1) Fractions, Decimals and Percentages

1) Fractions, Decimals and Percentages 1) Fractions, Decimals and Percentages Ref Description 1.1 Order fractions and decimals 1.2 Recognise equivalence and convert between fractions, decimals and percentages + - x , fractions and decimals, applying rules of BIDMAS where appropriate (including dividing by decimals (up to 2dp) by 1.3 transforming it to a problem involving division by an integer. 1.4 Understand ‘reciprocal’ as multiplicative inverse 1.5 Calculate fractions and percentages of a quantity 1.6 Express one quantity as a percentage of another 1.7 Calculate percentage increase and decrease, profit and loss 1.8 Solve problems involving simple/compound interest and depreciation. 1.9 Convert recurring decimals to fractions 1.10 Carry out calculations involving reverse percentages e.g. finding the cost price given the selling price and the percentage profit 2) Algebra Ref Description 2.1 Add, subtract, multiply and divide directed numbers 2.2 Use letters to express generalised numbers and express basic arithmetic processes algebraically 2.3 Substitute numbers for words and letters in formulae (involving powers) 2.4 Solve problems by substituting values into simple formulae 2.5 Simplifying expressions (+ - x ,) including expanding brackets and collecting like terms Solve linear equations in one unknown (unknown on either or both sides, equations involving brackets and where solutions are 2.6 negative / fractions) 2.7 Generate formulae and solve problems by writing and solving an equation 2.8 Change the subject of simple formula 2.9 Change the subject of a formula (including where the subject appears twice or where powers of the subject appear. 2.10 Manipulate algebraic fractions 3) Angle Ref Description 3.1 Use and interpret the geometrical terms: point, line, parallel, perpendicular, acute, right, obtuse and reflex angles Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons (up to decagon) and simple solid figures (including prism, 3.2 pyramid, cylinder and cone) Calculate unknown angles using the following geometrical properties: (a) Using angles in a straight line and angles at a point 3.3 (b) Using parallel lines to identify alternate and corresponding angles (c) Calculating unknown angles in triangles and quadrilaterals (equilateral, isosceles, right angles) (d) Calculating interior and exterior angles in polygons 3.4 Understanding a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices 3.5 Use angle properties of quadrilaterals (Square, Rectangle, Parallelogram, Trapezium and Rhombus) 3.6 Angle properties of irregular polygons 4) Limits of Accuracy Ref Description 4.1 Order quantities by magnitude and demonstrate familiarity with the symbols = , < > , Rounding to specified numbers of decimal places and significant figures, rounding answers to reasonable accuracy in the context 4.2 of a given problem 4.3 Estimate and check answers 4.4 Recognising that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction Obtain appropriate upper and lower bounds to solutions of simple problems (e.g. the calculation of the perimeter or area of a 4.5 rectangle) given data to a specified accuracy 5) Collecting Data Ref Description 5.1 Select suitable method to collect/summarise primary data including grouped data, considering appropriate equal class intervals 5.2 Select and justify a sampling scheme and a method to investigate a population 5.3 Questionnaires and surveys, understand bias etc 5.4 Design and use data collection sheets 5.5 Gather data from secondary sources 5.6 Design and use two-way tables 5.7 Dealing with practical problems such as non-response and missing / inaccurate data 6) Statistics Ref Description 6.1 Read, interpret and draw simple inferences from tables and statistical diagrams Construct and use: o Bar charts o Pie charts o Pictograms 6.2 o Simple frequency distributions o Histograms with equal intervals (+ Frequency polygons) o Scatter diagrams, including line of best fit (interpolate and extrapolate) o Stem and leaf diagrams 6.3 Understand what is meant by positive, negative and zero correlation 6.4 Calculate the mean, median and mode for discrete data, and distinguish between the purposes for which they are used 6.5 Calculate the range Construct and read histograms with equal and unequal intervals (areas proportional to frequencies and vertical axis labelled 6.6 ‘frequency density’) Estimate of the median using group frequency tables and histograms 6.7 Construct and use cumulative frequency diagrams 6.8 Find the median, quartiles and inter-quartile range from data and CF diagram 6.9 Construct and interpret box plots for grouped continuous data 6.10 Calculate an estimate of the mean for grouped and continuous data 6.11 Identify the modal class from a grouped frequency distribution 6.12 Use statistical measures / graphs to compare sets of data 7) Probability Ref Description 7.1 List all the outcomes for single events, and for successive events, in a systematic way 7.2 Identify mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1 7.3 Know when to add or multiply two probabilities i.e. p(A or B) = p(A) + p(B) and p(A and B) = p(A) x p(B) Use tree diagrams to represent outcomes of compound events, recognising when events are independent and understanding the 7.4 concept of conditional probability 7.5 Use Venn diagrams to represent solutions to probability problems and to calculate probabilities from a given data set. 7.6 Compare experimental data (Relative frequency) and theoretical probabilities Understand that if an experiment is repeated different outcomes may (and usually) occur, and