Interactive Coursebook (Online) of C15 Ratios and Proportions
C15 Ratios and Proportions
What’s on the Specification
| M3.1 | Understand and use scale factors, scale diagrams and maps. |
| M3.2 | Express a quantity as a fraction of another, where the fraction is less than $1$ or greater than $1$. |
| M3.3 | Understand and use ratio notation. |
| M3.4 | Divide a given quantity into two (or more) parts in a given part: part ratio. Express the division of a quantity into two parts as a ratio. |
| M3.5 | Apply ratio to real contexts and problems, such as those involving conversion, comparison, scaling, mixing and concentrations. Express a multiplicative relationship between two quantities as a ratio or a fraction. |
| M3.6 | Understand and use proportion. Relate ratios to fractions and to linear functions. |
| M3.7 | Identify and work with fractions in ratio problems. |
| M3.8 | Define percentage as ‘number of parts per hundred’. Interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively. Express one quantity as a percentage of another. Compare two quantities using percentages. Work with percentages greater than $100\%$. Solve problems involving percentage change, including percentage increase/decrease, original value problems and simple interest calculations. |
| M3.9 | Understand and use direct and inverse proportion, including algebraic representations. Recognise and interpret graphs that illustrate direct and inverse proportion. Set up, use and interpret equations to solve problems involving direct and inverse proportion (including questions involving integer and fractional powers). Understand that $x$ is inversely proportional to $y$ is equivalent to $x$ is proportional to $\frac{1}{y}$. |
| M3.10 | Compare lengths, areas and volumes using ratio notation. Understand and make links to similarity (including trigonometric ratios) and scale factors. |
| M3.11 | Set up, solve and interpret the answers in growth and decay problems, including compound interest, and work with general iterative processes. |
Learning Objectives
- Deconstruct complex multi-part ratio problems by expressing individual components as exact fractions of a total $\left(\frac{a}{a+b+c}\right)$, accurately navigating successive conditional withdrawals such as mixtures and sequential claiming scenarios.
- Execute successive percentage transformations strictly using decimal or fractional multipliers (e.g., $Q_0 \times\left(1+\frac{x}{100}\right)$ ) to model multi-step changes and avoid the mathematical error of additive combinations.
- Formulate precise algebraic equations for direct, inverse, and non-linear proportions ( $y=k x^n$ and $y=\frac{k}{x^n}$ ) to evaluate the cascading percentage impact on a dependent variable when independent parameters are altered.
- Translate linear scale factors $(k)$ into strict geometric area $\left(k^2\right)$ and volume $\left(k^3\right)$ transformations, and model continuous physical or financial growth and decay using compound iterative structures.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 10 | 90 min |
| Quiz | 10 | 20 min |
| Practice A | 30 | 75 min |
| Practice B | 20 | 75 min |
| Total | 70 | approx. 4-5 hrs |
Video Lecture (English):
Practice:
Practice:
You don’t have access to this lesson
Please purchase this course, or sign in if you’re already enrolled, to access the course content.
