VIEWS: 18 PAGES: 12 POSTED ON: 9/11/2012
Year 10 - Higher Tier TERM 1 19. Inequalities Derive a formula (19.6) pg 366 and formulae Use formulae from mathematics and other subjects (19.5) pg 364 Substitute numbers into a formula D (19.5, 2.2) pg 364, 17 clip 61 Substitute positive and negative numbers into expressions such as 3x² + D (19.5, 2.2) pg 364, 17 clip 61 4 and 2x³ (19.1-19.3) pg 358-360 Solve simple linear inequalities in one variable, and represent the (19.1-19.4) pg 358-361 solution set on a number line Use the correct notation to show inclusive and exclusive inequalities C (19.7, 19.8) pg 367, 369 clip Change the subject of a formula including cases where the subject is on 100 both sides of the original formula, or where a power of the subject C/A/A* (19.5, 2.2) pg 364, 17 clip appears 99/164 Substitute numbers into a formula Substitute positive and negative numbers into expressions such as 3x² + (19.5, 2.2) pg 364, 17 4 and 2x³ (19.5, 2.2) pg 364, 17 B Show the solution set of several inequalities in two variables on a graph C (19.4) pg 361 clip 144 Set up linear equations from word problems (13.5, 19.6) 216, 366 clip 98 20.Pythagoras Understand, recall and use Pythagoras’ theorem in 2-D, then in 3-D C (20.4, 20.5, 29.1, 29.2, 29.9) Theorem and problems A/A* Pg 383, 388, 551, 553, 571 trigonometry 1 Calculate the length of a line segment in a 2-D plan clip174 Recall and use the trigonometric ratios to solve 2- D and 3-D problems B/A/A* (20.2-20.5) pg 379-388 (20.4, 20.5, 29.1, 29.2, 29.9) Find angles of elevation and angles of depression clip175 (20.5) pg 388 Clip 110/147 Higher Tier Within two week WIZARD ASSESSMENT on chapters so far period beginning 03.10.11 do 21.More graphs Solve cubic functions by successive substitution of values of x (21.5) pg 410 and equations Use systematic trial and improvement to find approximate solutions of C (21.5) pg 410 clip 102 equations where there is no simple analytical method of solving them Understand the connections between changes of sign and location of (21.5) pg 410 roots Generate points and plot graphs of simple quadratic functions, C (21.1) pg 398 clip 108 then more general quadratic functions Find approximate solutions of a quadratic equation from the (21.1) pg 398 graph of the corresponding quadratic function Find the intersection points of the graphs of a linear and quadratic function, knowing that these are the approximate solutions of the A/A* (21.1) pg 398 clip 165 corresponding simultaneous equations representing the linear and quadratic functions Plot and recognise cubic, reciprocal, exponential and B/A (21.2-21.4, 22.10, 29.3) clip circular functions y = sin x and y = cos x, within the range -360º to 145/170 +360º (see above) Pg 403-408, 419, 557 Use the graphs of these functions to find approximate solutions to equations, eg given x find y (and vice versa) (21.2-21.4, 22.10, 29.3) Find the values of p and q in the function y = pqx given the graph Pg 403-408, 435, 557 of y = pqx (21.4) pg 408 Match equations with their graphs Recognise the characteristic shapes of all these functions Use calculators to explore exponential growth and decay B (21.2-21.4, 22.10, 29.3) pg 403-408, 419, 557 clip 146 (21.4) pg 408 Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier Plot and recognise cubic, reciprocal, exponential and (21.2-21.4, 22.10, 29.3) pg circular functions y = sin x and y = cos x, within the range -360º to 403-408, 435, 557 +360º (see above) Use the graphs of these functions to find approximate solutions to equations, eg given x find y (and vice versa) (21.2-21.4, 22.10, 29.3)pg Match equations with their graphs 403-408, 435, 557 Recognise the characteristic shapes of all these functions Construct the graphs of simple loci including the circle x² + y ²= r² for a circle of radius r centred at the origin of the coordinate A/A* (21.2-21.4, 22.10, 29.3) pg plane 403-408, 435, 557 clip 172 Find the intersection points of a