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?
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How can surds be simplified?
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What is a surd?
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What is the primary source of energy for photosynthesis?
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Which process releases energy from glucose and produces carbon dioxide and water as byproducts?
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What is the primary function of transportation in an organism?
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Which mode of nutrition involves obtaining energy from other organisms?
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What is the primary function of excretion in an organism?
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Which factor affects the rate of photosynthesis?
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What is the byproduct of photosynthesis that supports life on Earth?
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What is the type of respiration that occurs in the absence of oxygen?
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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
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Description
Understand the difference between rational and irrational numbers, including definitions, examples, and properties.