KS4 0607 and 0606 Extended Plus SOW.xlsx

	A	B	C	D	E	F
1		Y10	Suggested topic breakdown	Textbook reference	Syllabus reference	Learning objectives:
2			Extended Plus only 0606 Syllabus	Extended only

3	SPI	Physics bootcamp	Substitution and rearranging formuale	p. 89, p. 92-94	C2.5	Substitute numbers for words and letters in formulae.Rearrange simple formulae.Construct simple expressions and set up simple equations.
4	SPI	Physics bootcamp	Rearranging harder formulae (Physics Formulae sheet in the folder)	p. 242 - 248	E2.5	Substitute numbers for words and letters in complicated formulae.Construct and transform complicated formulae and equations, e.g. transform formulae where the subject appears twice.
5		Number - calculations	Types of numbers (also squares, primes, triangular numbers LCM and HCF). Focus on worded questions with LCM and HCF	p. 46, p 47 - 48	C1.1 and C1.3	Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square numbers, common factors and common multiples, rational and irrational numbers, real numbers, reciprocals. Includes expressing numbers as a product of prime factors. Finding the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers.
6			Venn diagrams - using, constructing and the use of proper notation. Note: The Venn diagram section has been removed from the 0606 syllabus but it still appears in the textbook. It may be used for extra exercises.	p. 377 or p. 2-25 of 0606	C9.1 - C9.4	Notation and meaning for: number of elements in A, (n(A)), an element of (∈), not an element of (∉), complement of A, (A′), empty set (∅ or { }), universal set (U), a subset of (⊆), a proper subset of (⊂). Sets in descriptive form { x \| } or as a list. Venn diagrams with at most three sets. Intersection and union of sets
7			Order of operation, negative numbers and special numbers	p. 86	C1.2 - C1.4	Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers
8			Calculating with fractions and decimals	p. 42	C1.2 and C1.7	Use the four rules for calculations with whole numbers, decimals and fractions (including mixed numbers and improper fractions
9			Fractions, decimals and percentages.	p. 44, p. 66	C1.7	Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts.Recognise equivalence and convert between these forms.
10			Converting recurring decimals to fractions	p. 45	E1.5	Conversion of recurring decimals to fractions
11			Meaning of exponents (powers, indices). Rules of exponents (index laws). Standard form		C1.7 and E1.7	Use the standard form A × 10n where n is a positive or negative integer, and 1 ≤ A < 10. Convert numbers into and out of standard form. Calculate with values in standard form.
12			Surds - all. Four calculations, expanding brackets. Rationalising the denominator.	p. 50	E1.10	Surds (radicals), simplification of square root expressions. Rationalisation of the denominator.
13		Algebra - Expressions	Manipulating with basic algebra. Collecting like terms. Expanding and factorising. Factorising with common term only	p. 95, p. 96, p. 114	C2.4, C2.7 and C2.8	Use letters to express generalised numbers and express basic arithmetic processes algebraically. Use brackets and extract common factors. Expanding and factorising.Expand products of algebraic expressions.
14			Index laws, evaluating expressions with indices including fractional and negative indices including the use of calculator	p. 235	C2.4	Understand the meaning of indices (fractional, negative and zero) and use the rule of indices. Use the rules of indices to simplify algebraic expressions.
15			Simplifying harder algebraic expressions including fractional and negative indices and brackets including the use of calculator	p. 237 - 241	E2.4	Solving exponential simple equations such as, 32x = 2 both algebraically and graphically
16			Solving linear equations, inequalities and sim. equations.	p. 98 - 107	C2.1 - C2.3, C2.6	Derive and solve simple linear equations in one unknown.
17			Expanding and factorising including quadratics where a is not 1 and the difference of two squares	p. 97, p. 115-118	E2.8	For extended learners, move on to examples where they will need to find the products of algebraic expressions, for example (x2 + 3x – 4)(x – 5). Building on the earlier factorising work, use examples to show learners how to factorise three-term quadratic equations,
18			Algebraic fractions (all four operations including simplifying fractions with numerators and denominators that are quadratic expressions)	p. 248-251	E2.9	Manipulate algebraic fractions
19			Quadratic functions, Discriminant and Quadratic inequalities (Complete Additional Mathematics Ch. 5)	p. 80-104	Section 2 of the 0606 syllabus	Find the maximum and minimum value of a quadratic function by any method. Use the maximum and minimum value of f(x) to sketch the graph (or determine the range for a given domain - can be covered here or introduced later in the function unit). Know the condition for f(x) = 0 to have - two real roots, two equal roots, no roots and the related conditions for a given line to intersect a given curve, be a tangent, not intersect a given curve
20			Discriminant
21			Quadratic Inequalities
22			Simultaneous equations including non-linear and the applications of the discriminant.	p. 92 -104	Section 6 of the 0606 syllabus	Solve simple simultaneous equations in two unknowns by elimination or substitution
23		Mensuration - check list of formulae given in the exam TAB 3	Units including units of area and volume	p. 132 and p. 150	C7.1	Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units. Convert between units including units of area and volume.