given straight line with this circle graphically (22.10) pg 435 Select and apply construction techniques and understanding of loci to draw graphs based on circles and (22.12) pg 439 perpendiculars of lines Solve exactly, by elimination of an unknown, two A/A* (22.10) pg 435 clip 165 simultaneous equations in two unknowns, one of which is linear in each unknown, and the other is linear in one unknown and quadratic in the other, or where the second equation is of (22.11, 22.12) pg 438, 439 the form x² + y ²= r² Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier TERM 2 22.Quadratic and Find the exact solutions of two simultaneous equations in two B (22.1) pg 419 clip 142 simultaneous unknowns equations Use elimination or substitution to solve simultaneous equations B (22.1) pg 419 clip 142 Interpret a pair of simultaneous equations as a pair of straight lines and their solution as the point of intersection. Consider the real life C (22.3) pg 423 clip 107 applications, eg mobile phone bills Set up and solve a pair of simultaneous equations in two variables (22.2) pg 421 Solve simple quadratic equations by factorisation and B (22.4-22.9) pg 424-433 clip completing the square 140 Solve simple quadratic equations by using the quadratic formula Select and apply algebraic and graphical techniques to solve A/A* (22.7-22.9) pg 430-433 clip simultaneous equations where one is linear and one quadratic 161 Solve equations involving algebraic fractions which lead to quadratic (22.11, 22.12) pg 438, 439 equations Solve quadratic equations by completing the square A/A* (22.8) pg 432 clip 162 (22.6) pg 428 Derive the quadratic equation by completing the square (22.5) pg 426 Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier TERM 3 23 Area and Convert between volume measures, including cubic centimetres and (23.7) pg 461 volume 2 cubic metres Solve problems involving more complex shapes and solids, A/A* (23.6) pg 458 clip 178 including segments of circles and frustums of cones Find the surface area and volumes of compound solids C (23.4-23.6, 23.8, 23.9) pg 455- constructed from; cubes, cuboids, cones, pyramids, spheres, hemispheres, A/A* 458, 462, 464 clip 113/177 cylinder, eg solids in everyday use Find the surface area of simple shapes (prisms) using the formulae for triangles and rectangles, and other shapes (23.8) pg 462 Give an exact answer to a question involving the area of a circle Calculate the lengths of arcs and the areas of sectors of circles (23.2) pg 451 Answers in terms of π may be required (23.1) pg 449 Find the surface area of a cylinder (23.2) pg 451 Find the area of a segment of a circle given the radius and length of the (23.9) pg 464 chord Convert between units of area (23.3) pg 453 Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier 24.Line diagrams Produce: composite bar charts, comparative and dual bar charts, pie and scatter graphs charts, frequency polygons, histograms with equal class intervals and (18.1, 18.4, 18.5, 18.6, 24.1, frequency diagrams for grouped discrete data, scatter graphs, line 24.2) pg 325, 331, 333, 335 graphs, frequency polygons for grouped data, grouped frequency D Clip 82, clip 83, tables for continuous data Interpret: composite bar charts, comparative and dual bar charts, pie (18.2, 18.4-18.7, 24.2) pg 326, charts, scatter graphs, frequency polygons and histograms 331-338, 477 Recognise simple patterns, characteristics and relationships in line graphs and frequency polygons (18.5, 24.1) pg 333, 474 From line graphs, frequency polygons and frequency diagrams: read off frequency values, calculate total population, find greatest and least values (18.5, 18.6, 24.1) pg 333, 335, Present findings from databases, tables and charts 474 Look at data to find patterns and exceptions, explain an isolated point on a scatter graph (Ch18, Ch24) Draw lines of best fit by eye, understanding what these represent. Use a line of best fit, or otherwise, to predict values