that increasing sample size generally 7.6 leads to better estimates of probability and population parameters 8) Indices and Surds Ref Description 8.1 Calculate squares, square roots, cubes and cube roots of numbers, including the use of trial and improvement Use and interpret positive, negative and zero indices (including index laws) abab，(a) xxx，, abab,(b) xxx,, abab(c) ()xx, 8.2 0x,1(d) 1,ax,(e) ax aaabbbxxx,,()()(f) n Use the standard form A ， 10to convert between numerical and standard form and in calculations 8.3 x8.4 Use and interpret (fractional) indices e.g. solve 32 = 2 aaabab,，Simplify and use surds using laws and ,8.5 bb8.6 Rationalise the denominator of surds 9) Numbers and Sequences Ref Description 9.1 Understanding even, odd and prime numbers 9.2 Finding factors and multiples of numbers 9.3 Finding HCF, LCM and prime factor decomposition Generate and Extend common integer sequences (including: sequences of odd or even integers; squared integers; powers of 2; 9.4 powers of 10; triangle numbers) 9.5 Use the term to term rule to generate or fill in missing terms in a sequence 9.6 Describe the nth term of a sequence using words and algebra and use the nth rule term to find the value of a particular term 9.7 Deduce expressions to calculate the nth term of quadratic sequences 9.8 Recognise and use simple geometric progressions 10) Coordinates and Graphs of Linear Functions Ref Description 10.1 Using axes and coordinates to specify points in all four quadrants and locate points with given coordinates 10.2 Finding the coordinates of points identified by geometrical information 10.3 Finding the coordinates of the midpoint of the a line segment 10.4 Construct tables of values and draw graphs for functions in which y is given explicitly in terms of x, or implicitly Understanding that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the y-10.5 intercept. Find the gradient and y-intercept when values for m and c are given Finding the gradient of a line. Exploring the gradients of parallel lines and lines perpendicular to each other. Finding the equation of 10.6 a line. 10.7 Constructing linear functions and plot the corresponding graphs arising from real-life problems. Discuss and interpret the results 11) Compound Measures Ref Description 11.1 Read clocks, dials and timetables; calculate times and time differences in terms of the 12- and 24-hour clocks 11.2 Know and use decimal equivalents of times given in hours and minutes 3311.3 Use the relationship between density, mass and volume to solve problems and convert between units of density (kg/m to g/cm) 11.4 Converting between area measures, including square centimetres and square metres 11.5 Converting between volume measures, including cubic centimetres and cubic metres 11.6 Use the relationship between distance, speed and time to solve problems 11.7 Convert between metric units of speed e.g. km/h to m/s 12) Simultaneous Equations (Linear) Ref Description 12.1 Solve simultaneous linear equations in two unknowns by graphical methods 12.2 Solve simultaneous linear equations in two unknowns by algebraic methods (e.g. elimination of one variable) 12.3 Solve problems involving simultaneous linear equations by the most appropriate method (e.g. elimination or substitution) 13) Factorising Ref Description 13.1 Extract common factors 13.2 Expanding the product of two linear expressions 13.3 Factorise quadratic expressions, including the difference of two squares 14) Quadratic Equations Ref Description Generating points and plotting graphs of quadratic functions 14.1 14.2 Finding approximate solutions of a quadratic equation from the graph of the corresponding quadratic function 14.3 Solving simple quadratic equations by factorising 14.4 Solve quadratic equations using the quadratic formula giving answers to 1dp and in surd form 14.5 Solve quadratic equations by completing the square 14.6 Complete the square of a quadratic function and use this to determine the min / max value of the function 15) Simultaneous Equations Ref Description 14.4 Estimate solutions to simultaneous equations (linear and quadratic) using graphical methods 22214.5 Constructing the graph of for a circle of radius r centred at the origin of coordinates xyr，, Finding graphically the intersection points of a given straight line with this circle and knowing that this corresponds to solving the 14.6 two simultaneous equations representing the line and the circle Solving exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear in each 222unknown, and the other is linear in one unknown and quadratic in the other, of where the second is of the form (Also xyr，,14.7 graphical solutions) 16) Mensuration Ref Description 15.1 Understand and use Pythagoras’ theorem in 2-D and 3D 15.2 Pythagoras on a coordinate grid: given the points A and B, calculate the length AB 15.3 Calculating perimeters and areas of shapes made from triangles and rectangles (including area of parallelogram / trapezium) Finding circumferences of circles and areas enclosed by circles, recalling relevant formulae (using surds and pi in exact 15.4 calculations without a calculator) 15.5 Calculating the lengths of arcs and sectors / segments of circles (using surds and pi in exact calculations without a calculator) 15.6 Solve problems involving the surface area of cuboids and prisms (including cylinders) 15.7 Solve problems involving the volume of cuboids and prisms (including cylinders) and given the formulae cones and pyramids. 