# GMC4: Using rules and formulae

This list contains a collection of resources to help meet General Mathematical Competency 4 (GMC4). More resources to support T level Science can be found on our T Level science resource packages page.

**GMC4 states:**

Students should be able to:

- Substitute values into a formula
- Manipulate formulae
- Solve equations

Students should know how to calculate the rate of reaction: amount of reactant or product/time

Students should know how the following gas laws describe the behaviour of gases in particular conditions:

- Boyle’s Law (P
_{1}V_{1}= P_{2}V_{2}) - Charles’s Law (V
_{1}T_{2}= V_{2}T_{1}) - the Pressure Law (P
_{1}/T_{1}= P_{2}/T_{2})

### Algebra

These resources cover a wide range of algebraic topics. They include solving linear equations, quadratic equations, rearranging formulas, the laws of indices, expanding brackets, inequalities and solving simultaneous equations.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of algebraic principles will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided

### Algebra

These resources cover a wide range of algebraic topics, many of which are suitable for students studying mathematics at Higher Level GCSE, or A Level, as well as those students for whom mathematics is an integral part of their course. Some of the topics covered include completing the square, factorising quadratics, partial fractions, integration, simultaneous linear equations, logarithms and polynomial division.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of algebraic principles will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided.

### Algebra Refresher

This algebra refresher resource has been designed to enable students to prepare for their university mathematics programme. There is a comprehensive review of algebraic manipulation including, removing brackets, surds, solving linear equations, transposition of formulae, quadratic equations and completing the square.

Although it has been produced for students who have completed an A Level in Mathematics, it is also a very useful resource for those following Higher Level GCSE.

### Body mass index (BMI)

This task involves substituting values into the BMI formula in order to make health decisions.

An introductory worksheet gives the height and mass of four people so that their BMI can be calculated and appropriate advice given. A further worksheet and excel file shows mass and height of a sample of 16 people both before and after a healthy living programme suitable for BMI calculations.

The resources includes teacher guidance and provides suggestions for extension activities such as statistical analysis of the two sets of BMIs covering topics such as stem and leaf diagrams and standard deviation.

### Body surface area

This resource introduces the formulae for the surface areas of cylinders, cones and spheres. Students are asked to use these to model parts of the body and calculate an estimate of their own body's surface area. Two formulae used in medicine for body surface area are also given so that comparisons can be made.

When calculating an estimate for their own body surface area students need to make decisions about measurements, estimates and calculations. They are also asked to substitute height and weight data into formulae. The Pearson product-moment correlation coefficient can be used to explore correlation.

### Cormathzadrine

In this resource students deal with the problem of administering doses of a prescribed drug so that the body does not have too little or an excess of the drug. An understanding of half life is required. Students do not need to use more complicated formulae for exponential decay but that could be introduced in an extension.

The resource includes teacher guidance, a student handout, specimen reports and assessment sheets which could be used to aid peer assessment of reports

### Physical Fitness

In this activity students create a graphical ready reckoner to assess physical fitness. The challenge is to construct the ready reckoner and ultimately use it in practical situations. Students are required to plot straight line graphs.