Methods 1

1
KEY
Methods 1
Methods 2
Applications 2
Applications 1
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AQA GCSE Linked Pair Pilot Route Map Higher
Tier (Year 10)
Year 10
Fractions , Decimals and Percentages
November Examinations
Basic Algebra
Indices and Powers
Basic Algebra
Number
Number
Fractions, Decimals and Percentages
January Examinations
Linear Programming
Ratio and Proportion
Coordinates and Graphs
Ratio and Proportion
Algebraic Argument
Equations, Graphs and Formulae
March Examinations
Equations, Formulae and Inequalities
Representing Data
Collecting Data
Statistical Measures
Scatter Graphs
Advanced Graphs
Limits
Finance
Probability
Probability
June Examinations
June Examinations
Number
Multiples, Factors and Primes
Revision
Year 11
3
AQA GCSE Linked Pair Pilot Route Map Higher
Tier (Year 11)
Year 11
November Examinations
Algebraic Manipulation
Equations
Coordi-nates
Transformations and Vectors
Venn Diagrams
Angles
Sequences
Similarity
January Examinations
Circle Theorems and Proof
Polygons and Circles
Shapes
Pythagoras and Trigonometry
Perimeter, Area and Volume
Approximation and Calculators
Number
March Examinations
Polygons and Circles
Trial and Improvement
Coordinates and Graphs
Equations
Measures
Percentage, Ratio and Proportion
Linear and Real Life Graphs
Shapes
Angles
Loci and Construction
Pythagoras and Trigonometry
Perimeter, Area and Volume
Transformations
Revision
Bearings
June Examinations
June Examinations
Year 10
4
Unit M1 Basic Algebra (Slide 1 of 2)
Specification reference Teachers own notes
Distinguish the different roles played by letter symbols in algebra, using the correct notation.
Distinguish in meaning between the words equation, inequality, formula and expression. The meaning of identity and knowledge of the identity symbol will also be expected.
5
Unit M1 Basic Algebra (Slide 2 of 2)
Specification reference Teachers own notes
Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, taking out common factors. Multiplying two linear expressions, factorising quadratic expressions including the difference of two squares, and simplifying rational expressions. This includes (x a) (x b) and (cx a) (dx b) at Higher tier. Candidates should be able to cancel rational expressions and apply the four rules to algebraic fractions. M2 (A2), A1 (A1)
6
Unit M1 Indices and Powers
Specification reference Teachers own notes
Understand and use numbers and their representations including powers, roots, indices (integers). Extend to fractional and negative indices, and use of standard index form.
7
Unit A1 Basic Algebra
Specification reference Teachers own notes
Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
8
Unit M1 Number (Slide 1 of 3)
Specification reference Teachers own notes
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
9
Unit M1 Number (Slide 2 of 3)
Specification reference Teachers own notes
Understand and use arithmetic of real numbersadd, subtract, multiply and divide any number. Understand and apply exact calculation with surds and p , as well as the simplification of surds including rationalising a denominator. Non-calculator arithmetic competency will be assessed in this unit. Calculations will be restricted to 3 digit integers and decimals up to two decimal places. Multiplication will be limited to 3- digit integers by 2-digit integers. For non-calculator work multiplication and division of decimals will be limited to multiplying or dividing by a single digit integer or decimal number to 1 significant figure. Addition and subtraction of fractions without a calculator will be assessed.
10
Unit M1 Number (Slide 3 of 3)
Specification reference Teachers own notes
Approximate to appropriate degrees of accuracy.
Use the concepts and vocabulary of factor (divisor), multiple and prime numbers. The explicit testing of these terms will be in M2.
Use calculators effectively and efficiently. Candidates should know not to round off values during the intermediate steps of a calculation.
11
Unit A1 Number
Specification reference Teachers own notes
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
Numbers and their representations including powers, roots, indices (integer values). Extend to fractional and negative indices, and use of standard index form.
Use calculators effectively and efficiently, including statistical functions. Candidates should know not to round off values during the intermediate steps of a calculation.
