
     • Lines of regression
   • Index Numbers and Time Series

Foundation: Fundamentals of Business Mathematics and Statistics flashcards for CMA (Cost & Management Accountancy)

19 of 50 cards from the Foundation: Fundamentals of Business Mathematics and Statistics deck — real questions with worked answers.

1. Define a ratio and state how a ratio $a:b$ relates to a fraction.

   A ratio is a comparison of two quantities of the same kind by division. The ratio $a:b$ (where $b \neq 0$) is equivalent to the fraction $\frac{a}{b}$; $a$ is the antecedent and $b$ is the consequent.

2. In a proportion $a:b::c:d$, what is the relationship between the terms, and which are the means and extremes?

   Four quantities are in proportion when $\frac{a}{b}=\frac{c}{d}$, i.e. $a\times d = b\times c$ (product of extremes = product of means). Here $a$ and $d$ are the extremes, $b$ and $c$ are the means.

3. Define the continued proportion and the mean proportional between two numbers $a$ and $b$.

   In continued proportion $a:b=b:c$, so $b^{2}=ac$. The mean proportional (geometric mean) between $a$ and $b$ is $\sqrt{ab}$, and $c=\frac{b^{2}}{a}$ is the third proportional.

4. State the key laws of indices for $a^{m}\cdot a^{n}$, $\frac{a^{m}}{a^{n}}$, $(a^{m})^{n}$, $a^{0}$ and $a^{-n}$.

   $a^{m}\cdot a^{n}=a^{m+n}$, $\quad \frac{a^{m}}{a^{n}}=a^{m-n}$, $\quad (a^{m})^{n}=a^{mn}$, $\quad a^{0}=1$ (for $a\neq 0$), $\quad a^{-n}=\frac{1}{a^{n}}$. Also $a^{1/n}=\sqrt[n]{a}$.

5. State the formula for Simple Interest and the corresponding Amount.

   $SI=\frac{P\times R\times T}{100}$, where $P$ is principal, $R$ is rate percent per annum, $T$ is time in years. The amount is $A=P+SI=P\left(1+\frac{RT}{100}\right)$.

6. State the Compound Interest amount formula for annual compounding and for compounding $n$ times per year.

   Annual: $A=P\left(1+\frac{R}{100}\right)^{T}$ and $CI=A-P$. For compounding $n$ times per year over $T$ years: $A=P\left(1+\frac{R}{100n}\right)^{nT}$.

7. How do you compute the effective rate of interest given a nominal rate $i$ compounded $m$ times a year?

   $\text{Effective rate}=\left(1+\frac{i}{m}\right)^{m}-1$, where $i$ is the nominal annual rate (as a decimal) and $m$ is the number of compounding periods per year. It expresses the true annual yield.

8. Define an annuity and distinguish between an ordinary annuity and an annuity due.

   An annuity is a sequence of equal periodic payments made at fixed intervals. In an ordinary annuity payments occur at the end of each period; in an annuity due payments occur at the beginning of each period.

9. State the present value formula of an ordinary annuity of $R$ per period at rate $i$ for $n$ periods.

   $PV=R\cdot\dfrac{1-(1+i)^{-n}}{i}$, where $R$ is the periodic payment, $i$ is the interest rate per period, and $n$ is the number of periods.

10. State the future (accumulated) value formula of an ordinary annuity.

    $FV=R\cdot\dfrac{(1+i)^{n}-1}{i}$, where $R$ is the periodic payment, $i$ the rate per period and $n$ the number of periods.

11. What is the present value of a perpetuity paying $R$ per period at rate $i$?

    $PV=\dfrac{R}{i}$, where $R$ is the constant periodic payment and $i$ is the interest rate per period. A perpetuity is an annuity that continues forever.

12. Define an Arithmetic Progression (AP) and give its $n$th term.

    An AP is a sequence in which each term differs from the previous by a constant common difference $d$. The $n$th term is $a_{n}=a+(n-1)d$, where $a$ is the first term.

13. State the formula for the sum of the first $n$ terms of an AP.

    $S_{n}=\frac{n}{2}\left[2a+(n-1)d\right]=\frac{n}{2}(a+l)$, where $a$ is the first term, $d$ the common difference, and $l$ the last term.

14. Define a Geometric Progression (GP) and give its $n$th term.

    A GP is a sequence in which each term is obtained by multiplying the previous term by a constant common ratio $r$. The $n$th term is $a_{n}=ar^{\,n-1}$, where $a$ is the first term.

15. State the sum of the first $n$ terms of a GP and the sum to infinity.

    $S_{n}=a\dfrac{r^{n}-1}{r-1}$ (for $r\neq 1$). For $|r|<1$, the sum to infinity is $S_{\infty}=\dfrac{a}{1-r}$.

16. In set theory, define union, intersection and complement of sets.

    Union $A\cup B$ = elements in $A$ or $B$ (or both). Intersection $A\cap B$ = elements in both $A$ and $B$. Complement $A'$ (or $A^{c}$) = elements in the universal set $U$ not in $A$.

17. State the cardinality (addition) formula for two sets and for the number of subsets of a set with $n$ elements.

    $n(A\cup B)=n(A)+n(B)-n(A\cap B)$. A set with $n$ elements has $2^{n}$ subsets (the power set).

18. State De Morgan's laws for sets.

    $(A\cup B)'=A'\cap B'$ and $(A\cap B)'=A'\cup B'$. The complement of a union is the intersection of complements, and vice versa.

19. State the basic laws of logarithms for product, quotient and power.

    $\log(mn)=\log m+\log n$, $\quad \log\!\left(\frac{m}{n}\right)=\log m-\log n$, $\quad \log(m^{p})=p\log m$. Also $\log_{a}a=1$ and $\log_{a}1=0$.

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