Ratio
Ratios are used to compare quantities. You can simplify a ratio, for example:
3km: 3m = (3 x 1000) : 3 = 3000 : 3.
To simplify a ratio, you need to divide a given quantity into a given ratio and work out the value of one part. For example, if Sarah, John, and James share £300 in the ratio of 3:4:5, you can calculate that each person receives £75, £100, and £125 respectively.
Ratios can be simplified using calculations and examples to make the process clearer. Simplifying ratios involves breaking down composite shapes into their component shapes to find the area and perimeter. For example, to calculate the perimeter and area of a given shape, it's important to find the measurements of each side and the total area and perimeter.
Composite shapes are made up of other shapes, and calculating their area and perimeter requires breaking them down into their component shapes.
Calculating the area and volume of composite shapes such as cylinders requires understanding the geometric properties and formulas involved. For example, the volume of a cylinder is found using the formula πr²h and the surface area is found using 2πrh + 2πr².
Statistical measures involve analyzing data sets and frequency distributions to calculate the mean, median, and mode. For example, using a frequency table to calculate the modal class, estimate the mean time taken, and work out the group that contains the median.
Other types of graphs, such as velocity-time graphs, linear graphs, and line graphs, are used to illustrate mathematical relationships and concepts. These graphs are used to visualize the velocity, distance, and speed of objects in various scenarios.
Understanding fractions involves multiplying and dividing fractions to find simplified forms. It's important to understand the rules for multiplying and dividing fractions, canceling diagonally, and converting mixed numbers to improper fractions.
Finding the nth term of a linear sequence involves identifying the pattern in the numbers and using a function machine to represent the sequence. For example, finding the expression for the nth term in a sequence that increases by the same amount each time.
Statistical diagrams such as line graphs are used to visualize changes over time and display trends in data. For example, using a line graph to show ice cream sales for Shelby's over the course of a year.
These foundation maths study notes cover a range of topics including ratio and simplifying ratios, composite shapes, area and volume, statistics, other graphs, fractions, number patterns, sequences, and statistical diagrams. For further details and examples, the foundation maths study notes PDF is available for free download.