12
Unit M1 Fractions, Decimals and Percentages
Specification reference Teachers own notes
Understand that 'percentage' means 'number of parts per 100' and use this to compare proportions.
Use multipliers for percentage change. Work with repeated percentage change solve reverse percentage problems.
Interpret fractions, decimals and percentages as operators. In non-calculator questions, candidates should be able to calculate 1 and 10 of quantities as a starting point and use build-up methods.
13
Unit A1 Fractions, Decimals and Percentages
Specification reference Teachers own notes
Understand that 'percentage' means 'number of parts per 100' and use this to compare proportions.
Use multipliers for percentage change. Work with repeated percentage change solve reverse percentage problems. Calculations with percentages in financial and other realistic contexts will feature in this unit
Interpret fractions, decimals and percentages as operators. Candidates should be able to use a calculator to apply the four rules to fractions and decimals in problems.
14
Unit M1 Algebraic Argument
Specification reference Teachers own notes
Use algebra to support and construct arguments. Use algebra to construct simple proofs.
15
Unit M1 Ratio and Proportion
Specification reference Teachers own notes
Understand and use the relationship between ratio, fractions and decimal representations. Including recurring and terminating decimals. Including reduction of a ratio to its simplest form.
Understand and use direct proportion. Extend to include inverse proportion.
Divide a quantity in a given ratio.
16
Unit A1 Ratio and Proportion
Specification reference Teachers own notes
Understand and use direct proportion. Extend to include inverse proportion.
Divide a quantity in a given ratio.
17
Unit M1 Coordinates and Graphs
Specification reference Teachers own notes
Use the conventions for coordinates in the plane and plot points in all four quadrants. 3D coordinate systems.
Recognise and plot equations that correspond to straight-line graphs in the coordinate plane.
18
Unit M1 Equations, Graphs and Formulae (Slide
1 of 2)
Specification reference Teachers own notes
Set up, and solve simple equations and inequalities.
Set up and use equations that describe direct and inverse proportion. Candidates would be expected to set up an equation using a constant of proportionality.
Set up, and solve simultaneous equations in two unknowns where one of the equations might include squared terms in one or both unknowns.
Solve quadratic equations approximately using a graph.
19
Unit M1 Equations, Graphs and Formulae (Slide 2
of 2)
Specification reference Teachers own notes
Derive a formula, substitute numbers into a formula and change the subject of a formula. At Foundation tier formulae to be rearranged will need at most two operations. Formulae where a power appears will not be tested at Foundation tier. In Higher tier questions the subject may appear twice.
20
Unit A1 Linear Programming
Specification reference Teachers own notes
Set up and solve problems in linear programming, finding optimal solutions.
21
Unit A1 Equations, Formulae and Inequalities
(Slide 1 of 3)
Specification reference Teachers own notes
Set up, and solve simple equations and inequalities.
Derive a formula, substitute numbers into a formula.
22
Unit A1 Equations, Formulae and Inequalities
(Slide 2 of 3)
Specification reference Teachers own notes
Solve linear inequalities in one variable, and represent the solution set on a number line. Solve linear inequalities in two variables, and represent the solution set on a suitable diagram. Candidates should know and use the symbols lt, gt, and . Candidates should know the convention of an open circle on a number line for a strict inequality and a closed circle for an included boundary. Higher tier candidates should identify regions on a 2D coordinate grid. The convention of a dashed line for strict inequalities and a solid line for an included inequality need not be known.
23
Unit A1 Equations, Formulae and Inequalities
(Slide 3 of 3)
Specification reference Teachers own notes
Set up and solve linear simultaneous equations in two unknowns.
24
Unit A1 Collecting Data (Slide 1 of 2)
Specification reference Teachers own notes
Understand and use the statistical problem solving process/handling data cycle which involves specifying the problem and planning collecting data processing and presenting the data interpreting and discussing the results. Including knowing and using the term hypothesis for a general prediction which is to be tested. Higher tier candidates will be expected to choose suitable sampling methods, discuss bias, provide sophisticated and rigorous interpretations of their data and provide an analysis of how significant their findings are.
