SCHEME OF WORK IGCSE MATHEMATICS (0580) YEAR 11 2012Suggested no. of weeksTopics / Sub topicsAssessment ObjectivesSuggested Activities / ApproachesSupplementary Resources

3 Weeks12. PROBABILITY

12.1 Definition of Probability

12.2 Probability of Combined Events

12.2.1 Possibility Diagrams

12.2.2 Tree Diagrams Calculate the probability of simple combined events,

Using possibility diagrams and tree diagrams where appropriate (impossibility diagrams outcomes will be represented by points on a grid and in tree diagrams outcomes will be written at the end of branches and probabilities by the side of the branches). Use simple examples to illustrate how possibility diagrams and tree diagrams can help to organise data.

Use possibility diagrams and tree diagrams to help calculate probabilities of simple combined events, paying particular attention to how diagrams are labelled.

Solve straightforward problems involving independent and dependent events, e.g. picking counters from a bag with and without replacement.Various problems involving probability athttp://nrich.maths.org/public/leg.php

IGCSE Mathematics (2nd edition) by Ric Pimentel and Terry Wall Pg 369-378

IGCSE Mathematics by Karen Morrison Pg 236-244

3 Weeks13. SETS

13.1 Set language and Notation

13.2 Set Operations

13.3 Venn Diagrams

Use language, notation and Venn diagrams to describe sets and represent relationships between sets as follows:

Definition of sets, e.g. A = {x: x is a natural number} B = {(x,y): y= mx+ c} C = {x: axb} D = {a, b, c, .....}

Notation: number of elements in set A n(A) .... is an element of .... .... is not an element of .... Complement of the set A A' The empty set Universal set A is a subset of B, A B A is a proper subset of B, A B A is not a subset of B , A B A is not a proper subset of B, A B Union of A and B , A B Intersection of A and B, A B Give examples from work already covered to illustrate the language and notation of sets. Distinguish between a subset and a proper subset.

Draw Venn diagrams and shade the regions which represent the sets A B, A B, A' B, A B', A' B, A B ', A' B' and A' B' . Show that (A B) ' is the same as A' B' and that (A B) ' is the same as A' B' .

Use Venn diagrams to solve problems involving sets. Information and references to activities for teachers at http://www.mathworld.wolfram.com/VennDiagram.html

IGCSE Mathematics (2nd edition) by Ric Pimentel and Terry Wall Pg 30-40

IGCSE Mathematics by Karen Morrison Pg 9-14

3 4 Weeks14. VECTORS 14.1 Vector Representation

14.2 Addition and Subtraction of Vectors

14.3 Multiplication by a Scalar

14.4 Column Vectors

14.5 Parallel Vectors

14.6 Magnitude

Describe a translation by using a vector represented by x, or a.

Add and subtract vectors and multiply a vector by a scalar.

Calculate the magnitude of a vector as . (Vectors will be printed as or a and their magnitudes denoted by modulus signs, e.g. or . In their answers to questions candidates are expected to indicate a in some definite way, e.g. by an arrow or by underlining, thus or a ).

Represent vectors by directed line segments.

Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors.

Use position vectors.

Use the concept of translation to explain a vector.

Use simple diagrams to illustrate column vectors in two dimensions, explaining the significance of positive and negative numbers.

Introduce the various forms of vector notation.

Show how to add and subtract vectors algebraically and by making use of a vector triangle.

Show how to multiply a column vector by a scalar and illustrate this with a diagram.

Use simple diagrams to help show how to calculate the magnitude of a vector (Pythagoras theorem may have to be revised).

Define a position vector and solve various straightforward problems in vector geometry.Interactive work on vector sums at http://www.standards.nctm.org/document/eexamples/chap7/7.1/part2.htm

IGCSE Mathematics (2nd edition) by Ric Pimentel and Terry Wall, Pg 278 289

IGCSE Mathematics by Karen MorrisonPg 255 - 261

2 Weeks15. NUMBER SEQUENCE Continue a given number sequence;

Recognise patterns in sequences and relationships between different sequences,

Generalise to simple algebraic statements (including expressions for the nth term) relating to such sequences.

Define a sequence of numbers. Work with simple sequences, e.g. find the next two numbers in a sequence of even, odd, square, triangle or Fibonacci numbers, etc. Find the term-to-term rule for a sequence, e.g. the sequence 3, 9, 15, 21, 27, .... has a term-to-term rule of +6 Find the position-to-term rule for a sequence, e.g. the nth term in the sequence 3, 9, 15, 21, 27, .... is 6n - 3 .

Class activity: Square tables are placed in a row so that 6 people can sit around 2 tables, 8 people can sit around 3 tables, and so on. How many people can sit around n tables?Various problems involving sequences of numbers at http://nrich.maths.org/public/leg.php

IGCSE Mathematics (2nd edition) by Ric Pimentel and Terry Wall Pg 25 29

IGCSE Mathematics by Karen MorrisonPg 7 - 8

3 Weeks16. MENSURATION

16.1 Perimeter and Areas

16.1.2 Common Figures

16.1.3 Composite Figures

16.2 Arc Length and Area of Sector

16.3 Volume and Surface Area

16.3.1 Common Solids

16.3.2 Composite Solids

Carry out calculations involving the perimeter and area of a rectangle and triangle, the circumference and area of a circle, the area of a parallelogram and a trapezium.

Solve problems involving the arc length and sector area as fractions of the circumference and area of a circle.

Carry out calculations involving the volume of a cuboid, prism and cylinder and the surface area of a cuboid and a cylinder.

Solve problems involving the surface area and volume of a sphere, pyramid and cone (given formulae for the sphere, pyramid and cone).Revise, using straightforward examples, how to calculate the circumference and area of a circle, and the perimeter and area of a rectangle and a triangle. Extend this to calculating the area of a parallelogram and a trapezium.

Class activity: Using isometric dot paper investigate the area of shapes that have a perimeter of 5, 6, 7, units.

Use straightforward examples to illustrate how to calculate arc length and the area of a sector.

Starting with simple examples draw the nets of various solids. Show, for example, that the net of a cube can be drawn in different ways.

Class activity: Draw nets on card and make various geometrical shapes.Use nets to illustrate how to calculate the surface area of a cuboid, a triangular prism, a cylinder, a pyramid and a cone. Show how to obtain the formula r(r+l) for the surface area of a cone. Calculate the surface area of a sphere using the formula 4r .

Use straightforward examples to illustrate how to calculate the volume of various prisms (cross-sectional area x length). Calculate the volume of a pyramid (including a cone) using the formula x area of base x perpendicular height. Calculate the volume of a sphere using the formula 4/3r .

Class activity: Find the surface area and volume of various composite shapes.

Class activity: An A4 sheet of paper can be rolled into a cylinder in two ways. Which gives the biggest volume? If the area of paper remains constant but the length and width can vary investigate what width and length gives the maximum cylinder volume.

IGSCE Mathematics (2nd Edition) by Ric Pimentel and Terry Wall,pg 250 - 276

Calculating areas of parallelograms and trapeziums athttp://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/areaandvolumerev1.shtml

Try the dipstick investigation athttp://www.ex.ac.uk/cimt/resource/dipstick.htm

Try the dipstick investigation athttp://www.ex.ac.uk/cimt/resource/dipstick.htmIGCSE Mathematics by Karen MorrisonPg 150 154Pg 157 160

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