Port Regis - Tomorrow's School for Today's Child

Port Regis
Motcombe Park,
Shaftesbury, Dorset
SP7 9QA. United Kingdom.
Registered No: 440436
Charity No: 306218

Tel: (+44) 01747 857800
Fax: (+44) 01747 857810
Email: office@portregis.com

A form Programme of Study

Number and Algebra

Decimal system and Place value	Problems using decimals, fractions and percentages. Four rules applied to decimals. Approximation and Estimation.
Fractions and percentages	Four rules of fractions. Percentages of amounts, expressing two quantities as a percentage Harder ratio and proportion.
Use of a calculator	Further practice at using the calculator for suitable problems using 1/x, yx, x2, x!, Öx, %, p, memory, brackets and constant function.
Algebraic skills	Forming algebraic expressions, forming equations, graphs of functions, Harder equations including negative numbers and fractions. Substitution using negative numbers, indices and fractions. Further trial and improvement. Factorising and expanding brackets Indices - combining 3a2 x 5a4, (4b3)2, 24m3n4 ¸ 6m6n4 etc. Give in words the rule for the nth term of the sequence 3, 5, 7, 9

Shape, Space and Measures

Areas and volumes

Perimeter and areas of triangles, quadrilaterals, composite shapes, circles

Volumes and surface areas of prisms (except cylinder)

Properties of 2-D shapes

Properties of different types of triangle, quadrilateral, and other polygons; calculate angles in problems involving any of these shapes; angle chasing including parallel lines; scale drawings and bearings.

Transformation geometry

Reflection, rotation, translation and enlargement.

Handling Data

Revision of all forms of Data Handling covered in B forms

Use various data collected from practical activities; draw and interpret travel graphs, conversion graphs, pie charts, scatter graphs; draw frequency diagrams and calculate mean, mode median and range; calculate probability and represent information in various ways.

Further Topics for Level 3

Fractions	Four rules of mixed numbers.
Substitution	Harder problems involving negative and fractional values.
Inequalities and equations	Solve simple inequalities and harder equations.
Algebraic fractions	Simplify numerical and algebraic fractions
Various trial and improvement problems.	Solve, for example, x(5x + 2) = 16 by trial and improvement, using a table of values to identify the solution.
Simultaneous equations	Solve equations by algebraic and graphical methods.
Problems related to the circle	Arcs, sectors, quadrants semicircles, segments etc.
Pythagoras theorem	Use of the theorem to solve problems, including distance between two points on a co-ordinate grid.
Volume and Surface area	Harder problems with prisms, including cylinders

Scholarship Topics

Vectors II

Equivalent, addition, negative vectors. Length of vectors using Pythagoras

Sets III

More set notation - n(A),AÇ B,B ÈA Equivalent sets - A'ÇB' = (A ÇB)'

No. of elements in regions n(CÈD)=n(C)+n(D)-n(CÇD), Problems -Venn diagrams

Solids

Platonic solids, make solids from nets Euler's theorem Surface areas of solids

Volumes of pyramids prisms

Brackets and Equations

BIODMAS - order of operations Multiply binomials Difficult equations (x as denominator)

Problem solving using equations Calculation aids

Four operations, mixed operations Approximations

Memory - storing, recalling, adding x , yx, square root, % and 1/x keys

Scientific notation and indices Using brackets

Factors and Indices

Multiply algebraic terms. Take out common factors. Simplify algebraic fractions

Product of two brackets. Difference of two squares. Factorise trinomials

Percentages II

Harder ratio – eg. 98 in ratio 3:4:2:5 Linear scale factor. Reverse flow

Brackets and Equations IV

Simple modelling algebraic expressions Modelling equations to solve problems

Operations with algebraic fractions Change of subject of a formula

Isometries

Translate on a grid – shift vectors Reflect in lines parallel to x & y, x=y

Rotate – 180, 90 and multiples of 45 Describe transformations on a grid

Graphs and Equations

Guess relations Gradients and intercepts of linear equations

Use gradients, intercepts to draw lines Find the equation of a line

Measurement III

Compare masses and volumes Lines of best fit Density Use formulae

Inequalities

Write down inequalities Solve inequalities Inequalities with two variables

Operators and Functions

Define and solve operations Commutative , associative operations

Integer and fraction functions Define and combine functions

Identity and inverse functions

Scale Factors

Linear, area and volume scale factors Problem solving using scale factors

Quadratics

Parabolas Drawing graphs of quadratics

Solving quadratic equations Solving equations graphically

Probability 1

Experimental probability Combined probability Probability theory and Venn diagrams

Congruencies

Transformations from matrices Modular arithmetic Problems with functions, operations

Enlargement

Enlarge using centre and scale factor Enlarge on axes – use of matrices

Similar triangles – calculate sides and areas

Curves and Equations

Solve equations , draw curves Quadratic inequalities

Problems in Algebra 1

More difficult equations Simplify expressions Solve problems

Probability II

Permutations Pascal’s triangle and binary choice

Addition law of probability Multiplication law of probability

Number Theory

Calculate and simplify indices Understand square roots Degree of accuracy

Problems in Algebra II

Transformation of formulae Simultaneous equations with indices

Simultaneous equations with variables as denominators Rational and irrational numbers

Sequences

Terms – look for connections Differences of terms Series, sums and consolation

Planes and Space

2 and 3 dimensional diagrams 2 dimensional and 3 dimensional investigations

Nets and Solids

Nets 3-D Pythagoras Volume of a sphere, pyramid, cone

Logic