25
Unit A1 Collecting Data (Slide 2 of 2)
Specification reference Teachers own notes
Design an experiment or survey, identifying possible sources of bias. An understanding of the terms primary data and secondary data is expected.
Design data-collection sheets distinguishing between different types of data. Includes observation, controlled experiment, data logging questionnaires and surveys.
Extract data from publications, charts, tables and lists.
26
Unit A1 Representing Data (Slide 1 of 3)
Specification reference Teachers own notes
Design, use and interpret two-way tables for discrete and grouped data.
Look at data to find patterns and exceptions. For example identifying a rogue value from a scatter diagram.
Compare distributions and make inferences. Comparisons of average and range at tier F, and average and inter-quartile range attier H.
Produce and interpret charts and diagrams for categorical data including bar charts, multiple bar charts, pie charts and pictograms.
27
Unit A1 Representing Data (Slide 2 of 3)
Specification reference Teachers own notes
Produce and interpret diagrams for grouped and ungrouped numerical data, including tally charts, vertical line graphs, stem-and-leaf diagrams, frequency polygons and histograms with equal class intervals.
Produce and interpret diagrams for grouped discrete data and continuous data, including histograms with unequal class intervals. Candidates should be able to read information from and interpret these charts and diagrams.
Produce and use cumulative frequency graphs and box-and-whisker plots.
28
Unit A1 Representing Data (Slide 3 of 3)
Specification reference Teachers own notes
Work with time series including their graphical representation. Work with moving averages including their graphical representation. Candidates will be expected to comment on and use the trends shown by the moving average, and use it to predict further values.
29
Unit A1 Statistical Measures
Specification reference Teachers own notes
Calculate, median, mean, range, mode and modal class. For grouped data, estimate quartiles and inter-quartile range. From charts, diagrams, lists and tables of data, including median and range from a stem-and-leaf diagram.
Discuss and start to estimate risk.
30
Unit M1 Advanced Graphs (Slide 1 of 2)
Specification reference Teachers own notes
Use y mx c and understand the relationship between gradients of parallel and perpendicular lines. Candidates will be expected to obtain the equation of a line perpendicular to a known line.
Draw, sketch, recognise graphs of linear, quadratic simple cubic functions, the reciprocal function y with x 0, the function y kx for integer values of x and simple positive values of k, the trigonometric functions y sin x, y cos x and y tan x.
31
Unit M1 Advanced Graphs (Slide 2 of 2)
Specification reference Teachers own notes
Understand and use the Cartesian equation of a circle centred at the origin and link to the trigonometric functions.
Construct the graphs of simple loci.
Sketch simple transformations of a given function.
32
Unit A1 Scatter Graphs
Specification reference Teachers own notes
Recognise correlation and draw and/or use lines of best fit by eye, understanding and interpreting what these represent, and appreciating that correlation does not imply causality. Candidates will be required to recognise when correlation is weak or strong, positive or negative, but will not be asked to comment on the reliability of the data. Candidates should understand that using a line of best fit outside the plotted range may not be reliable.
33
Unit A1 Limits
Specification reference Teachers own notes
Approximate to appropriate degrees of accuracy.
Understand and use upper and lower bounds. Including maximum and minimum. Questions will be set in context and could be linked to statistical problems.
34
Unit A1 Finance (Slide 1 of 2)
Specification reference Teachers own notes
Carry out calculations relating to enterprise, saving and borrowing, appreciation and depreciation. Understand AER. Candidates should be familiar with common terms such as VAT, income tax and interest rates. Compound interest calculations will be required on higher tier.
Use mathematics in the context of personal and domestic finance including loan repayments, budgeting, RPI and CPI exchange rates and commissions.
35
Unit A1 Finance (Slide 2 of 2)
Specification reference Teachers own notes
Use spreadsheets to model financial, statistical and other numerical situations. Including the use of a simple formula.
Construct and use flow charts. These may be set in financial or other contexts.