24			Area and perimeter (all 2D shapes including circles and compound shapes)	p. 128- 136	C7.2-C7.3	Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.
25			Arc length and sector area	p. 138-142	C7.3	Carry out calculations involving the circumference and area of a circle; Answers may be asked for in multiples of π. Solve simple problems involving the arc length and sector area as fractions of the circumference and area of a circle.
26			Surface area and volume (including sphere, pyramid and cone)	p. 142-152	C7.4	Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder; answers may be asked for in multiples of π. Carry out calculations involving the surface area and volume of a sphere, pyramid and cone; formulae will be given for the surface area and volume of the sphere, pyramid and cone in the question.
27			Solving problems with 3D compound shapes	worksheet	C7.5	Carry out calculations involving the areas and volumes of compound shapes; answers may be asked for in multiples of π.
28	GDC	Algebra - use of GDC	Solving quadratic equations	p. 118 - 125	E2.10	Solution of quadratic equations: by factorisation; using a graphic display calculator; using the quadratic formula (given).
29	GDC		Use of a graphic display calculator to solve equations, including those which may be unfamiliar	worksheet	C2.11	e.g 2x = x^2
30	GDC		Use of a graphic display calculator to solve equations, including those which may be unfamiliar.	worksheet	E2.11	e.g. 2x - 1 = 1/x^3
31			Investigation tasks - past papers (paper 5 or 6)
32			Christmas
33	SPI	Number - Percentages and Estimation	Rounding and approximation (please note in the IGCSE exam if not otherwise stated all answers are to be rounded to 3sf, answers in degrees should be rounded to 1dp). Science Plug - In. Please discuss the levels of accuracy used in science.	p.53	C1.11	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.
34			Percentages including applications such as interest and profit. Includes both simple and compound interest. Knowledge of reverse percentages is not required at Core.	p. 67 - 72	C1.8	Calculate a given percentage of a quantity.Express one quantity as a percentage of another.Calculate percentage increase or decrease. Simple and compound interest.
35			Harder calculations with percentages including reverse percentages and percentiles.	worksheet	E1.8	Carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage profit.
36			Speed, distance, time.	p. 73	C1.3	Problems involving speed, distance and time
37		Algebra - Functions	Function notation. Domain and range. Mapping diagrams.	p. 157	C3.1	Use function notation, e.g. f(x) = 3x – 5, f: x ⟼ 3x – 5, to describe simple functions. Domain id Real numbers unless stated otherwise.
38			Inverse and composite functions.	p. 161	E3.7 and E3.9	Find inverse functions. Form composite functions as defined by gf(x) = g(f(x)).
39			Functions (Complete Additional Mathematics Ch. 4)	p. 60 -79	Section 1 of the 0606 syllabus	Understand the terms: function, domain, range (image set), one-one function, inverse function and composition of functions. Understand the relationship between y=f(x) and y=\|f(x)\|, where f(x) can be linear, quadratic or trigonometric. Explain in words why a given function is a function or why it doesn't have an inverse, Find an inverse algebraically and graphically (using sketches of graphs)
40	GDC		Sketching graphs. Asymptotes.	p. 165	C3.5	Understanding of the concept of asymptotes and graphical identification of simple examples parallel to the axes.
41	GDC		The absolute value function	p. 163	E1.6 and E 3.2	Evaluating expressions with absolute value. Sketching graphs with and without a calculator.
42	GDC		Use of a graphic display calculator to: sketch the graph of a function produce a table of values find zeros, local maxima or minima find the intersection of the graphs of functions.	p. 165	C3.6	Including unfamiliar functions not mentioned explicitly in this syllabus. Vertex of quadratic
43			The quadratic function. Note: Transformations of graphs will be covered fully in Y11.	p.170	E3.2	Using properties of the quadratic function to find the equation, given zeros and a point, vertex or zeros and a-value, the vertex and another point
44		Geometry	Language of geometry. Properties of 2D shapes	p. 187	C5.1 - C5.4	Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence. Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets.
