20 Questions
What is the formula to calculate the gradient of a line?
$\frac{y_2 - y_1}{x_2 - x_1}$
Which of the following is NOT a way to represent a relationship between variables?
Scatter plot
What is the term for a quantity that can change?
Variable
What is the purpose of interpreting graphs?
To visualize the relationship between variables
What is the term for the rate of change between variables in a graph?
Gradient
Which of the following is a feature to consider when interpreting graphs?
Shape of the graph
What is the term for the points where a graph crosses the axes?
Intercepts
What is the purpose of a flow diagram in representing a relationship between variables?
To show the calculations needed to transform input into output
What is the term for the result after applying a function to an input?
Function value
Which of the following is a type of representation of a relationship between variables?
All of the above
Which representation of a relationship between variables is particularly useful for visualizing the relationship between two variables?
Graph
What does the gradient of a line passing through two points represent?
The rate of change between the x and y variables
Which of the following is a characteristic of a function?
Each input has exactly one output
What is the purpose of finding the intercepts of a graph?
To find the points where the graph crosses the axes
What is a common use of flow diagrams in representing relationships between variables?
To show the calculations needed to transform input into output
What can be inferred about the relationship between variables from the shape of the graph?
The type of function (linear, quadratic, etc.)
Which representation of a relationship between variables is particularly useful for identifying patterns and trends?
Graph
What is the term for the specific output corresponding to a given input?
Function value
Which of the following is a key feature to consider when interpreting graphs?
The continuity of the graph
What does the continuity of a graph indicate about the relationship between variables?
Whether the graph is a continuous line or has breaks/discontinuities
Study Notes
Functions, Patterns, and Graphs
Representations of Relationships
- Relationships between variables can be represented in multiple ways, including flow diagrams, tables, formulas, verbal descriptions, and graphs.
Gradient of a Line
- The gradient (or slope) of a line can be calculated using the formula:
Gradient = (y2 - y1) / (x2 - x1)
Understanding Functions
- A function describes a relationship between two variables where each input has exactly one output.
- Functions can be represented in various ways, including:
- Tables: displaying values of input and corresponding output
- Flow diagrams: showing the calculations needed to transform input into output
- Formulas: algebraic expressions that define the function
- Graphs: visual representations of the function on a coordinate plane
Key Concepts in Functions
- A variable is a quantity that can change.
- An input number is the value substituted into a function.
- An output number is the result after applying the function to the input.
- A function value is the specific output corresponding to a given input.
Interpreting Graphs
- Graphs provide a visual method to understand the relationship between variables.
- Key features to consider when interpreting graphs include:
- Slope/Gradient: indicates the rate of change between variables
- Intercepts: points where the graph crosses the axes
- Continuity: whether the graph is a continuous line or has breaks/discontinuities
- Shape of the Graph: linear, quadratic, exponential, etc., which provides insights into the nature of the relationship
Functions, Patterns, and Graphs
Representations of Relationships
- Relationships between variables can be represented in multiple ways, including flow diagrams, tables, formulas, verbal descriptions, and graphs.
Gradient of a Line
- The gradient (or slope) of a line can be calculated using the formula:
Gradient = (y2 - y1) / (x2 - x1)
Understanding Functions
- A function describes a relationship between two variables where each input has exactly one output.
- Functions can be represented in various ways, including:
- Tables: displaying values of input and corresponding output
- Flow diagrams: showing the calculations needed to transform input into output
- Formulas: algebraic expressions that define the function
- Graphs: visual representations of the function on a coordinate plane
Key Concepts in Functions
- A variable is a quantity that can change.
- An input number is the value substituted into a function.
- An output number is the result after applying the function to the input.
- A function value is the specific output corresponding to a given input.
Interpreting Graphs
- Graphs provide a visual method to understand the relationship between variables.
- Key features to consider when interpreting graphs include:
- Slope/Gradient: indicates the rate of change between variables
- Intercepts: points where the graph crosses the axes
- Continuity: whether the graph is a continuous line or has breaks/discontinuities
- Shape of the Graph: linear, quadratic, exponential, etc., which provides insights into the nature of the relationship
This quiz covers the basics of functions, patterns, and graphs, including representations of relationships, gradient of a line, and understanding functions.
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