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Foundation plus - Ratio, proportion and rates of change
infoWhy this? Ratio and proportion help us compare quantities, scale amounts, and model direct and inverse relationships. Applying these ideas to speed, density, pressure, and distance–time graphs connects numerical calculations with units, graphical representations, and practical interpretations of change.
scheduleWhy now? The preceding algebraic manipulation unit supports substitution into formulae and the representation of proportional relationships. Establishing proportional reasoning here prepares us to interpret enlargement scale factors in transformations, percentage multipliers, and later relationships between similar shapes.
neurologyYou need to know
- A ratio compares two or more quantities, showing how many times one value contains or is contained within the other.
- To share a quantity into a given ratio, the total is divided into parts proportional to the values in the ratio.
- Direct proportion means that as one quantity increases, the other increases at a constant rate (y = kx).
- Inverse proportion means that as one quantity increases, the other decreases so that their product is constant (xy = k).
- The difference between two values in a ratio can be used to find the actual values when the total or part of the total is known.
- Ratios can be combined or simplified to solve more complex problems involving multiple relationships.
- Proportion can be used to scale quantities up or down, such as in recipes.
- On a direct proportion graph, the relationship is linear and passes through the origin.
- The rate of change in a direct proportion graph is constant and can be deduced from the gradient.
- Average speed is calculated as total distance divided by total time.
- Density is calculated as mass divided by volume (density = mass/volume).
- Pressure is calculated as force divided by area (pressure = force/area).
- Distance-time graphs represent how distance changes over time, and their gradients represent speed.
rocket_launchYou must be able to
- Share a quantity into a given ratio, including finding individual parts.
- Solve worded problems involving direct proportion, including setting up and solving equations.
- Solve worded problems involving inverse proportion, including setting up and solving equations.
- Solve problems when given the difference between two values in a ratio.
- Solve problems by combining two or more different ratios to find unknown values.
- Use proportion to solve recipe problems, including scaling quantities up or down.
- Deduce rates of change (gradients) from direct proportion graphs.
- Calculate average speeds, distances, and times using the formula speed = distance/time.
- Calculate density, mass, and volume using the formula density = mass/volume.
- Calculate pressure, area, and force using the formula pressure = force/area.
- Draw and interpret distance-time graphs, including identifying periods of rest, constant speed, and changes in speed.
Revision Quiz
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