Key competencies (student abilities)

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Gervais Norris
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1 Year 9 Mathematics Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding. Successful Cambridge IGCSE Mathematics candidates gain lifelong skills, including: the development of their mathematical knowledge, confidence by developing a feel for numbers, patterns and relationships, an ability to consider and solve problems and present and interpret results, communication and reason using mathematical concepts and a solid foundation for further study. S Ward Head of Mathematics Topic/Term Key competencies (student abilities) Standard form Term 1 - Number Use the standard form A 10 n where n is a pos or neg integer, and 1 A <10 Estimation Make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem. Number, set notation and language Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square numbers, common factors and common multiples, rational and irrational numbers (e.g. π, 2 ), real numbers; 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. Squares and cubes Calculate squares, square roots, cubes and cube roots of numbers. Limits of accuracy Give appropriate upper and lower bounds for data given to a specified accuracy (e.g. measured lengths). Ratio, proportion, rate Demonstrate an understanding of the elementary ideas and notation of ratio, direct and inverse proportion and common measures of rate;

2 divide a quantity in a given ratio; use scales in practical situations; calculate average speed. Vulgar and decimal fractions and percentages Percentages Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts; recognise equivalence and convert between these forms. Calculate a given percentage of a quantity; Express one quantity as a percentage of another; calculate percentage increase or decrease. Personal and household finance Percentages Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest (knowledge of compound interest formula is not required), discount, profit and loss; extract data from tables and charts. Carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage profit. Use of an electronic calculator Use an electronic calculator efficiently; apply appropriate checks of accurcy Assessment End of unit test Links to CES Inquirers learning Knowledgeable Charter/IB Thinkers learner profile Communicator

3 Topic/Term Key competencies (student abilities) Term 2 - Algebra and Graphs Expand on Algebra techniques from previous years and consolidate knowledge to enable students to Algebra Outcomes Distinguish the different roles played by letter symbols in equations, identities, formulae and functions Use index notation for integer powers and simple instances of the index laws Simplify or transform algebraic expressions by taking out single-term common factors Substitute numbers into expressions and formulae Add simple algebraic fractions Know and use the index laws in generalised form for multiplication and division of integer powers Square a linear expression; expand the product of two linear expressions of the form x ± n and simplify the corresponding quadratic expression Establish identities such as a 2 b 2 = (a + b)(a b) Factorise quadratic expressions, including the difference of two squares, e.g. x 2 9 = (x + 3)(x 3); cancel common factors in rational expressions, e.g. 2(x + 1) 2 / (x + 1) Simplify simple algebraic fractions to produce linear expressions; use factorisation to simplify compound algebraic fractions Graphing Outcomes Explore the graphical representation of algebraic equations and interpret how properties of the graph are related to features of the equation, e.g. parallel and perpendicular lines Interpret the meaning of various points and sections of straight-line graphs, including intercepts and intersection, e.g. solving simultaneous linear equations Explore simple properties of quadratic functions; plot graphs of simple quadratic and cubic functions, e.g. y = x 2, y = 3x 2 +4, y = x 3 Understand that equations in the form y = mx+c represent a straight line and that m is the gradient and c is the value of the y-intercept; investigate the gradients of parallel lines and lines perpendicular to these lines, plot these graps

4 Identify the equations of straight-line graphs that are parallel; find the gradient and equation of a straight-line graph that is perpendicular to a given line Find approximate solutions of a quadratic equation using a graph method Identify and sketch graphs of linear and simple quadratic and cubic functions Assessment End of unit tests Links to CES Inquirers learning Knowledgeable Charter/IB Thinkers learner profile Communicator Topic/Term Key competencies (student abilities) Term 3 - Geometry, Trigonometry and Mensuration Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text. Explain how to find, calculate and use: 1. the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; 2. the interior and exterior angles of regular polygons Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle Solve multi-step problems using properties of angles, of parallel lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text Know that the tangent at any point on a circle is perpendicular to the radius at that point; explain why the perpendicular from the centre to the chord bisects the chord Work out angles with circle theorems and know the following facts that: 1. the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference 2. the angle subtended at the circumference by a semicircle is a right angle 3. angles in the same segment are equal 4. opposite angles on a cyclic quadrilateral sum to 180 Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT

5 Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS) Make accurate mathematical constructions on paper Understand from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not Find the locus of a point that moves according to a more complex rule Pythagoras and Trigonometry Use Pythagoras' Theorem to find missing sides in right-angled triangles Use Pythagoras theorem to solve more complex 3-D problems Understand and use trigonometric relationships in right-angled triangles, and use these to solve problems, including those involving bearings Use trigonometric relationships in right-angled triangles to solve 3-D problems, including finding the angles between a line and a plane Mensuration Solve problems involving measurements in a variety of contexts; convert between area measures (e.g. mm2 to cm2, cm2 to m2, and vice versa) Know and use the formulae for the circumference and area of a circle Calculate the surface area of prisms Solve problems involving surface areas of cylinders Solve problems involving surface areas of cylinders, pyramids, cones and spheres (Set 1) Understand and use the formulae for the length of a circular arc and area and perimeter of a sector (Set 1) Assessment End of unit tests Links to CES Inquirers learning Knowledgeable Charter/IB Thinkers learner profile Communicator

6 Examples of homework tasks Study equipment needed Useful websites Contact in school Exercises from text books Research tasks Calculator Ruler Compasses Protractor

Unit 3: Number, Algebra, Geometry 2

Unit 3: Number, Algebra, Geometry 2 Number Use standard form, expressed in standard notation and on a calculator display Calculate with standard form Convert between ordinary and standard form representations