Year 8 Exam > Year 8 Notes > Year 8 Mathematics (Cambridge) > Sequences and Functions
Sequences and Functions | Year 8 Mathematics (Cambridge) PDF Download
Identifying and Extending Sequences
Definition of Sequence
A sequence is a list of numbers arranged in a specific order.
Identifying Sequences
- A sequence can be arithmetic or geometric.
- Arithmetic Sequence: A sequence where each term is obtained by adding a constant difference to the previous term.
- Example: 2, 5, 8, 11, 14,…
- Geometric Sequence: A sequence where each term is obtained by multiplying the previous term by a constant ratio.
- Example: 3, 6, 12, 24, 48,…
Extending Sequences
- To extend a sequence, identify the pattern (arithmetic or geometric) and continue applying the pattern to find subsequent terms.
- Example: Extend the sequence 1, 4, 7, 10,… (Arithmetic sequence with a difference of 3).
Understanding Functions
Definition of a Function
- A function relates each element of a set (domain) to exactly one element of another set (range).
Characteristics of Functions
- Domain: Set of all possible input values.
- Range: Set of all possible output values.
- Mapping: Representation of how elements of the domain are mapped to elements of the range.
Types of Functions
- Linear Function: A function that forms a straight line when graphed.
- Example: f(x) = 2x + 3
- Quadratic Function: A function where the highest degree of the variable is 2.
- Example: f(x) = x2 + 4x + 3
- Exponential Function: A function where the variable is an exponent.
- Example: f(x) = 2x
Question for Sequences and FunctionsTry yourself: Which type of sequence is represented by the following sequence: 3, 9, 27, 81, ...?View Solution
Graphing Linear Functions
Graphing Process
- Identify the Equation: For example, f(x) = 2x + 3.
- Plot Points: Choose values for x, calculate corresponding y, and plot points.
- Draw the Line: Connect the points to form a straight line.
Key Elements of a Linear Graph
- Slope: The steepness of the line.
- Intercept: The point where the line crosses the y-axis (y-intercept).
Example
- Graph the function f(x) = 2x + 1.
- Choose values for x = 0, 1, −1.
- Calculate corresponding y: f(0) = 1, f(1) = 3, f(−1) = −1.
- Plot points: (0, 1), (1, 3), (−1, −1).
- Draw the line through these points.
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FAQs on Sequences and Functions - Year 8 Mathematics (Cambridge)
| 1. What are some common examples of sequences and functions in UK school curriculums? |  |
Ans. Common examples of sequences and functions in UK school curriculums include arithmetic sequences, geometric sequences, linear functions, quadratic functions, and exponential functions.
| 2. How are sequences and functions used in real-life applications that UK schools teach? | |
Ans. Sequences and functions are used in real-life applications to model patterns, growth rates, and relationships in various fields such as finance, engineering, and natural sciences.
| 3. What is the importance of understanding and graphing linear functions in UK school mathematics? | |
Ans. Understanding and graphing linear functions is important in UK school mathematics as it provides a foundation for more complex functions and helps students analyze and interpret data in a visual way.
| 4. How can students identify and extend sequences effectively in UK school exams? | |
Ans. Students can identify and extend sequences effectively in UK school exams by looking for patterns, determining the rule or formula, and applying it to find missing terms or future terms in the sequence.
| 5. What resources or tools are commonly used in UK schools to help students learn about sequences and functions? | |
Ans. Common resources or tools used in UK schools to help students learn about sequences and functions include textbooks, online interactive platforms, graphing calculators, and educational websites with practice problems and tutorials.
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Dec 22, 2024 Last updated |
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