### eBook of Forty Risps

This ebook provided by RISPs constitutes a collection of forty open-ended investigative activities for use in the A Level pure mathematics classroom. The book consists of two parts: the first part of the ebook lists all activities indexed by topic together with the teachers' notes. The second part advises on how to make the…

- 5/5
- Publication year: 2000 - 2009
- Activity sheet

### Generic/Miscellaneous Risp Ideas

The first of two RISP activities, Venn Diagrams explores lines in co-odinate geometry and quadratic functions although the idea can be extended to cover other topics. Students are given a Venn diagram with the sets defined. Students are required to find pairs of lines which fit into each of the eight regions. The task is then repeated…

- 5/5
- Publication year: 2000 - 2009
- Activity sheet

### Vectors

Odd One Out, provided by RISPs, helps students focus on mathematical properties to determine which of three numbers or expressions is the odd one out. For example, given the triplet 2, 3, 9: 2 could be the odd one out because it is even and the others are odd. 3 could be the odd one out because it is the only triangle number. 9…

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### Integration 3: Differential Equations

The first of two RISP activities, Modelling the Spread of a Disease requires students to carry out a simulation of a disease spreading. Students carry out an experiment then pool their results to estimate the proportion of the population that will have caught the disease. The experiment is then modelled mathematically using differential…

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### Parametric Equations

This RISP activity is in the form of a puzzle in which students are given a general parametric equation with missing coefficients. A number of clues are given such as a point through which the curve passes. Students have to use their understanding of parametric equations to find the missing numbers. There are a variety of different…

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- Publication year: 2000 - 2009
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### Trigonometry 2

The first of two RISP activities, Radians and Degrees, students are set the task of finding an angle whose sine value is the same whether measured in radians or degrees. Solving the problem leads to further discussion about the relationship between radians and degrees and general trigonometric equations. The second, Generating the…

- 3/5
- Publication year: 2000 - 2009
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### Algebra 2

The first of four RISP activities, Exploring Pascal's Triangle, explores Pascal's triangle, combinations and binomial coefficients. Doing and Undoing the Binomial Theorem and Extending the Binomial Theorem use different approaches to investigate the binomial theorem using negative and fractional indices. Advanced Arithmagons…

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### Proof 2

Two Repeats covers the revision of algebraic topics including changing the subject of a formula, graphical solution of equations, solving simultaneous and quadratic equations and manipulating surds. Given a simple starting premise, students have to solve the puzzle by solving a number of different kinds of equations, working logically…

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### Integration 2

This RISP activity, The answer's 1: what's the question? gives students graphs containing shaded areas enclosed by two functions. Examples of a straight line and a quadratic graph, a cubic graph and an exponential graph are used. Given that the enclosed area has a value of one, students are asked to find the functions.…

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### Differentiation 2

Two Special Cubes is a RISP activity designed to introduce the idea of implicit differentiation. Students are presented with two cubes of length x and y and are told that volume, the surface area and the edge length form an arithmetic progression. Students are asked to find the maximum value for y and hence the corresponding value…

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### Numerical Methods

This RISP activity Polynomial Equations with Unit Coefficients sets students the task of finding the roots of polynomials with a large number of terms. Students are required to use a graph plotter to compare the graphs of several polynomials looking for common points and differences. The task leads to a numeriacal method, iteration,…

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### Functions

The first of two RISP activities, Periodic Functions, asks students to write down as many periodic functions as they can. The activity progresses to look at what happens to the period when graphs with different periods are combined. Topics covered are periodic functions, odd functions, even functions, composite functions and transformation…

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### Logarithms

RISP activity Building Log Equations requires students to form equations given a set of cards and to determine, with examples, whether the equation is always, sometimes or never true and to attempt to say why. Students must include at least one log card in their equation. Students need to be familiar with logs in different number…

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### Trigonometry

This RISP activity gives students four properties - one side is 3cm, one angle is 90 degrees, one side is 4cm and one angle is thirty degrees. Students are required to find as many triangles as they can which contain any three of these four properties. Once the triangles have been found, students are asked to find the area and perimeter…

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### Integration

Two RISP activities designed for students to explore or consolidate ideas about integration. Introducing e requires students to use a graphing package to explore a variety of functions of the form y equals x to the power of n and attempt to find the value for k for which the area under the graph between 0 and k is exactly one.…

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### Differentiation

This RISP activity introduces the subject of differentiation. Rather than start from first principles or learning a rule, the activity suggests using a graphing package to generate data. Starting with a quadratic graph, students find the gradient of the curve using a straight line graph and are encouraged arrive at a rule for differentiating…

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### Sequences and Series

Sequence Tiles requires students to define a position to term rule for a sequence and is extended to iterative sequences, using the set of cards given. Students have to decide the nature of their sequence: convergent and divergent increasing, decreasing, oscillating or periodic. In Geoarithmetic sequences students are required…

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### The Language of Mathematics and Proof

This RISP activity is ideal for introducing, consolidating or revising the idea of proof using a mathematical argument and appropriate use of logiocal deduction. Students are asked to choose two triangular numbers and find when the difference is a prime number. Students should then be encouraged to attempt to prove their conjecture.…

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### Indices and Surds

This RISP activity from can be used when either consolidating or revising ideas of curve-sketching and indices. The numbers phi, e and pi are used in this investigation where students are asked to estimate the size numbers generated when raising these numbers to different powers. It is suggested that a graphing package would prove…

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### Uncertainty and Inequalities

This RISP, Almost Identical, is an activity designed to consolidate work on hyperbolics, exponentials, percentage error and curve sketching. Students are told that the shape of the curve formed by a chain suspended from two points is called a catenary and are asked to attempt to fit a parabola to the curve as best they can, then…

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### Curve Sketching

Five RISP starters revise ideas of polynomials and curve-sketching, cover expanding brackets, solving equations graphically, and knowing how to sketch the graphs of curves. Gold and Silver Cuboid requires the students to use a graph plotter to explore the effects of changing coefficients of a cubic equation. The investigation…

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### Polynomials

The first of three RISP activities exporing polynomials, The Gold and Silver Cuboid requires students to find a connection between the volume of a cuboid, the surface area and the edge length. The second part of the activity asks students to find the maximum and minimum volume of a cuboid gives certain constraints. Venn Diagrams…

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### Coordinate Geometry

Seven RISP activities covering a range of topics, each one having some activity which explores coordinate geometry. Circle Property: Students generate two coordinates. The coordinates form the end points of the diameter of a circle. Students have to find the equation of the circle formed, compare their results with colleagues…

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### Basic Algebra

Three RISP activities designed to introduce or consolidate basic algebraic skills. Brackets Out, Brackets In: students are asked to insert integers into a statement containing brackets in order to obtain as many different results as they can. This activity can be used to introduce, consolidate or revise simple expanding brackets…

- 5/5
- Publication year: 2000 - 2009
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