Linear Equations: y=mx+c

This page introduces the fundamental equation for linear functions: y=mx+c. This equation is crucial for understanding and graphing straight lines.

Definition: In the equation y=mx+c:

• y is the dependent variable
• x is the independent variable
• m is the gradient (slope) of the line
• c is the y-intercept (where the line crosses the y-axis)

The page includes a graph illustrating the components of a linear equation, helping students visualize the relationship between the equation and its graphical representation.

Example: For the equation 2 = 3x + 4:

• The gradient (m) is 3
• The y-intercept (c) is 4

Highlight: When plotting linear equations, remember that the gradient determines the steepness and direction of the line, while the y-intercept determines where the line crosses the y-axis.

The page concludes with an exercise asking students to identify the y-intercept and gradient of a given line, reinforcing the practical application of the y=mx+c equation.

Mean, Median, Mode, and Range

This page introduces the fundamental concepts of how to calculate mean, median, mode, and range. These measures of central tendency and spread are essential for understanding and summarizing datasets.

The mean is calculated by adding all numbers and dividing by the count of numbers. For example, the mean of 1, 0, 2, and 3 is (1+0+2+3) ÷ 4 = 1.5.

Definition: The median is the middle value when numbers are ordered.

Example: For the set 5, 4, 3, 2, 1, the median would be 3.

The mode is the most frequently occurring number in a dataset.

Example: In the set 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, the mode would be both 2 and 5.

The range is calculated by subtracting the smallest number from the largest number in a dataset.

Highlight: When given the mean and asked to find a missing number, use the formula: (mean × total count) - sum of known numbers = missing number.

The page also includes an example of finding a possible set of 6 numbers given specific conditions about their median, range, and mode.

Averages from Frequency Tables

This page focuses on calculating averages from frequency tables, which is a crucial skill for interpreting frequency tables for averages.

The main example presented is a frequency table showing the number of pints of milk used by 40 families in a week. The table includes columns for pints (1-6) and their corresponding frequencies.

Example: To calculate the mean from a frequency table:

1. Multiply each value by its frequency
2. Sum these products
3. Divide by the total frequency

In this case, the mean is calculated as 140 ÷ 40 = 3.5 pints.

Highlight: The mode can be easily identified from a frequency table as the value with the highest frequency. In this example, the mode is 3 pints.

The page also includes questions about finding the mode and the total number of pints used, reinforcing the understanding of frequency table interpretation.