of one variable given (Ch18, Ch24) values of the other variable Distinguish between positive, negative and zero correlation using lines (24.4) pg 481 of best fit Understand that correlation does not imply causality (24.3) pg 478 Appreciate that correlation is a measure of the strength of the (24.3) pg 478 association between two variables and that zero correlation (24.3) pg 478 does not necessarily imply ‘no relationship’ During two week WIZARD ASSESSMENT period beginning 12.12.11 Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier TERM 4 25. Indices, Use index notation for integer powers of 10 (25.2) pg 492 standard form and Use standard form, expressed in conventional notation C (25.2) pg 492 clip 90 surds Be able to write very large and very small numbers presented in a C context in standard form (25.2) pg 492 clip 90 Convert between ordinary and standard form representations C (25.2) pg 492 clip 90 Interpret a calculator display using standard form C (25.2) pg 492 clip 90 Calculate with standard form B (25.2) pg 492 clip 135 Use index laws to simplify and calculate numerical expressions involving C (1.5, 25.1, 25.3) pg 10, 491, powers, eg (23 25) 24, 40, 8–2/3 D Clip 103 497 clip 45 Find the value of calculations using indices Know that, eg x3 = 64 x = 82/3 (25.1-25.3) pg 491-497 clip A/A* 156 1 3 1 Rationalise the denominator, eg = , and, eg write (18 3 1 2 A/A* (25.3) pg 497 Clip 157/158 +10) 2 in the form p + q2 (25.4) pg 499 clip 157/158 Give an answer in the use of Pythagoras’ Theorem as √13 (25.4) pg 499 26. Similar shapes Understand the effect of enlargement for perimeter, area and volume of (26.1, 26.2) pg 505, 508 shapes and solids Understand that enlargement does not have the same effect on area (26.2) pg 508 and volume Use simple examples of the relationship between enlargement (26.1, 26.2) pg 505, 508 and areas and volumes of simple shapes and solids Use the effect of enlargement on areas and volumes of shapes and solids (26.1, 26.2) pg 505, 508 Know the relationships between linear, area and volume scale factors of mathematically similar shapes and solids (26.3) pg 510 Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier 27. Proportion 2 Calculate an unknown quantity from quantities that vary in direct or A/A* (16.4, 16.5, 27.1) 268, 270, inverse proportion 516 clip 159 Set up and use equations to solve word and other problems involving direct proportion or inverse proportion and relate algebraic solutions to (27.1-27.5) pg 516-523 graphical representation of the equations Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier 28.Probability Write probabilities using fractions, percentages or decimals (28.1) pg 529 Understand and use estimates or measures of probability, including (28.1, 28.3) pg 529, 536 relative frequency Use theoretical models to include outcomes using dice, spinners, coins (28.1, 28.4) og 529, 538 etc Find the probability of successive events, such as several throws of a (28.1) pg 529 single dice Estimate the number of times an event will occur, given the probability (28.4) pg 538 and the number of trials List all outcomes for single events, and for two successive events, D (28.1) pg 529 clip 85 systematically Use and draw sample space diagrams (28.1) pg 529 Add simple probabilities, eg from sample space diagrams (28.2) pg 533 Identify different mutually exclusive outcomes and know that (28.2) pg 533 clip 85 the sum of the probabilities of all these outcomes is 1 D (28.2) pg 533 Use 1 − p as the probability of an event not occurring where p is the probability ofthe event occurring (28.2) pg 533 Find a missing probability from a list or table A/A* (28.7) pg 543 clip 182 Understand conditional probabilities (28.5, 28.7) pg 539, 543 Understand selection with or without replacement (28.6) pg 541 Draw a probability tree diagram based on given information B (28.7) pg 543 clip 154 Use a tree diagram to calculate conditional probability (28.3) pg 536 