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CURRICULUM SUMMARY – January to April 2017 SUBJECT: Mathematics Extended / Additional Week Dates 1 2-5 Jan 2 9 -13 Jan YEAR GROUP: Y11 Learning objectives Activities (in brief) BEARINGS AND TRIGONOMETRY - REVISION Know and understand the sine, cosine and tangent ratios for an acute angle of a rightangled triangle. Know and use the concept of an angle of elevation and an angle of depression. Extend sine and cosine values to angles between 90° and 180°. Know and use sine and cosine rules Know and use formula for an area of a triangle Applying Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle. Solving trigonometrical problems in two dimensions involving angles of elevation and depression. Solving trigonometrical problems involving sine and cosine rules. Calculating areas of triangles. Finding sides and angles of different triangles. Solving trigonometrical problems involving sine and cosine rules. Calculating areas of triangles. Finding sides and angles of different triangles. Solve trigonometrical problems in three dimensions including angle between a line and a plane. 1 3 16-20 Jan 4 23-27 Jan TEACHER: Agata Piskorz 𝐴 = 2 𝑎𝑏𝑠𝑖𝑛(∡𝐶) Know how to find an angle between a line and a plane. CONSTRUCTIONS AND LOCI Revise constructions. Use the definition of a locus. Use the method of intersecting loci for sets of points in two dimensions. ALGEBRA AND GRAPHS Apply the idea of rate of change to easy kinematics. Understand direct and inverse proportionality. Construct and transform complicated formulae Constructing a triangle given the three sides using ruler and pair of compasses only. Constructing other simple geometrical figures from given data using ruler and protractor as necessary. Constructing angle bisectors and perpendicular bisectors using straight edge and pair of compasses only. Finding sets of points in two dimensions which are: • at a given distance from a given point • at a given distance from a given straight line • equidistant from two given points • equidistant from two given intersecting straight lines. Solving problems involving distance-time and speed-time graphs, acceleration and deceleration. Calculate distance travelled as area under a linear speed-time graph. Express direct and inverse variation in algebraic terms and use this form of expression to find unknown quantities. and equations. Give appropriate upper and lower bounds for data given to a specified accuracy. 5 6 7 30 Jan-3 Feb 6 – 10 Feb 13 - 17 Feb MOCK EXAMS MOCK EXAMS SETS AND PROBABILITY – REVISION Basic concepts of set theory - members (elements) of a set; the empty set; equal sets; subsets; appropriate notation. The universal set. Complement of a set. The relationship between sets of natural numbers, integers, rational numbers and real numbers. Set of prime numbers; multiples and factors. Venn diagrams to illustrate set operations. Venn diagram regions. Mid-Term Break SEQUENCES - REVISION Know linear sequences, quadratic and cubic sequences, exponential sequences and simple combinations of these. 8 20 – 24 Feb 27 Feb -3 Mar 9 6 – 10 Mar GEOMETRY - REVISION Similar figures relationship between lengths, areas and volumes. Surface area of a cuboid, prism, cylinder, pyramid, cone and sphere. Area and volume of compound solids. 10 13 – 17 Mar STATISTICS- REVISION Transforming formulae where the subject appears twice. Manipulating algebraic fractions. Factorising and simplifying rational expressions. Obtain appropriate upper and lower bounds to solutions of simple problems given data to a specified accuracy. Use language, notation and Venn diagrams to describe sets and represent relationships between sets. Using the set-builder notation of sets e.g. A = {x: x is a natural number} B = {(x,y): y = mx + c} C = {x: a < x < b}. Using correct symbols : ; ; 𝐴′ ∅; 𝐴 ⊂ 𝐵; 𝐴 ⊆ 𝐵; 𝐴 ∩ 𝐵; 𝐴 ∪ B. Shading regions in Venn diagrams – Interactive White Board activity. Solving practical problems – numbers in regions of Venn diagrams. Using the set builder notation. Problem solving with Venn diagrams. Continue a given number sequence. Recognise patterns in sequences and relationships between different sequences. Find the nth term of sequences. Use sequences to solve practical problems. Calculating lengths of similar figures. Using the relationships between areas of similar triangles, with corresponding results for similar figures and extension to volumes and surface areas of similar solids. Carrying out calculations involving the volume of a cuboid, prism and cylinder and the surface area of a cuboid and a cylinder. Carrying out calculations involving the surface area and volume of a sphere, pyramid and cone. Carry out calculations involving the areas and volumes of compound shapes. Using trigonometry to find unknown lengths or angles. Revising properties of angles and polygons. Calculating the mean, median, mode and range for individual and 11 12 13 20 – 24 Mar 27 – 31 Mar 3 – 7 Apr Know and interpret the mean, median and mode for discrete data and distinguish between the purposes for which they are used. Know the mean for grouped and continuous data. Know the modal class from a grouped frequency distribution. Construct and use cumulative frequency diagrams. Understand what is meant by positive, negative and zero correlation with reference to a scatter diagram. Find and use the line of best fit. REVISION REVISION REVISION discrete data. Calculating quartiles and interquartile range for individual and discrete data. Calculating an estimate of the mean for grouped and continuous data. Identifying the modal class from a grouped frequency distribution. Constructing cumulative frequency tables. Drawing cumulative frequency diagrams. Estimate and interpret the median, percentiles, quartiles and inter-quartile range. Drawing scatter diagrams. Estimating correlation form the scatter diagram. Drawing a straight line of best fit by eye. Solving past paper problems. Solving past paper problems. Solving past paper problems.