45			Symmetry, rotational symmetry and properties of 2D shapes	p. 199	C5.2	Recognise rotational and line symmetry (including order of rotational symmetry) in two dimensions. Includes properties of triangles, quadrilaterals and circles directly related to their symmetries. Recognise symmetry properties of the prism (including cylinder) and the pyramid (including cone).
46			Angle facts - in a line, at a point, in parallel lines, in regular polygons - recap	p. 187	C5.1 - C5.4	Use angle facts to find missing angles. Candidates will be expected to use the correct geometrical terminology when giving reasons for answers.
47			Pythagoras' theorem recap	p. 193	C5.6	Pythagoras’ Theorem in two dimensions (Extended: also in 3D). Including: chord length, distance of a chord from the centre of a circle, distances on a grid.
48			Similar shapes	p. 202	C5.5	Calculate lengths of similar figures.
49			Congruence	p. 207	C5.5	Identfy and use properties of congruent shapes
50			Similar shapes - calculations with area and volume	p. 208 - 214	C5.6	Use the relationships between areas of similar triangles, with corresponding results for similar figures and extension to volumes and surface areas of similar solids.
51			Circle theorems (may be have to be covered after half term)	p. 215	C5.7	Properties of circles: tangent perpendicular to radius at the point of contact, tangents from a point, angle in a semicircle
52			Circle theorems - extended	p. 215 - 222	E5.7	Use and interpret vocabulary of circles. Properties of circles: tangent perpendicular to radius at the point of contact, tangents from a point, angle in a semicircle, angles at the centre and at the circumference, on the same arc, cyclic quadrilateral, alternate segment.
53			February half term
54		Coordinate Geometry	Coordinates and plotting straight line graphs. Symmetry of diagrams or graphs in the Cartesian plane	p. 278	C4.1, C4.8	Demonstrate familiarity with Cartesian coordinates in two dimensions. Find the gradient of a straight line. Plot straight line graphs.
55			Gradient	p. 279	C4.4	Calculate the gradient of a straight line from the coordinates of two points on it.
56			Midpoint and length of a line segment	p. 279 and worksheet	C4.2	Calculate the length and the coordinates of the midpoint of a straight line from the coordinates of its end points
57			y = mx+c	p. 281 -282	C4.6	Interpret and obtain the equation of a straight line graph in the form y = mx + c. Problems will involve finding the equation where the graph is given.
58			Parallel lines	worksheet	C3.5 and E3.5	Determine the equation of a straight line parallel to a given line. E.g. find the equation of a line parallel to y = 4x – 1 that passes through (0, –3).
59			Parallel and perpendicular lines	worksheet	E3.6	Find the gradient of parallel and perpendicular lines, e.g. find the gradient of a line perpendicular to y = 3x + 1. Find the equation of a line perpendicular to one passing through the coordinates (1, 3) and (–2, –9).
60			Coordinate geometry	p. 133 - 147	Section 8 of the 0606 syllagus	Interpret the equation of a straight line graph in the form y = mx +c. Solve questions involving mid points and lentght of a line. Know and use the condition for two lines to be parallel or perpendicular, including finding the equation of perpendicular bisectors.
61		Number - Ratio and Proportion	Ratio and proportion (calculating with Speed, Distance and Time)	p. 59	C1.5	Demonstrate an understanding of ratio and proportion.To include numerical problems involving direct and inverse proportion. Use ratio and scales in practical situations. Formulae for other rates will be given in the question e.g. pressure and density.
62			Map scales	p. 63	C1.5	Use of map scales
63			Direct and inverse proportion (direct and inverse variation)	p. 266	E2.13	Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.
64		Transformations	Transformations recap	p. 355	C6.4	Transformations on the Cartesian plane: translation, reflection, rotation, enlargement (reduction). Description of a transformation.
65			Inverse of a transformation and combined transformations.	p. 367	E6.4	Includes negative scale factors for enlargements for extended learners.
66			Investigation tasks - past papers (paper 5 or 6)
67			Easter
68		Trigonometry	Right-angled triangle trigonometry	p. 312	C8.1	Three-figure bearings and North, East, South, West. Problems in two dimensions.
69			Bearings	p. 317	C8.7	Interpret and use three-figure bearings; measured clockwise from the North, i.e. 000°–360°
70			Solving problems with trigonometry and Pythagoras in 3D.	p. 325	E6.5	Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.
71			Angles of elevation and depression	p. 320	E8.7	Solve trigonometric problems in two dimensions involving angles of elevation and depression. Know that the perpendicular distance from a point to a line is the shortest distance to the line
72			Exact values for the trigonometric ratios of 0°, 30°, 45°, 60°, 90°.	p. 323	E8.2
73	GDC		Properties of the graphs of y = sinx, y = cosx, y = tanx. Extension to the four quadrants, i.e. 0°–360°. Transformations of graphs with trig functions will be covered in Y11.	p. 327	E8.8	Recognise, sketch and interpret graphs of simple trigonometric functions. Graph and know the properties of trigonometric functions.
