Questions and Answers
Which of the following is an example of an irrational number?
What is the definition of a rational number?
What is the notation for the square root of a number x?
What is the purpose of indices in mathematics?
Signup and view all the answers
How can surds be simplified?
Signup and view all the answers
What is a surd?
Signup and view all the answers
What is the primary source of energy for photosynthesis?
Signup and view all the answers
Which process releases energy from glucose and produces carbon dioxide and water as byproducts?
Signup and view all the answers
What is the primary function of transportation in an organism?
Signup and view all the answers
Which mode of nutrition involves obtaining energy from other organisms?
Signup and view all the answers
What is the primary function of excretion in an organism?
Signup and view all the answers
Which factor affects the rate of photosynthesis?
Signup and view all the answers
What is the byproduct of photosynthesis that supports life on Earth?
Signup and view all the answers
What is the type of respiration that occurs in the absence of oxygen?
Signup and view all the answers
Study Notes
Rational Numbers
- A rational number is a real number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
- Rational numbers can be expressed as finite decimals or recurring decimals.
- Examples: 3/4, 22/7, 0.5, 0.333...
Irrational Numbers
- An irrational number is a real number that cannot be expressed as the ratio of two integers.
- Irrational numbers have infinite non-repeating decimals.
- Examples: π, e, √2, √3...
Square Roots
- A square root of a number is a value that, when multiplied by itself, gives the original number.
- Square root of a number x is denoted by √x.
- A square root can be positive or negative, e.g., √16 = ±4.
- Square roots of non-perfect squares are irrational numbers.
Indices
- An index (or exponent) is a small number that indicates the power to which a base number should be raised.
- Indices are used to simplify expressions and equations.
- Examples: 2^3, 5^2, x^4...
Surds
- A surd is a square root of a number that cannot be simplified to a whole number or a rational number.
- Surds are irrational numbers that can be expressed using square roots.
- Examples: √2, √3, 2√5...
- Surds can be simplified by combining like terms, e.g., 2√2 + 3√2 = 5√2.
Numbers
- A rational number can be expressed as the ratio of two integers (p/q), where p and q are integers and q ≠ 0.
- Rational numbers can be expressed as finite decimals or recurring decimals.
- Examples of rational numbers include 3/4, 22/7, 0.5, and 0.333...
Irrational Numbers
- An irrational number cannot be expressed as the ratio of two integers.
- Irrational numbers have infinite non-repeating decimals.
- Examples of irrational numbers include π, e, √2, and √3.
Square Roots
- A square root of a number is a value that, when multiplied by itself, gives the original number.
- The square root of a number x is denoted by √x.
- A square root can be positive or negative, for example, √16 = ±4.
- Square roots of non-perfect squares are irrational numbers.
Indices
- An index (or exponent) is a small number that indicates the power to which a base number should be raised.
- Indices are used to simplify expressions and equations.
- Examples of indices include 2^3, 5^2, and x^4.
Surds
- A surd is a square root of a number that cannot be simplified to a whole number or a rational number.
- Surds are irrational numbers that can be expressed using square roots.
- Examples of surds include √2, √3, and 2√5.
- Surds can be simplified by combining like terms, for example, 2√2 + 3√2 = 5√2.
Life Processes
Photosynthesis
- Defined as the process where green plants, algae, and some bacteria convert light energy into chemical energy in the form of glucose
- Occurs in the presence of light, CO2, and H2O, producing glucose and oxygen as byproducts
- Equation: 6CO2 + 6H2O + light energy → C6H12O6 (glucose) + 6O2
- Crucial for producing oxygen, supporting life on Earth, and providing energy and organic compounds for plants and animals
- Factors influencing photosynthesis include light intensity, temperature, water availability, and CO2 concentration
Respiration
- Defined as the process where cells generate energy from glucose, releasing CO2 and H2O as byproducts
- Equation: C6H12O6 (glucose) + 6O2 → 6CO2 + 6H2O + energy (ATP)
- Types: aerobic respiration (with oxygen) and anaerobic respiration (without oxygen)
- Essential for providing energy for cellular activities and maintaining life
- Occurs in the mitochondria of cells
Transportation
- Defined as the movement of substances within an organism, including nutrients, oxygen, and waste products
- Mechanisms: diffusion (passive), osmosis (passive), and active transport (energy-dependent)
- Crucial for maintaining cellular homeostasis and enabling cells to respond to environmental changes
- Occurs through various transport mechanisms, including blood vessels, nerves, and cellular membranes
Nutrition
- Defined as the process where an organism obtains and utilizes nutrients for energy, growth, and maintenance
- Modes: autotrophic nutrition (self-nutrition, e.g., photosynthesis) and heterotrophic nutrition (other-organism nutrition, e.g., ingestion)
- Essential for growth, development, and maintenance of life
- Influences health and well-being, as optimal nutrition supports overall health
Excretion
- Defined as the process where an organism removes waste products from its body
- Mechanisms: excretory organs (e.g., kidneys, liver) and excretory systems (e.g., urinary, digestive)
- Crucial for maintaining cellular homeostasis and preventing toxic buildup of waste products
- Occurs through various excretory systems, including kidneys, liver, and skin
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Understand the difference between rational and irrational numbers, including definitions, examples, and properties.
