Algebra Terms And Examples

Front 1

Quadratic Equation

Back 1

A Quadratic Equation is an equation of the form:

Hint 1

ax2 + bx + c = 0, where a, b and c are numbers and a ≠ 0

For example:

x2 + 2x + 3 = 0

2x2 + 5x – 7 = 0

2x2 + 5x = 8 is a quadratic equation because it can be changed to
2x2 + 5x – 8 = 0

x2 + x = 0 is a quadratic with c = 0

2x2 – 7 = 0 is a quadratic with b = 0

2x + 3 = 0 is not a quadratic because a cannot be 0

Front 2

Equations

Back 2

An equation consists of two expressions separated by an equal sign. The expression on one side of the equal sign has the same value as the expression on the other side.

Hint 2

For example:
a. 4 + 6 = 5 × 2
b. l = 3 × w
c. 3w + 4xy + 5 = 2w + 3

Front 3

Expressions

Back 3

An expression is made up of one or more terms.

Hint 3

For example:

3w + 4xy + 5

Front 4

Terms

Back 4

A term can be any of the following:

* a constant: e.g. 3, 10, π, 1/2
* the product of a number (coefficient) and a variable: e.g. –3x, 11y, 2/3 a
* the product of two or more variables: e.g. x2, xy, 2y2, 7xy

Hint 4

Like terms are terms that differ only in their numerical coefficients. For example: 3a, 22a, 2/3 a are like terms.

Front 5

Matrices

Back 5

(singular: matrix, plural: matrices) have many uses in real life. One application would be to use matrices to represent a large amount of data in a concise manner so that we can process the data in various ways more conveniently.

Hint 5

For example, the sales of different types of pre-packed food from 3 stalls during a given period of time could be shown in the form of a table here:


Stall A


Stall B


Stall C

Packs of noodles sold


36


21


43

Packs of rice sold


27


56


35

This table can be represented as a matrix:

This matrix could then be added with another that represents the sales for a different period of time to get the total for the two periods of time, etc.

Front 6

Describing Matrices (Rows and Columns)

Back 6

A matrix consists of a set of numbers arranged in rows and columns enclosed in brackets.

Hint 6

Row 1 | 6 10 |
| 5 3 |
| 0 2 |

Front 7

Compound Inequality

Back 7

Students learn that when solving a combined inequality "or" means "union", or everything that's mentioned in the two inequalities. And when solving a combined inequality "and" means "intersection", or only what's in common to the two inequalities.

Hint 7

So when graphing a combined inequality, the first step is to graph the inequalities above the number line, then combine them on the number line based on "or" (bring everything down to the number line) or "and" (only bring down the parts where the graphs overlap).