# Foundation Level Two Tier GCSE Mathematics - DOC by u8BO3ah

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```									                               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
       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
     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 + q2                                             (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

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