36
Unit M1 Probability (Slide 1 of 3)
Specification reference Teachers own notes
Understand and use the vocabulary of probability and the probability scale. Words used will be impossible, very unlikely, unlikely, evens, likely, very likely and certain.
Use Venn diagrams to represent the number of possibilities and hence find probabilities. Questions will involve knowledge and use of set notation, A, A, A n B, A U B.
Use tree diagrams to represent outcomes of compound events, recognising when events are independent or dependent.
37
Unit M1 Probability (Slide 2 of 3)
Specification reference Teachers own notes
Know when to add or multiply probabilities if A and B are mutually exclusive, then the probability of A or B occurring is P(A) P(B) if A and B are independent events, the probability of A and B occurring is P(A) P(B). Includes conditional probability.
Compare experimental data and theoretical probabilities, and make informal inferences about the validity of the model giving rise to the theoretical probabilities. Knowledge of the term relative frequency is expected.
38
Unit M1 Probability (Slide 3 of 3)
Specification reference Teachers own notes
Understand that when a statistical experiment or survey is repeated there will usually be different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics.
39
Unit A1 Probability (Slide 1 of 2)
Specification reference Teachers own notes
Understand and use the vocabulary of probability and the probability scale. In this unit, probability questions will be about applying probability theory to statistical problems.
Understand and use theoretical models for probabilities including the model of equally likely outcomes.
Understand and use estimates of probability from relative frequency.
40
Unit A1 Probability (Slide 2 of 2)
Specification reference Teachers own notes
Understand that when a statistical experiment or survey is repeated there will usually be different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics.
41
Unit M2 Number (Slide 1 of 3)
Specification reference Teachers own notes
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
Arithmetic of real numbers. Including exact calculation with surds and p Answers may be required in these forms.
Numbers and their representations including powers, roots, indices (integers).
42
Unit M2 Number (Slide 2 of 3)
Specification reference Teachers own notes
Approximate to specified degrees of accuracy including a given power of ten, number of decimal places and significant figures. Nearest ten, hundred or thousand at Foundation tier.
Understand that 'percentage' means 'number of parts per 100' and use this to compare proportions.
Understand and use the relationship between ratio and fractions.
43
Unit M2 Number (Slide 3 of 3)
Specification reference Teachers own notes
Find proportional change, using fractions, decimals and percentages. Including repeated proportional change.
Use calculators effectively and efficiently. Including trigonometric functions. Candidates should know not to round off values during the intermediate steps of a calculation.
44
Unit M2 Multiples, Factors and Primes
Specification reference Teachers own notes
Use the concepts and vocabulary of factor (divisor), multiple, common factor, common multiple, highest common factor, least common multiple, prime number and prime factor decomposition.
Understand that factors of a number can be derived from its prime factorisation.
45
Unit M2 Venn Diagrams
Specification reference Teachers own notes
Understand and use Venn diagrams to solve problems. Simple numerical problems where the use of a Venn diagram aids the solution. Set notation will not be assessed in this unit
46
Unit M2 Algebraic Manipulation
Specification reference Teachers own notes
Distinguish the different roles played by letter symbols in algebra, using the correct notation.
Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, taking out common factors. Multiplying two linear expressions, factorising quadratic expressions including the difference of two squares, and simplifying rational expressions.
47
Unit M2 Angles
Specification reference Teachers own notes
Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and vertically opposite angles.
Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals. Candidates should know the meaning and properties of alternate, corresponding, interior and vertically opposite angles. Colloquial terms such as Z angles should not be used. Candidates should know the names and properties of isosceles, equilateral, right-angled and scalene triangles.
48
Unit M2 Equations
Specification reference Teachers own notes
Set up, and solve simple equations.
Solve quadratic equations exactly by factorising, completing the square and using the formula.
Recognise and use equivalence in numerical, algebraic and graphical representations. Candidates should be able to move from one form of representation to another to get different perspectives on the problem.
