**Important Short Answer Questions for Business Mathematics I.Com Part 1**

**Define ratio.**

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

**Express 3.2as percentage.**

Multiply by 100: 3.2 × 100 = **320%**

**Define discount.**

A deduction from the usual cost of something, typically given for prompt or advance payment or to a special category of buyers

**Write the formulas to calculate rate and simple interest.**

I(Interest) = p(Principle)r(Rate)t(Time)

Solve for r

I = prt……………divide both sides by pt and you get:

Interest

————- = rate

pr * time

**Define annuity due.**

An annuity whose payment is to be made immediately, rather than at the end of the period

Or

An annuity due requires payments to be made at the beginning of the period. For example, in many lease arrangements, the first payment is due immediately and each successive payment must be made at the beginning of the month.

Source: http://www.investopedia.com/terms/a/annuitydue.asp

**Define a function.**

A function is a special relationship between values: Each of its input values gives back exactly one output value.

**Find x and y, intercept of 3y + x = 12.**

3y + x = 12

3(0) + x = 12

0 + x = 12

X = 12

3y + x = 12

3y + 0 = 12

3y = 12

y = 12/3

y = 4

**Define quadratic equation.**

An equation in which the highest power of an unknown quantity is a square

**Define a diagonal matrix.**

A square matrix in which all the entries except those along the diagonal from upper left to lower right are zero.

**Convert (101) ^{2} to base 10.**

The Process:

1. Divide the “desired” base (in this case base 2) INTO the number you are trying to convert.

2. Write the quotient (the answer) with a remainder like you did in elementary school.

3. Repeat this division process using the whole number from the previous quotient (the number in front of the remainder).

4. Continue repeating this division until the number in front of the remainder is only zero.

5. The answer is the remainders read from the bottom up.

5_{10} = 101_{2} (a binary conversion)

Source: http://mathbits.com/MathBits/CompSci/Introduction/frombase10.htm

**Convert 93 to binary system.**

To convert any number in any base to another base, simply iteratively divide by the second base, using the rules of arithmetic for the first base, recording the remainders in reverse order, until the quotient is zero.

93 divided by 2 is 46 remainder 1

46 divided by 2 is 23 remainder 0

23 divided by 2 is 11 remainder 1

11 divided by 2 is 5 remainder 1

5 divided by 2 is 2 remainder 1

2 divided by 2 is 1 remainder 0

1 divided by 2 is 0 remainder 1

Source: http://wiki.answers.com/Q/How_do_you_convert_decimal_number_93_to_binary

**If 9-times of a number are 180, find the number.**

180/9

20

**24 is what percent of 192?**

24 / 192 = 0.125 x 100 = 12.5 %

**Write the name of different types of proportions.**

- Direct proportion
- Inverse proportion
- Continued proportion

**Define profit and loss.**

An account compiled at the end of an accounting period to show gross and net profit or loss.

**What is 3% of 20?**

3% = 3/100

3/100 = .03

.03 x 20 = .6

**What is principal?**

1. The amount borrowed, or the part of the amount borrowed which remains unpaid (excluding interest). here also called principal amount.

2. The part of a monthly payment that reduces the outstanding balance of a mortgage.

3. The original investment.

4. The entity on whose behalf an agent acts.

5. The role a broker/dealer plays when buying or selling securities for its own account.

6. An important company executive.

Source: http://www.investorwords.com/3839/principal.html#ixzz2aApMJbYr

**What is amount or maturity value?**

The amount that will be received at the time a security is redeemed at its maturity. For most securities, maturity value equals par value.

Source: http://www.investorwords.com/3020/maturity_value.html#ixzz2aApmw8El

**What is an even function?**

The function *f*(*x*) is said to be ‘even’ if and only if *f*(*x*) is a real-valued function of a real variable *x*, and* f*(*-x*) = *f*(*x*).

