Algebra, Company Reporting and Grammar Flashcards

Flashcards for reviewing key vocabulary and concepts from Algebra, Company Reporting, and Grammar lectures.

Algebra

Branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts resulting from them.

Notation

A system of characters, symbols, or abbreviated expressions.

Algebraic number

An algebraic number can be expressed as the solution to a polynomial equation with integer coefficients.

Coefficient

A number that is multiplied by the variable(s) in a single term

Constant

A term that does not contain any variables.

Expression

A term or a combination of terms and operators.

Operator

A symbol for expressing a mathematical operation.

Variable

A literal expression representing an unknown number.

Equation

A mathematical statement that asserts that one expression or quantity is equal to another.

Identity

An equation which is always true, no matter what values are substituted.

Solve an equation

To find all values of a specified variable in the equation for which the statement is true.

Equivalent equations

Algebraic equations having identical solutions or roots.

Linear equation

Any equation that can be written in the form ax + b = 0 where a and b are real numbers and a ≠ 0.

Quadratic equation

An equation equivalent to one of the form ax² + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.

Clear the equation of fractions

Multiply both sides of the equation by the least common multiple (LCM) of denominators

Expand parentheses

Eliminate or remove expressions / parentheses

Combine like terms

Use the commutative property to rearrange terms and collect like terms

Isolate the variable

Add or subtract to isolate the variable and move all terms with variable on one side and other terms on the other side

Inequality

An inequality is a statement involving two expressions, numerical or literal, separated by one of the inequality symbols

Solutions of the inequality

Values that make the statement true

Equivalent inequalities

Two inequalities having exactly the same solution set (they are true for the same values of the unknowns) are called equivalent.

warping

bending or twisting out of shape

revolutionized

to bring about a radical change

evolved

to develop gradually, esp. from a simple to a more complicated form

reveals

to make known (something concealed or unknown)

propels

to move, drive or push something forward or in a particular direction

acceleration

the increase in the speed at which something happens

hypotenuse

the side opposite the right angle of a right-angled triangle

formula

a mathematical rule expressed in a set of numbers and letters

vertices

a point where two lines meet to form an angle

sphere

a solid figure that is completely round

pure

not mixed with anything else; with nothing added; clear

particle

a very small piece of matter

reigning

theories of widespread influence

encapsulates

to express the most important parts of something in a few words

observed

to watch somebody/something carefully

seeds

the beginning; the early stages

backbone

the most important part of a system, an organization, etc.

theorem

a principle or idea

Finance

Enables it to start, operate, and grow. It provides the necessary resources to cover expenses, make strategic investments, and navigate the business environment

Capital

The financial foundation necessary for business operations.

Loans

Funds that must be repaid with interest.

Shares

Certificate representing ownership units in the company.

Shareholders

Investors claiming partial ownership of the business.

Bonds

Loans that accrue interest and are repaid at a predetermined future date.

Debt

Money owed to others.

Liabilities

Debts owed to suppliers for goods or services provided on credit.

Working capital

Funds a business uses for day-to-day expenses.

Revenue

All incoming funds to a company within a specific timeframe.

Dividend

Share of profit disbursed to shareholders.

Retain

Portion of profits kept for future use.

Listed companies

Financial statements that have to present their accounts to the public

Annual report

A comprehensive document that provides detailed information about a company's financial performance.

Accounts

Records used to track the financial activities of a business

Assets

Items that a company or individual owns that have monetary value and can be used to generate future economic benefits

Liabilities

Debts or obligations that a company owes to external parties, such as loans, accounts payable, and accrued expenses

Equity

The ownership interest in a company, representing the residual value of assets after deducting liabilities

Revenue

the total amount of money earned by a business from its primary activities

Expenses

Costs incurred by a business in its day-to-day operations to generate revenue

Gross profit

The difference between a company's total revenue and the cost of goods sold. It represents the profit generated from the core business activities before deducting operating expenses.

Operating activities

The day-to-day business activities involved in generating revenue for a company.

Overheads

Regular and ongoing expenses incurred by a business that are not directly tied to a specific product or service.

Net income

The total profit earned by a company after deducting all expenses, taxes, and other deductions from total revenue.

Investing activities

Relates to the acquisition and disposal of long-term assets or investments

Financing activities

Activities undertaken by a company to raise capital or finance its operations.

Monomial

Product of two or more factors each of which is either a number, a letter or a power of a letter

Variable

A literal expression representing an unknown number, value of which, when substituted for it, makes the equation true

Equation

A mathematical statement that asserts that one expression or quantity is equal to another

An identity

If the equation is true for all values of the variables

Solution set

Set of solutions of a given equation

Inequality

Compares two values, showing if one is less than, greater than, or simply not equal to another value

Operator

A symbol for expressing a mathematical operation

Like terms

Terms that have the same variable but may have different coefficients

Roots

The numbers that make a conditional equation true

Linear equation

algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable

Constant

Some number that always has the same value, such as 3 or 14.89

Quadratic equation

Having the form ax2+ bx +c=0 where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0