Compare experimental data and theoretical probabilities C (28.3) pg 536 clip 125 Compare relative frequencies from samples of different sizes Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier 29.Pythagoras’ Understand, recall and use Pythagoras’ theorem in 2-D, then in 3-D (20.4, 20.5, 29.1, 29.3, 29.9) Theorem and problems Pg 383, 388, 551, 557, 571 trigonometry 2 Recall and use the trigonometric ratios to solve 2- D and 3-D problems (20.4, 20.5, 29.1, 29.2, 29.9) Understand the language of planes, and recognise the diagonals of a Pg 383, 388, 551, 553, 571 cuboid Calculate the length of a diagonal of a cuboid (29.2) pg 553 Find the angle between a line and a plane (but not the angle between two planes or between two skew lines) (29.1) pg 551 Find the unknown lengths, or angles, in non right-angle triangles using A/A* (29.2) pg 553 the sine and cosine rules (29.5-29.9) pg 563-571 clip 173 Find the area of triangles given two lengths and an included angle A/A* (29.4) pg 560 clip 176 Plot and recognise cubic, reciprocal, exponential and circular functions y = sin x and y = cos x, within the range -360º to A/A* (21.2-21.4, 22.10, 29.3) pg +360º (see above) 403-408, 435, 557 clip 168 Use the graphs of these functions to find approximate solutions to equations, eg given x find y (and vice versa) (21.2-21.4, 22.10, 29.3) pg 403-408, 435, 557 Recognise the characteristic shapes of all these functions TERM 5 30. Apply to the graph of y = f(x) the transformations y = f(x) + a, y = A/A* (30.2, 30.3) pg 581, 585 clip Transformations of f(ax), y = f(x + a), y = af(x) for linear, quadratic, sine and cosine functions A/A* 167/169 functions Select and apply the transformations of reflection, rotation, (30.2-30.4) pg 581-589 enlargement and translation of functions expressed algebraically Interpret and analyse transformations of functions and write the (30.1-30.4) pg 580-589 functions algebraically Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier 31. Circle Understand and use the fact that the tangent at any point on a B (31.2) pg 595 Clip 150 Geometry circle is perpendicular to the radius at that point Understand and use the fact that tangents from an external point are B (31.2) pg 595 clip 150 equal in length Find missing angles on diagrams (Ch31) clip 150 Give reasons for angle calculations involving the use of tangent B theorems (31.2) pg 595 clip 150 Prove and use the facts that: – the angle subtended by an arc at the centre of a circle is B (31.3, 31.4) pg 597 clip 150 twice the angle subtended at any point on the circumference – the angle in a semicircle is a right angle – angles in the same segment are equal – opposite angles of a cyclic quadrilateral sum to 180º – alternate segment theorem – the perpendicular from the centre of a circle to a chord bisect the chord 32. Algebraic Simplify rational expressions by cancelling, adding, subtracting, and A/A* (32.1-32.3) pg 608-612 clip fractions and multiplying 163 algebraic proof TERM 6 33. Vectors Understand that 2a is parallel to a and twice its length A/A* (33.4) pg 620 clip 180 Understand that a is parallel to a and in the opposite direction (33.4) pg 620 clip 180 Use and interpret vectors as displacements in the plane (with an (33.1) pg 620 clip 180 associated direction) Use standard vector notation to combine vectors by addition, eg AB + BC = AC and a + b = c (33.3) pg 623 clip 180 Represent vectors, and combinations of vectors, in the plane Solve geometrical problems in 2-D, eg show that joining the (33.1-33.5) pg 620-630 midpoints of the sides of any quadrilateral forms a parallelogram clip 180 (33.5) pg 630 clip 180 Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan Higher Tier 16.05 onwards Do student self assessment and revise topics highlighted by them first. 25.06 Students sit the actual new style 2012 GCSE papers to identify further topics for revision until end of term Edexcel Linear Two-Tier GCSE Mathematics - Medium Term Plan