# Level 3 (Advanced) resources

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**Level 3 Personal finance activities**

**House price moving averages **This activity uses UK house prices to introduce moving averages and weighted moving averages.

**Credit cards** Students use a recurrence relation to work out how long it takes to pay off a credit card loan and how much it costs. They can use a graphic calculator and/or spreadsheet to do the working.

**Annual Percentage Rate (APR)** Students calculate the APR in the simplest case where a sum of money is borrowed at a particular time and paid back, with interest, in a single payment at a later date.

**APR with more than one instalment** This resource shows students how to check and then find the APR in more difficult cases when a loan or debt is repaid in several annual instalments.

**Measuring inflation using Laspeyres index** Students use a formula to calculate Laspeyres index to obtain a measure of price changes during different periods of time. They use a spreadsheet and/or a calculator to do the working.

**Working with percentages** Use this activity to check what percentage methods students use, and to encourage them to use efficient multiplier methods.

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**Level 3 Data analysis activities **

**HE applications** Students draw statistical diagrams and calculate statistical measures, then write a short report summarising their findings.

**Anthropometric data** Students investigate relationships between anthropometric variables and write a report on their findings. This may include the use of scatter diagrams, lines of best fit, regression lines, and correlation coefficients.

**DISCUSS regression and correlation** Students use an online statistics module to learn about regression and correlation, with guidance from our student sheets and teacher notes.

**Parking permits**** **Students learn about collecting data by stratified sampling and designing a questionnaire.

**Pay rates for men and women ** Students are shown how to draw and format cumulative frequency graphs in Excel.

**Stature** Students use simulated stature data for men and women in eight countries to draw histograms and look for general results.

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**Level 3 Algebra activities **

**Maximum and minimum problems** Using graphical methods to solve maximum and minimum problems in industry and in working life, using a spreadsheet or graphic calculator.

**Climate prediction **** **There are two versions of this activity.

Students create (A) spreadsheets or use (B) graphic calculators to model what would happen to the temperature of the Earth if there were to be a sudden change in the amount of radiation entering or leaving the planet. Then they investigate polynomial and exponential functions to find the best model.

**Gas guzzlers**** **Students use graphical methods to find a suitable model to connect two sets of data. Students can use their model(s) to make predictions. They should also be encouraged to work out percentage errors to test and compare the accuracy of their model(s).

**Coughs and sneezes** Students use polynomial and trigonometric functions to model the number of people suffering from a cold over several weeks.

**Cup of coffee** Students model data from measuring how long caffeine from tea, coffee or cola stays in the human body’s bloodstream. This involves drawing graphs, then finding functions and parameters to fit different models to the graphs.

**Smoke strata** Practice in using logarithmic graphs to check that a power law is a good model for data and find the associated parameters.

**Water flow** Students use linear and quadratic functions to model data, and calculate percentage errors.

**Test run** Students interpret a speed–time graph for a car during a test run, and fit linear and quadratic models to the graph.

**Completing the square** Students match cards to practise completing the square and relating the competed square form to the graph of the function.

**Ozone hole** Students suggest types of function to model ozone hole data (given in a table and also a graph) before using a graphic calculator or spreadsheet to find at least two particular models. They then consider how well their functions model the data and what they predict for the future.

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**Level 3 Calculus activities**

**Exponential rates of change** This activity introduces the differentiation of exponential functions. Students find gradients by drawing tangents and by using small incremental changes in a spreadsheet.

**What's it worth?** Students solve differential equations to find functions to model the value of a car in terms of its age. Then they compare their results with real data.

**Stationary points** This activity shows students how to use differentiation to find stationary points on the curves of polynomial functions. It includes the use of the second derivative to determine the nature of the stationary point. Students will learn how to use this and other information to sketch the curves, then use graphic calculators to check their answers.

**Maxima and minima** Students use differentiation to find maximum and minimum points in polynomial functions in order to solve a variety of real-life problems.

**Coastal erosion A Estimating area** Students approximate the area of a piece of land with an irregular coastline, and the area lost to coastal erosion over time.

**Coastal erosion B Integrating area** Students use integration to approximate the area of a piece of land with an irregular coastline, and the area lost to coastal erosion over time.

