Mapping Docs

8094 /www/nrich/html/content/id/8094/ 1 0000-00-00T00:00:00 <mdoxml version="1.0"><table border="1" cellpadding="0" cellspacing="0" classtable="" style="border-collapse:collapse;border:none"> <tbody> <tr> <td style="width:265.3pt;border:solid windowtext 1.0pt; background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt" valign="top" width="354"> AS Core Content </td> <td style="width:265.35pt;border:solid windowtext 1.0pt; border-left:none;background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt" valign="top" width="354"> A2 Core Content </td> <td style="width:265.35pt;border:solid windowtext 1.0pt; border-left:none;background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt" valign="top" width="354"> Further Pure Content </td> </tr> <tr style="height:18.45pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:18.45pt" valign="top" width="1061"> Indices and Surds </td> </tr> <tr> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt" valign="top" width="354"> Rational indices (positive, negative and zero) Laws of indices <a href="http://nrich.maths.org/7039">Power Stack</a> W Equivalence of Surd and Index notation Properties of Surds; rationalising denominators. <a href="http://nrich.maths.org/901">The Root of the Problem</a> A <a href="http://nrich.maths.org/324">Climbing Powers</a> B <a href="http://nrich.maths.org/7448">Irrational Arithmagons</a> B <a href="http://nrich.maths.org/7040">Quick Sum</a> W </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt" valign="top" width="354"> </td> </tr> <tr style="height:1.5pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.5pt" valign="top" width="1061"> Polynomials </td> </tr> <tr style="height:53.05pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:53.05pt" valign="top" width="354"> Addition, subtraction, multiplication of polynomials; collecting like terms, expansion of brackets, simplifying. <a href="http://nrich.maths.org/7042">Common Divisor</a> W Completing the square; using this to find the vertex. The discriminant of a quadratic polynomial; using the discriminant to determine the number of real roots. <a href="http://nrich.maths.org/6406">Implicitly</a> B Solution of quadratic equations, and linear and quadratic inequalities in one unknown. <a href="http://nrich.maths.org/7105">Inner Equality</a> W <a href="http://nrich.maths.org/7051">Unit Interval</a> W <a href="http://nrich.maths.org/7041">Quad Solve</a> W Solution of simultaneous equations, one linear and one quadratic. <a href="http://nrich.maths.org/543">System Speak</a> A Solutions of equations in x which are quadratic in some function of x. <a href="http://nrich.maths.org/6333">Direct Logic</a> A </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:53.05pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:53.05pt" valign="top" width="354"> Using relationships between the roots of a quadratic/cubic and the coefficients. Using substitution to get equations with roots simply related to the roots of an original equation. </td> </tr> <tr style="height:1.0pt"> <td colspan="2" style="width:530.65pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="708"> Coordinate Geometry and Graphs </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Polar Coordinates </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Finding length, gradient and midpoint of a line segment given its endpoints Equations of straight lines (y=mx+c, y-y1=m(x-x1), ax+by+c=0 Gradients of parallel or perpendicular lines <a href="http://nrich.maths.org/785">Parabella</a> A Equation of a circle with centre (a,b) and radius r: (x-a)2+(y-b)2=r2 Circle geometry: equation of a circle in expanded form x2+y2+2gx+2fy+c=0, angle in a semicircle is a right angle, perpendicular from centre to chord bisects the chord, radius is perpendicular to tangent. Solving equations using intersections of graphs, interpreting geometrically the algebraic solution of equations. <a href="http://nrich.maths.org/5438">Intersections</a> B Curve sketching: y=kxn, where n is an integer and k is a constant y=k?x where k is a constant y=ax2+bx+c where a, b and c are constants y=f(x), where f(x) is the product of at most 3 linear factors, not necessarily distinct <a href="http://nrich.maths.org/6493">Curve Match</a> B Transformations of graphs: Relationship between y=f(x) and y=af(x), y=f(x) + a, y=f(x+a), y=f(ax) where a is constant. <a href="http://nrich.maths.org/6842">Erratic Quadratic</a> B <a href="http://nrich.maths.org/6500">Whose Line Graph Is It Anyway?