49
Unit M2 Coordinates
Specification reference Teachers own notes
Use the conventions for coordinates in the plane and plot points in all four quadrants.
Use geometric information to complete diagrams on a co-ordinate grid.
50
Unit M2 Transformations and Vectors (Slide 1
of 2)
Specification reference Teachers own notes
Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations. Enlargements by positive fractional and negative scale factors.
Use 2D vectors to describe translations.
51
Unit M2 Transformations and Vectors (Slide 2
of 2)
Specification reference Teachers own notes
Use vectors to solve simple geometric problems and construct geometric arguments. Understand and use vector notation calculate and represent graphically the sum of two vectors the difference of two vectors and a scalar multiple of a vector calculate the resultant of two vectors understand and use the commutative and associative properties of vector addition.
52
Unit M2 Similarity
Specification reference Teachers own notes
Understand congruence and similarity, including the relationship between lengths, in similar figures. Including the relationship between areas and volumes of similar shapes.
53
Unit M2 Sequences
Specification reference Teachers own notes
Generate terms of a sequence using term-to-term and position-to-term definitions.
Form linear expressions to describe the nth term of a sequence. Form quadratic expressions to describe the nth term of a sequence.
54
Unit M2 Polygons and Circles (Slide 1 of 2)
Specification reference Teachers own notes
Calculate and use the sums of the interior and exterior angles of polygons. Candidates should be able to calculate the values of the interior angle, exterior angle and angle at the centre of regular polygons. At Foundation tier these will be restricted to triangle, square, pentagon, hexagon, octagon, nonagon and decagon.
Solve problems in the context of tiling patterns and tessellation. Candidates will be required to know that the sum of the angles at a point is 360º
55
Unit M2 Polygons and Circles (Slide 2 of 2)
Specification reference Teachers own notes
Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
56
Unit M2 Shapes
Specification reference Teachers own notes
Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.
Recognise reflection and rotation symmetry of 2D shapes.
57
Unit M2 Perimeter, Area and Volume
Specification reference Teachers own notes
Calculate perimeters and areas of shapes made from triangles and rectangles. Extend to other compound shapes. e.g. shapes made from circles or part circles with other known shapes.
Calculate volumes of right prisms and of shapes made from cubes and cuboids. Including cylinders.
Solve mensuration problems involving more complex shapes and solids. Including cones and spheres. Including compound shapes and frustums.
58
Unit M2 Pythagoras and Trigonometry
Specification reference Teachers own notes
Use Pythagoras theorem in 2D. Extend to 3D.
Use the trigonometric ratios to solve 2D and 3D problems. Use the sine and cosine rules to solve problems in 2D and 3D.
Calculate the area of a triangle usingab sin C.
59
Unit M2 Circle Theorems and Proof (Slide 1 of
2)
Specification reference Teachers own notes
Understand, prove and use circle theorems and the intersecting chords theorem. Includes cyclic quadrilaterals angle at centre is twice angle at circumference angle in a semi-circle is 90º angles in the same segment are equal opposite angles in cyclic quadrilateral sum to 180º alternate segment theorem.
Understand and use the midpoint and the intercept theorems. The two forms of the midpoint theorem should be known.
60
Unit M2 Circle Theorems and Proof (Slide 2 of 2)
Specification reference Teachers own notes
Understand and construct geometrical proofs using formal arguments, including proving the congruence, or non congruence of two triangles in all possible cases.
61
Unit A2 Number
Candidates should be able to Teachers own notes
Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
Find circumferences of circles and areas enclosed by circles.
62
Unit A2 Approximation and Calculators
Candidates should be able to Teachers own notes
Approximate to specified degrees of accuracy including a given power of ten, number of decimal places and significant figures. Nearest ten, hundred or thousand at Foundation tier.
Use calculators effectively and efficiently. Including trigonometric functions. Candidates should know not to round off values during the intermediate steps of a calculation.
63
Unit A2 Trial and Improvement
Candidates should be able to Teachers own notes
Find approximate solutions of equations using systematic trial and improvement.