**Maximising and minimising** Students consider some maximisation/ minimisation problems and then devise some of their own. There are no student sheets.

**Drug clearance** This activity explores the rate of drug clearance from the body, both for common analgesic compounds and for caffeine.

**Derivative matching** Matching activities to check whether students can identify the derivatives of quadratic and cubic functions and their graphs.

**Mean values** Students learn how to find the mean values of quantities varying with time. This involves finding the area under graphs, initially by using geometrical formulae for areas. It is followed by the use of integration in a variety of real life situations.

**Gradients ** An introduction to differentiation. Students are shown how to use a spreadsheet to find the gradients of functions of the form x^{n}. This leads to the general rule for gradients of functions of this type.

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**Level 3 Dynamics activities**

**Newtonian modelling** An introduction to Newton’s Laws of Motion and how they can be applied in modelling real situations.

**Solve friction problems** In this activity the friction model *F*≤*μR* is used to solve two sets of problems. The first set consists of simple problems involving bodies in limiting equilibrium. Problems in the second set are more complex, and students solve these by combining the friction model with Newton’s Second Law and the constant acceleration equations.

**Projectile problems** Students use the equations for motion in a straight line with constant acceleration, and the projectile model, to solve problems involving the motion of projectiles in real contexts

**Galileo's projectile model** A practical activity in which students analyse and validate Galileo’s model for the motion of a projectile. Students will need to be familiar with the uniform acceleration equations for motion in a straight line.

**Vectors ** Basic manipulation of vectors in component form is reviewed, and then vectors are used to solve real-life two-dimensional problems. These involve the use of the uniform acceleration formulae and Newton’s Laws of Motion in vector form.

**Model the motion** Students match descriptions of a variety of real scenarios involving motion with the corresponding velocity–time and displacement–time graphs.

**Investigating friction** A practical activity in which students investigate the relationship between the normal contact force and limiting friction. They should discover that friction is a variable force and its maximum value is proportional to the normal contact force.

**Runaway train** Students collect data about a trolley rolling down a slope. They use this to simulate the motion of a train by fitting a quadratic curve to their data, using a graphic calculator or spreadsheet.The main emphasis of the activity is the modelling cycle.

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**Level 3 Decision maths**

**Chinese postman problem ** An introduction to the concept, and an investigation of the minimum distance someone would have to travel to deliver leaflets along all the streets near to a college, starting at and returning to the same place. Then students to find an Eulerian trail for a network with four odd nodes.

**Sightseeing tour** This resource can be used as a classroom activity or an assignment. It involves students setting up their own network as the basis for a sightseeing tour. In identifying their route, students will need to make use of the Chinese Postman Algorithm and/or the Travelling Salesman Algorithm, depending on whether their route involves visiting the edges or the vertices of their network.

**Networks **This activity introduces the terms used when working with networks, and gives students practice in using them.

**Cable TV ** This activity shows students how to use Kruskal’s and Prim’s algorithms to solve minimum connector problems. A cable TV problem introduces the topic and the rules for the two algorithms. The students are then set a second problem involving a theme park.

**Refurbishing a room ** An introduction to critical path analysis. The tasks are based on decorating and furnishing a bedroom, and take students through the process of constructing an activity network and calculating the minimum completion time for the project.

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**Level 3 Hypothesis testing **

**Successful HE applicants** Students carry out significance tests on proportions to test hypotheses about successful applicants to higher education.

**Gender differences** Students carry out significance tests on means in order to test hypotheses about the body measurements of boys and girls at different ages.

**Parking permits **Students learn about collecting data by stratified sampling and designing a questionnaire.

**Probability **Students use relative frequency to estimate probability. They find theoretical probabilities including probabilities of combined events. They use probabilities to predict the expected number of trials in which an event will occur.

**Laws of probability** The addition law for probabilities of mutually exclusive events and the multiplication law for probabilities of independent events are introduced. Students then use these laws to tackle some probability problems.

**Rain or shine** Students use sunshine and rainfall data to carry out significance tests on the difference between sample means. As part of this activity students use either a calculator or a spreadsheet to calculate mean and standard deviation values.

**Can they tell the difference?** Students use a triangle test to decide whether or not people can tell the difference between a product and a healthier alternative.