74			Sine and cosine rules. Area of a triangle 1/2absinC.	p. 330	E8.4-E8.6	Solve problems using the sine and cosine rules for any triangle and the formula for the area of a triangle. Includes problems involving obtuse angles.All formulae given in the exam.
75			Trigonometric functions and equations (Complete additional mathematics Ch.10)	p. 173 - 191	Section 10 of the 0606 syllabus	Use unit circle to derive trig functions. Know properties of the sinx, cosx and tanx. Solve equations with trig functions.
76		Algebra 4 - Sequences	Sequences. N-th term including simple quadratic sequences.	p. 253	C2.12	Continuation of a sequence of numbers or patterns. Determination of the nth term. Use of a difference method to find the formula for a linear sequence or a simple quadratic sequence.
77		Algebra 4 - Sequences	Sequences including linear, quadratic, cubic and geometric.	p. 261	E2.12	Use of a difference method to find the formula for a linear sequence, a quadratic sequence or a cubic sequence. Identification of a simple geometric sequence and determination of its formula.
78		Algebra 5 - Differentiation	Differentiation (Complete additional mathematics Ch.10 and Ch. 13 p. 208-213)	p. 148 - 172	Larger part of section 14 (just the differentiation part) of the 0606 syllabus	Understand the idea of a derived function • use the derivatives of the standard functions x^n (for any rational n), together with constant multiples, sums and composite functions of these • apply differentiation to gradients, tangents and normals, stationary points, and practical maxima and minima problems • use the first and second derivative tests to discriminate between maxima and minima
79		Statistics	Reading and interpretation of graphs or tables of data. Discrete and continuous data.	p. 403	C11.1 - C11.2	Read, interpret and draw simple inferences from tables and statistical diagrams.
80			Constructing statistical diagrams	p. 403	C11.1 - C11.3	Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal intervals and scatter diagrams.
81	GDC		Averages, quartiles and range from a list or for grouped discrete data. Mean for continuous data. Use of GDC.	p. 417	C11.4 - C11.5	Mean, mode, median, quartiles and range from lists of discrete data and from grouped discrete data. Mean from continuous data. Cumulative frequency table and curve. Median, quartiles and interquartile range Read from curve. Use of a graphic display calculator to calculate mean, median and quartiles for discrete data and mean for grouped data
82			Cumulative frequency diagram. Estimating percentiles only for Extended. (NOTE: Histograms have been removed from the syllabus but they still appear in the textbook)	p. 430	C11.6	Construct and use cumulative frequency diagrams. Estimate and interpret the median, percentiles, quartiles and inter-quartile range
83			Understanding and description of correlation (positive, negative or zero) with reference to a scatter diagram. Straight line of best fit (by eye) through the mean on a scatter diagram.	p. 438	C11.8
84	GDC		Use a graphic display calculator to find equation of linear regression.	p. 443	E11.8
85		Probability	Recap Venn diagrams and Set notation.
86			Calculating simple probabilities	p. 386	C10.1	Calculate the probability of a single event as either a fraction, decimal or percentage. Problems could be set involving extracting information from tables or graphs. Understand and use the probability scale from 0 to 1.Understand that the probability of an event occurring = 1 – the probability of the event not occurring.
87	GDC		Relative frequency	p. 388	C10.2 - C10.3	Understand relative frequency as an estimate of probability. Expected frequency of occurrences.
88			Mutually exclusive and independent events.	p.393	E10.4
89			Tree diagrams, Venn diagrams and possibility diagrams	p. 395	C10.6	Probabilities from Venn diagrams and tables. Tree diagrams including successive selection with or without replacement. For Core students - simple cases only.
90			Conditional probability from diagrams	p. 395	E10.4 - E10.6	Calculate conditional probability using Venn diagrams, tree diagrams and tables.For example, two dice are rolled. Given that the total showing on the two dice is 7, find the probability that one of the dice shows the number 2.
91			Permutations and combinations (Complete additional mathematics Ch. 3)			Recognise and distinguish between a permutation case and a combination case • know and use the notation n! (with 0! = 1), and the expressions for permutations and combinations of n items taken r at a time, answer simple problems on arrangement and selection (cases with repetition of objects, or with objects arranged in a circle, or involving both permutations and combinations, are excluded)
92			Mock Exam
93			Mini Exploration (IB style)
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