# Midlands Mathematical Experiment Volume Two GCE Part B

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This resource was written to cover work in the Midland Mathematics Experiment ‘O’-level course. The topics covered are:

• [b]Matrices[/b]: translations, enlargements, area scale factor, combinations of transformations, finding and using determinants, finding the inverse of a matrix and solving simultaneous equations using matrices.

• [b]Shape and Size. Solid Figures[/b]: hexominoes, nets of solids, exploring relationships between length, surface area and volume and three dimensional graphs.

• [b]Equations and Problems[/b]: a wide variety of examples and exercises requiring students to form and solve linear equations.

• [b]Sequences, Series and Limits[/b]: investigating series of fractions, converging and diverging sequences, finding sums of series, exploring limits of series and recurring decimals.

• [b]Vectors and Matrices[/b]: definition of vectors, vector addition, dimensional vectors, using column vectors, scalar product, understanding other uses of matrices,

• [b]The Distributive Rule[/b]: an explanation of the distributive rule, the distributive law in action; factorising quadratic equations, solving quadratic equations, the distributive law in other algebras such a vector addition and set theory and the expansion of brackets to higher powers.

• [b]Speed and Time Graphs[/b]: the relationship between distance, velocity and time and the exploration of speed-time graphs.

• [b]Modular Arithmetic and Groups[/b]: exploring modular arithmetic, addition modulo 5, the notion of a group, examples of groups, cyclic groups and inverses.

• [b]Regions of a Plane. Linear Programming[/b]: graphing inequalities, representing inequalities by shading regions of a graph and solving linear programming problems graphically.

• [b]Vectors. Ratio and Incidence[/b]: position vectors, vector geometry and ratios of vectors.

• [b]Probability[/b]: theory of simple probability, using Venn diagrams, mutually exclusive events, independent events and combined probabilities.

• [b]Boolean Algebra[/b]: ‘water-tap’ arithmetic, parallel and serial circuits, truth tables, not gates and Boolean algebra.

• [b]Scalar Product[/b]: properties of scalar products, commutative law, distributive law, length property and using scalar property in vector geometry.

• [b]The Sine Rule. Circular Measure[/b]: explanation of the sine rule, applications of the sine rule, radians, the area of a sector of a circle and length of an arc.

• [b]Revision Examples[/b]: one hundred revision questions.

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