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CURRICULUM SUMMARY – September to December 2016 SUBJECT: Mathematics Extended / Additional YEAR GROUP: Year 11 TEACHER: Agata Piskorz Week Date Learning objectives Activities (in brief) 1 EXPONENTS Revise laws of exponents Negative and fractional powers Revise factorization methods Simplifying algebraic expressions with powers. Finding value of a power with negative or fractional index – more difficult examples. Factorising algebraic expression with powers Solve exponential equations algebraically Know and use definition of a logarithm Use logarithms to solve exponential equations Know the change – base rule for logarithms Revise graphs Construct tables of values and draw graphs for functions of the form , where a is a positive integer. Solve associated equations approximately by graphical methods. Draw and interpret graphs representing exponential growth and decay problems. Solving exponential equations . Using calculators to find the value of a logarithm. Revising. Writing a test Feedback of a test. Construct tables of values and draw graphs for functions of the form where a is a rational constant, and n = –2, –1, 0, 1, 2, 3, and simple sums of not more than three of these. Graphing by hand or by using technology Using GEOGEBRA software. Solving different equations approximately by graphical methods. Finding gradients of a curve. 5-9 Sep 2 12 -16 Sep 3 19-23 Sep 4 26-30 Sep 5 3-7 Oct Use the standard form n where n is a positive or negative integer, and Use the compound interest formula where P is the amount invested, r is the percentage rate of interest and n is the number of years of compound interest. VECTORS - revision Understand coordinates of a vector as a movement of x units in the x-direction and y-units in the y-direction. Understand equal vectors and zero vector Add and subtract vectors Multiply a vector by a scalar. Represent vectors by directed line segments Calculating using money and converting from one currency to another. Extracting data from tables and charts. Using given data to solve problems on personal and household finance involving earnings, simple interest and compound interest. Revising. Writing a test Feedback of a test. Writing vectors as number pairs. Drawing vectors. Performing some algebraic operations on vectors. Describe a translation by using a vector. Constructing given translations and enlargements of simple plane figures. Using different notations of a vector. 6 10-14 Oct 7 17-21 Oct 8 24-28 Oct MATRICES AND TRANSFORMATIONS Know what is a matrix and use it to display information Know rows, columns and order of a matrix. Calculate the product of a matrix and a scalar quantity. Use the algebra of 2 × 2 matrices including the zero and identity 2 × 2 matrices. Know determinant of a matrix Know how to find an inverse matrix Know how to find an image of a point and a simple figure Recognise and describe different transformations and their combinations. Describe transformations using co-ordinates and matrices 31 Oct – 4 Nov 9 7 -11 Nov 10 14 – 18 Nov Know different notation for a vector Know the magnitude of a vector Know and use position vectors and their linear combination Finding coordinates of a vector given two points. Calculating the magnitude of a vector Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors Revising Writing a test Displaying information in the form of a matrix of any order. Adding and subtracting matrices. Multiplying a matrix by a scalar. Multiplying two matrices. Multiplication by a unit matrix. Calculating the determinant IAI and inverse of a non-singular matrix Reflecting simple plane figures in horizontal or vertical lines. Rotating simple plane figures about the origin, through multiples of 90°. Using positive, fractional and negative scale factors for enlargements Describing reflections, rotations, translations and enlargements Revising Writing a test Test feedback. Mid-Term Break BEARINGS AND TRIGONOMETRY - REVISION Know and understand the sine, cosine and tangent ratios for an acute angle of a right-angled 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°. 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 rightangled 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. Know and use sine and cosine rules Know and use formula for an area of a triangle Know how to find an angle between a line and a plane Solve trigonometrical problems in three dimensions including angle between a line and a plane Revising. Writing a test Feedback of a test. 11 21 – 25 Nov ALGEBRA AND GRAPHS Represent inequalities graphically. Apply the idea of rate of change to easy kinematics. 12 Understand direct and inverse proportionality Construct and transform complicated formulae and equations. 28 Nov – 2 Dec 13 5 Dec – 9 Dec 14 SEQUENCES - REVISION Know linear sequences, quadratic and cubic sequences, exponential sequences and simple combinations of these. CONSTRUCTIONS AND LOCI Revise constructions Use the definition of a locus Use the method of intersecting loci for sets of points in two dimensions 12 Dec – 16 Dec Using graphical representations of inequalities in the solution of simple linear programming problems. Solving problems involving distance-time and speed-time graphs, acceleration and deceleration. Calculate distance travelled as area under a linear speed-time graph. Divide a quantity in a given ratio. Express direct and inverse variation in algebraic terms and use this form of expression to find unknown quantities. Transforming formulae where the subject appears twice. Manipulating algebraic fractions. Factorising and simplifying rational expressions. Revising. Writing a test Feedback of a test. Continue a given number sequence. Recognise patterns in sequences and relationships between different sequences. Find the nth term of sequences. 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. Revising. Writing a test Feedback of a test.