64
Unit A2 Measures (Slide 1 of 2)
Candidates should be able to Teachers own notes
Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements.
Convert measurements from one unit to another. Metric conversions should be known. Imperial to metric conversions will be limited to 5 miles 8 kilometres, 4.5 litres 1 gallon, 2.2 pounds 1 kilogram and 1 inch 2.5 centimetres.
Make sensible estimates of a range of measures.
65
Unit A2 Measures (Slide 2 of 2)
Candidates should be able to Teachers own notes
Understand and use compound measures in familiar and unfamiliar contexts. Including area, volume and speed at Foundation tier. Including density at Higher tier. Other measures will be defined in the question.
66
Unit A2 Percentage, Ratio and Proportion
Candidates should be able to Teachers own notes
Understand that 'percentage' means 'number of parts per 100' and use this to compare proportions.
Find proportional change. Repeated proportional change, exponential growth/decay, its relationship with repeated proportional change including financial and scientific applications.
Divide a quantity in a given ratio.
67
Unit A2 Equations
Candidates should be able to Teachers own notes
Set up, and solve simple equations.
68
Unit A2 Coordinates and Graphs
Candidates should be able to Teachers own notes
Use the conventions for coordinates in the plane and plot points in all four quadrants.
Recognise and plot equations that correspond to straight-line graphs in the coordinate plane.
Find approximate solutions of equations using graphical methods.
69
Unit A2 Linear and Real Life Graphs (Slide 1
of 2)
Candidates should be able to Teachers own notes
Find and interpret gradients and intercepts of straight line graphs in practical contexts.
Construct linear functions from real-life problems and plot their corresponding graphs. Extend to quadratic and other functions.
Interpret the gradient at a point on a curve as the rate of change.
Recognise and use graphs that illustrate direct proportion. Extend to inverse proportion. Including distance-time graphs.
70
Unit A2 Linear and Real Life Graphs (Slide 2 of
2)
Candidates should be able to Teachers own notes
Discuss, plot and interpret graphs (which may be non-linear) modelling real situations, including journeys / travel graphs. Including periodic graphs.
Calculate areas under graphs consisting only of straight lines and interpret the result. Extend to estimates of areas under curves.
71
Unit A2 Shapes
Candidates should be able to Teachers own notes
Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.
Recognise reflection and rotation symmetry of 2D shapes.
Use 2D representations of 3D shapes.
72
Unit A2 Polygons and Circles
Candidates should be able to Teachers own notes
Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
Find circumferences of circles and areas enclosed by circles.
73
Unit A2 Pythagoras Theorem and Trigonometry
Candidates should be able to Teachers own notes
Use Pythagoras theorem in 2D. Extend to 3D.
Use the trigonometric ratios to solve 2D and 3D problems. Sine and cosine rule will not be assessed in this unit.
74
Unit A2 Angles
Candidates should be able to Teachers own notes
Measure and draw lines and angles.
Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and vertically opposite angles.
Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals. Candidates should know the names and properties of isosceles, equilateral, right-angled and scalene triangles.
75
Unit A2 Bearings
Candidates should be able to Teachers own notes
Understand and use bearings.
76
Unit A2 Transformations
Candidates should be able to Teachers own notes
Understand congruence and similarity, including the relationship between lengths, in similar figures. Including the relationship between areas and volumes of similar shapes.
77
Unit A2 Perimeter, Area and Volume
Candidates should be able to Teachers own notes
Calculate perimeters and areas of shapes made from triangles and rectangles. Extend to other compound shapes. e.g. shapes made from circles or part circles with other known shapes.
Calculate volumes of right prisms and of shapes made from cubes and cuboids. Including cylinders.
Solve mensuration problems involving more complex shapes and solids. Including cones and spheres. Including compound shapes and frustums
78
Unit A2 Loci and Constructions
Candidates should be able to Teachers own notes
Use and interpret maps and scale drawings.
Draw triangles and other 2D shapes using a ruler, pair of compasses and protractor.
Use straight edge and a pair of compasses to do constructions.
Construct loci.