15.8 Solving problems involving volumes of compound shapes made from cones, pyramids, etc (including frustums) 17) Trigonometry Ref Description 16.1 Interpret and use 3 figure bearings measured clockwise from north Apply the sine, cosine and tangent ratios for acute angles to the calculation of a side or angle of a right-angled triangle (angles will 16.2 be quoted in, and answers required in, degrees and decimals to one decimal place) 16.3 Solve problems using the sine and cosine rules for any triangle 1Calculate the area of triangle using Areasin,abC 16.4 2 16.5 Solve problems using Pythagoras and trigonometry in 3 dimensions 16.6 Finding the angles between a line and a plane 18) Ratio and Proportion Ref Description 17.1 Using ratio notation, including reduction to its simplest form and it various links to fractions notation 17.2 Dividing a quantity in a given ratio 17.3 Solving word problems about ratio, including using informal strategies and the unitary method of solution 17.4 Using and interpreting maps and scale drawings 1k1k22yy,,,yy,,,Interpret direct and inverse proportions as algebraic functions (, , , ) yxykx,,,yxykx,,,17.5 22xxxx17.6 Use algebraic functions for direct and inverse proportionality, with their value of k, to find unknown values 19) Constructions and Loci Ref Description Drawing approximate constructions of triangles and other 2-D shapes, using a ruler and protractor, given information about side 18.1 lengths and angles Similar Triangles - Understand from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are 18.2 unique, but SSA are not Construct: , Triangles, given three sides (using compasses and straightedge only) , Simple geometric figures (e.g. a regular hexagon inside a circle) 18.3 , Perpendicular bisector of a line segment (using compasses and straightedge only) , Bisector of an angle (using compasses and straightedge only) , 30º, 45º, 60º, 90º angles Use the following loci and the method of intersecting loci for sets of points in 2D which , are at a given distance from a given point 18.4 , are at a given distance from a given straight line , are equidistant from two given points , are equidistant from two given intersecting straight lines 20) Drawing and Constructing 2-D / 3-D Shapes Ref Description 19.1 Recognise and represent 3-D shapes through 2-D projections and cross-sections, including plan and elevation 19.2 Recognise 3-D shapes from their nets 19.3 Draw / Construct accurate nets of solids 21) Graphs of Functions Ref Description Plotting graphs of , simple cubic functions 1,y,, reciprocal function with x0 x20.1 x, exponential function for integer values of x and simple positive values of k yk, , the functions y = sin x and y = cos x, using a spreadsheet or graph plotter as well as pencil and paper 20.2 Recognising the characteristic shapes of all these functions Starting with the graph of y = f(x) perform the following transformations y = f(x) + a, y = f(ax), y=f(x+ a), y = af(x) for linear, 20.3 quadratic, sine and cosine functions f(x) Drawing, sketching and describing the graphs of trigonometric functions for angles of any size, including transformations involving 20.4 scalings in either or both the x and y directions 22) Circle Theorem Ref Description 21.1 Understanding that the tangent at any point on a circle is perpendicular to the radius at that point 21.2 Understanding and using the fact that tangents from an external point are equal in length 21.3 Explaining why the perpendicular from the centre to a chord bisect the chord Proving and using the fact that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on 21.4 the circumference 21.5 Proving and using the fact that the angle subtended at the circumference by a semicircle is a right angle 21.6 Proving and using the fact that angles in the same segments are equal 21.7 Proving and using the fact that opposite angles of a cyclic quadrilateral sum to 180 degrees 21.8 Proving and using the alternate segment theorem 23) Inequalities Ref Description 22.1 Solving linear inequalities in one variable 22.2 Represent the solution set on a number line 22.3 Represent inequalities graphically 22.4 Solving several linear inequalities in two variables and finding the solution set on a graph using appropriate shading 24) Symmetry and Transformations Ref Description Recognise symmetry properties (e.g. plane symmetry and order of rotational symmetry about an axis) for prisms and pyramids, 23.1 including cylinders and cones 23.2 Reflect simple plane figures in horizontal, vertical and diagonal lines 23.3 Rotate simple plane figures about the origin, vertices or mid-points of edges of the figures, through multiples of 90? 23.4 Construct given translations and enlargements of simple plane figures 23.5 Recognise and fully describe reflections, rotations, translations and enlargements Understand that shapes produced by translation, rotation and reflection are congruent to its image and use this to make geometric 23.6 inferences 23.7 Recognising that enlargements preserve angle but not length, and find the length of missing sides on similar shapes 23.8 Understanding the implications of enlargement for perimeter 23.9 Understand and use the effect of enlargement on areas and volumes of shapes and solids Understanding and using SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and 23.10 to verify standard ruler and compass constructions 25) Vectors Ref Description 24.1 Understanding and using vector notation 24.2 Calculating, and representing graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector 24.3 Calculating the resultant of two vectors 24.4 Understanding and using the commutative and associative properties of vector addition 24.5 Solving simple geometrical problems in 2-D using vector methods