Key Mathematical Terms with Definitions and Examples
Understanding and using maths terminology is crucial for excelling in math classes and solving complex problems. In this section, we’ll break down some of the subject's fundamental terms.
Adding
Addition is the operation of combining two or more numbers to find their sum. It is represented by the "+" symbol. For example:
- 3 + 5 = 8
- 12.5 + 7.3 = 19.8
- 2 + (-3) = -1 (adding a negative number subtracts)
- Addition is commutative, meaning the order of numbers does not affect the result: a + b = b + a.
Algebra
Algebra uses symbols and numbers to solve problems, even when we don't have all the information. It's vital for understanding and solving real-world problems in science, engineering, and economics.
Overall, algebra is the math of symbols and numbers. Equations find missing values, expressions describe values, and functions show how things relate. These concepts are essential for solving problems and making decisions in many different fields.
Algorithm
In complex mathematical problems, an algorithm is the order of steps you must take to solve it.
Angles
An angle is formed when two rays or line segments share a common endpoint, called the vertex. Angles are measured in degrees (°) and can range from 0° (a straight angle) to 360° (a full circle).
Types of Angles: There are various types of angles, including:
- Acute Angle: An angle measuring less than 90°.
- Right Angle: An angle measuring exactly 90°.
- Obtuse Angle: An angle measuring more than 90° but less than 180°.
- Straight Angle: An angle measuring 180°.
- Reflex Angle: An angle measuring more than 180° but less than 360°.
- Complementary and Supplementary Angles: Complementary angles add up to 90°, while supplementary angles add up to 180°.
Arithmetic
Arithmetic covers basic math operations: addition, subtraction, multiplication, and division. You may have even learned some of this in kindergarten math; they’re familiar terms taught to us from a young age. They form the foundation for everyday math and advanced concepts. Let's dive into each operation.
Average
Also known as the Mean, the average is the number you get when you add all of a group of numbers together and divide that sum by the number of numbers.
Basic Operations
Basic operations encompass fundamental mathematical actions such as addition, subtraction, multiplication, and division. These operations are applied to numbers or quantities to perform calculations.
BEDMAS (Or PEMDAS)
An acronym used to help people remember in which order to solve complex equations. The letters of BEDMAS stand for:
- Brackets (Or Parentheses)
- Exponents
- Division and Multiplication
- Addition and Subtraction
When solving an algebra equation, Division/multiplication and Addition/Subtraction must be done in the order in which they occur within the equation.
Calculus
Calculus is used in physics to study the motion of objects. When you calculate the speed of a car at different times during a trip, you are using calculus to understand how the car's velocity changes over time.
Calculus is fundamental in fields like physics, engineering, economics, and computer science. It's used to solve problems involving rates of change, optimization, and understanding complex systems.
Calculus often requires a fundamental knowledge of math basics first, like the skills taught in pre-calculus.
Derivatives
Derivatives measure the rate at which a function changes. They represent the slope of a function's tangent line at a particular point and can tell us how a quantity is changing with respect to another.
Derivatives are crucial for understanding motion, optimization, and solving problems involving change. They are used extensively in physics, engineering, and economics.
Dividing
Division is the operation of splitting a quantity into equal parts or finding out how many times one number is contained within another. It is represented by the "÷" or "/" symbol. For example:
- 16 ÷ 4 = 4
- 10.5 ÷ 2.1 = 5.0
- 12 ÷ (-3) = -4 (dividing by a negative number changes the sign)
- Division is not commutative: a ÷ b ≠ b ÷ a in most cases.
Ellipse
An ellipse is similar to a circle that has been slightly flattened. It is still a round shape with the width and the height being different lengths.
Equations
Equations are math sentences that show two things are equal, usually with an equal sign (=). We use them to find missing numbers. Equations help us solve math problems, express relationships between numbers, and figure out unknown values.
Even Number
Any number that can be divided by two and return a whole number (2, 4, 36, 48, etc)
Exponents
Exponents are shortcuts to represent repeated multiplication and are essential for handling large or small numbers, often used in science and engineering.
Expressions
Expressions are like math phrases with numbers, letters, and operations (like +, -, *, and /). They show the value of something. Expressions help us describe math relationships and do calculations. They're the building blocks for equations and functions.
Functions
Functions are math rules that link one thing to another using 'x' and 'y'. We can express them as equations or graphs. They help us understand how one thing changes when something else changes. They're super useful in science, engineering, and economics for making predictions and decisions.
Geometry
Geometry studies shapes, sizes, and properties of objects and spaces. It's crucial in fields like architecture, engineering, art, and physics.
Geometry isn't just about shapes and angles; it helps solve spatial problems, design buildings, create art, and navigate. It's a fascinating math branch used daily in science and technology.
Integrals
Integrals are the opposite of derivatives. They represent the accumulation or total of a quantity over an interval. Integrals can help find areas, volumes, and the net change of a function.
They’re essential in physics, engineering, and geometry for calculating areas, volumes, and understanding accumulations. They also help solve problems involving motion and accumulation.
Limits
Limits are fundamental to calculus as they define the behavior of functions as they approach a particular value. They help us understand what happens when we get closer and closer to a certain point.
Limits help with defining derivatives and integrals. They provide the foundation for understanding continuity and the behavior of functions, especially in cases where functions have discontinuities or behave strangely at certain points.
Lines
- Line Segment: A line segment is a part of a line with two endpoints. It has a definite length and can be measured.
- Ray: A ray is a part of a line that starts at one endpoint and extends infinitely in one direction.
- Line: A line is a straight path that extends infinitely in both directions. It has no endpoints.
Multiplying
Multiplication is the operation of repeated addition. It involves finding the product of two or more numbers. It is represented by the "×" or "*" symbol. For example:
- 4 × 3 = 12
- 5.2 × 2.5 = 13.0
- (-2) × (-7) = 14 (multiplying two negatives gives a positive result)
- Multiplication is commutative: a × b = b × a.
Odd Numbers
Any number that cannot be divided by two and return a whole number (3, 5, 45, 67, etc)
Ratios and Proportions
Ratios compare two quantities, while proportions express that these ratios are equal. They're used to maintain balance in various applications, from cooking to geometry problems.
Roots
Roots are the opposite of exponents and help find original values that are useful in various problem-solving scenarios.
Simple Math Functions
Simple math functions are operations or rules that take one or more numbers as input and produce a specific output based on those numbers. Common examples include addition, subtraction, multiplication, and division.
Shapes
- Polygon: A polygon is a closed shape made up of line segments. Common polygons include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), and so on.
- Circle: A circle is a round shape with all points equidistant from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is the diameter.
- Rectangle: A rectangle is a four-sided polygon with opposite sides equal in length and all angles equal to 90°.
- Triangle: A triangle is a polygon with three sides and three angles. There are various types of triangles, including equilateral (all sides and angles are equal), isosceles (two sides and angles are equal), and scalene (no sides or angles are equal).
- Quadrilateral: A quadrilateral is a four-sided polygon. Examples include rectangles, squares, parallelograms, and trapezoids.
Subtracting
Subtraction is the operation of taking one number away from another to find the difference. It is represented by the "-" symbol. For example:
- 10 - 4 = 6
- 15.7 - 3.2 = 12.5
- 8 - (-3) = 11 (subtracting a negative number adds)
- Subtraction is not commutative, meaning the order of numbers does affect the result: a - b ≠ b - a in most cases.
Now that we’ve gone through some words related to maths, you hopefully feel a bit more familiar and comfortable with the subject. The next time you’re prepping for a test in math class, think back on these terms as you study.
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