**If 1/4 of an amount is Rs. 60, what is the amount?**

1/4 = 60

60 x 4 = 240

**Divide Rs. 60,000 in the ratio 5 : 7.**

A = 5/12 x 60,000 = 25,000

B = 7/12 x 60,000 = 35,000

**Express 14% as a fraction.**

14% is 14/100

**Find x from the proportion 8 : 2 :: x : 40**

8/2 = x/4

From cross multiplication we found

2x = 8×4

x = 32/2

x = 16

**200 is 10% of what number?**

200 x 100 / 10 = 2000

**Define ordinary annuity.**

An annuity paid in a series of more or less equal payments at the end of equally spaced periods.

**Solve x ^{2} + 3x – 4 = 0 by quadratic formula.**

This quadratic happens to factor:

*x*^{2} + 3*x* – 4 = (*x* + 4)(*x* – 1) = 0

…so I already know that the solutions are *x* = –4 and *x* = 1. How would my solution look in the Quadratic Formula? Using *a* = 1, *b* = 3, and *c* = –4, my solution looks like this:

Then, as expected, the solution is ** x = –4, x = 1**.

Source: http://www.purplemath.com/modules/quadform.htm

**Define direct proportion.**

A relationship where a number increases or decreases together with another number at the same ratio. Directly proportional is the opposite of inversely proportional.

Source: http://www.toolingu.com/definition-550220-24911-directly-proportional.html

**A tables cost Rs. 225 is sold for Rs. 450. Find the percentage of gain.**

Sales – Cost = Profit

450 – 225 = 225

Cost = Profit

Percentage = 100 %

**Define compound interest.**

Interest calculated on both the principal and the accrued interest

Or

Interest which is calculated not only on the initial principal but also the accumulated interest of prior periods. Compound interest differs from simple interest in that simple interest is calculated solely as a percentage of the principal sum.

The equation for compound interest is: P = C(1+ r/n)nt

Where:

P = future value

C = initial deposit

r = interest rate (expressed as a fraction: eg. 0.06 for 6%)

n = # of times per year interest is compounded

t = number of years invested

Source: http://www.investorwords.com/1013/compound_interest.html#ixzz2aBJwVZGn

**Differentiate between ordinary annuity and annuity due.**

An annuity due is an annuity where the payments are made at the beginning of each time period; for an ordinary annuity, payments are made at the end of the time period.

**Define perpetual annuity and give example.**

Annuity derived from an asset (such as an income generating security) where the life span of the annuitant (security holder or his or her beneficiary) is of no consequence.

Source: http://www.businessdictionary.com/definition/perpetual-annuity.html#ixzz2aBLGlg2y

**Define domain.**

The domain is the x the range is the y.

The domain is an independent variable because it is not influenced by anything. The y is dependent because it is influenced by the independent variable.

Solve the equation x^{2} – 5x + 6 = 0

x^{2}-3x-2x+6=0

x(x-3)-2(x+3)=0

(x-3)(x-2)=0

x-3=0

x=3

x-2=0

x=2

so your answer should be x= 3 or 2

**Define an identity matrix.**

A square matrix with 1′s along the diagonal from upper left to lower right and 0′s in all other positions.

**Define the column matrix and give one example.**

A matrix which has only one column is called a Column Matrix.

**Write down the different numbers systems.**

- Binary
- Fraction
- Decimal

**What do you understand by perpetuity? **

Perpetuity can be well defined as an annuity without any end, or it can be said that perpetuity features a stream of cash payments continuing forever.

**Write two consecutive integers whose sum is 41. **

x + (x + 1) = 41

x + x + 1 = 41

Combine the two x’s to get:

2x + 1 = 41

2x = 40

x = 40/2 = 20

Since the two integers are x and x + 1, the integers are 20 and 20 + 1 or 20 and 21.

**What will be the simple interest on Rs. 1000 for 5 years at 10% annually?**

I = ptr

1000 x 10% x 5 = 500

**Write four types of functions.**

- Constant Function
- Algebraic Function
- Polynomial Function
- Linear Function
- Quadratic Function
- Cubic Function
- Identity Function
- Rational Function
- Trigonometric Function
- Exponential Function
- Logarithmic Function
- Hyperbolic Function
- Inverse Hyperbolic Functions
- Explicit Function
- Implicit Function
- Parametric Function
- Even Function

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