I.Com (Intermediate in Commerce) Principles of Business Mathematics Syllabus

How do you find x% of a quantity Q?

x% of Q = (x/100) x Q. Example: 20% of 250 = (20/100) x 250 = 50.

Define cost price (CP), selling price (SP), and how profit and loss are determined.

CP is the price at which an item is bought; SP is the price at which it is sold. If SP > CP, there is a Profit = SP - CP. If SP < CP, there is a Loss = CP - SP.

State the formulas for Profit Percentage and Loss Percentage.

Profit % = (Profit / CP) x 100. Loss % = (Loss / CP) x 100. Both are calculated on the cost price.

How do you find the Selling Price when Cost Price and Profit% (or Loss%) are given?

SP = CP x (100 + Profit%)/100 for profit; SP = CP x (100 - Loss%)/100 for loss.

How do you find the Cost Price when Selling Price and Profit% are given?

CP = SP x 100 / (100 + Profit%). For a loss, CP = SP x 100 / (100 - Loss%).

What is discount, and on what value is it calculated?

Discount is a reduction from the marked price (list price). It is calculated on the marked price: Discount = (Discount% / 100) x Marked Price.

State the relationship between Marked Price, Discount, and Selling Price.

Selling Price = Marked Price - Discount. Equivalently, SP = Marked Price x (100 - Discount%)/100.

What is the formula for the single equivalent discount of two successive discounts of x% and y%?

Single equivalent discount = x + y - (xy/100) percent.

Define commission and state how it is calculated.

Commission is the remuneration paid to an agent for buying or selling goods, usually a percentage of the sale (or purchase) value. Commission = (Rate% / 100) x Total Sales (turnover).

Define brokerage and who is a broker.

Brokerage is the fee or commission charged by a broker for arranging a transaction between a buyer and seller. A broker is an agent who brings parties together but does not own the goods. Brokerage = (Rate% / 100) x Value of transaction.

What is net sales proceeds (the amount an agent remits to the principal) after commission?

Net sales proceeds = Total Sales - Commission. The principal receives the sales value minus the agent's commission (and any other charges).

Define principal, rate, time, and amount in the context of interest.

Principal (P) is the sum borrowed or invested; Rate (R) is the percentage charged per period (usually per annum); Time (T) is the duration in years; Amount (A) is principal plus interest.

State the formula for Simple Interest.

Simple Interest (S.I.) = (P x R x T)/100, where P = principal, R = rate per annum, T = time in years.

How do you find the Amount under simple interest?

Amount A = Principal + Simple Interest = P + (P x R x T)/100 = P(1 + RT/100).

Under simple interest, how do you find the Principal if S.I., R, and T are known?

P = (S.I. x 100)/(R x T).

What is compound interest, and how does it differ from simple interest?

Compound interest is interest calculated on the principal plus accumulated interest of previous periods (interest on interest). Simple interest is calculated only on the original principal, so compound interest grows faster over time.

State the formula for the Amount under compound interest (annual compounding).

A = P(1 + R/100)^n, where P = principal, R = rate per annum, n = number of years. Compound Interest = A - P.

How is the compound interest amount formula adjusted when interest is compounded more than once a year (e.g., quarterly)?

A = P(1 + (R/100)/k)^(k x n), where k is the number of compounding periods per year (k=4 for quarterly, k=2 for half-yearly) and n is the number of years.

Write the formula for Compound Interest and state how it relates to the amount.

Compound Interest (C.I.) = A - P = P[(1 + R/100)^n - 1].

Define Future Value (FV) and Present Value (PV).

Future Value is the worth of a present sum at a future date after earning interest. Present Value is the current worth of a future sum, discounted back at a given rate.

State the formula for the Present Value of a future amount under compound interest.

PV = FV / (1 + R/100)^n, where FV is the future value, R is the rate per period, and n is the number of periods. This process is called discounting.

State the formula for the Future Value of a present sum under compound interest.

FV = PV(1 + R/100)^n, where PV is the present value, R is the rate per period, and n is the number of periods.

What is a linear equation in one variable, and what is its general form?

A linear equation in one variable is an equation of the first degree (highest power of the variable is 1). General form: ax + b = 0, where a is not equal to 0. Its solution is x = -b/a.

What is the standard form of a linear equation in two variables, and what does its graph look like?

Standard form: ax + by + c = 0 (a and b not both zero). Its graph is a straight line.

What is a quadratic equation, and what is its standard (general) form?

A quadratic equation is a second-degree equation in one variable. Standard form: ax^2 + bx + c = 0, where a is not equal to 0.

State the quadratic formula for solving ax^2 + bx + c = 0.

x = [-b plus or minus square root of (b^2 - 4ac)] / (2a).

What is the discriminant of a quadratic equation, and what does its sign indicate about the roots?

Discriminant D = b^2 - 4ac. If D > 0, two distinct real roots; if D = 0, two equal (real) roots; if D < 0, no real roots (roots are imaginary/complex).

State the relationship between the roots and coefficients of ax^2 + bx + c = 0.

If the roots are p and q, then sum of roots p + q = -b/a, and product of roots pq = c/a.

What are simultaneous (linear) equations, and what does their solution represent?

Simultaneous linear equations are two or more linear equations in the same variables solved together. Their solution is the set of values satisfying all equations at once; graphically, it is the point of intersection of the lines.

Name the algebraic methods used to solve a pair of simultaneous linear equations.

The substitution method, the elimination (addition/subtraction) method, the comparison method, and the cross-multiplication method.