</a> B </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Composition of transformations of graphs ? relationship between y=f(x) and y=af(x+b) The modulus function, the relationship between the graphs y=f(x) and y=|f(x)| Parametric equations of curves; converting between parametric and cartesian forms </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Converting equations between Cartesian and polar form. Sketching simple polar curves. <a href="http://nrich.maths.org/2679">Polar Flower</a> A Finding the area of a sector using integration. </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Differentiation and Integration </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Gradient of a curve as the limit of gradients of a sequence of chords. <a href="http://nrich.maths.org/7060">Gradient Match</a> W Derivative and second derivative; notation f'(x) and f''(x), dy/dx, d2y/dx2 The derivative of xn where n is rational, together with constant multiples, sums, differences. Gradients, tangents, normals, rates of change, increasing/decreasing functions, stationary points, classifying stationary points. <a href="http://nrich.maths.org/7087">Calculus Analogies</a> C <a href="http://nrich.maths.org/7197">Patterns of Inflection</a> C <a href="http://nrich.maths.org/7084">Turning to Calculus</a> C <a href="http://nrich.maths.org/7085">Curvy Catalogue</a> C <a href="http://nrich.maths.org/7091">The Sign of the Times</a> W Indefinite integration as the reverse process of differentiation. <a href="http://nrich.maths.org/6412">Integration Matcher</a> C Integrating xn for rational n (n?-1) together with constant multiples, sums and differences. Definite integrals, constants of integration. Using integration to find the area of a region bounded by curves and lines. Estimating areas under curves using the Trapezium Rule. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Derivative of ex and ln x, together with constant multiples, sums and differences. Chain rule, product rule, quotient rule. <a href="http://nrich.maths.org/6552">Calculus Countdown</a> B dx/dy as 1 ÷ dy/dx <a href="http://nrich.maths.org/6406">Implicitly</a> B Integral of ex and 1/x together with constant multiples, sums and differences Integrating expressions involving a linear substitution. Volumes of revolution <a href="http://nrich.maths.org/6426">Brimful</a> A <a href="http://nrich.maths.org/6430">Brimful 2</a> A <a href="http://nrich.maths.org/6495">The Right Volume</a> W Derivative of sin x, cos x and tan x together with constant multiples, sums and differences. <a href="http://nrich.maths.org/7059">Trig Trig Trig</a> W Derivatives of functions defined parametrically. Integration of trigonometric functions (through the notion of "reverse differentiation) <a href="http://nrich.maths.org/6382">Mind Your Ps and Qs</a> B Integration of rational functions Integration of functions of the form y=kf'(x)/f(x) Integration by parts </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Derivatives of inverse trig functions, hyperbolic functions, inverse hyperbolic functions. Derivation of first few terms of Maclaurin series of simple functions. <a href="http://nrich.maths.org/4750">Towards Maclaurin</a> B Integrals such as 1/?(a2-x2), 1/?(x2-a2), 1/( a2+x2), 1/?(x2+a2), using appropriate trigonometric or hyperbolic substitutions. Reduction formulae to evaluate definite integrals Using areas of rectangles to estimate or bound the area under a curve or to derive inequalities concerning sums. </td> </tr> <tr style="height:1.0pt"> <td colspan="2" style="width:530.65pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="708"> Trigonometry </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Hyperbolic Functions </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Sine and Cosine rules. Area formula for triangles A=½ab sinC Relationship between degrees and radians Arc length s=r?, Area of a sector A = ½r2? <a href="http://nrich.maths.org/7475">Stand Up Arcs</a> W <a href="http://nrich.maths.org/6328">Curved Square</a> B Graphs, periodicity and symmetry for sine, cosine and tangent functions <a href="http://nrich.maths.org/7063">Trigger</a> W Identities tan ? = sin ?/cos ?, cos2? + sin2?=1 <a href="http://nrich.maths.org/7052">Geometric Trig</a> W Exact values of sine, cosine and tangent of 30° , 45° , 60° <a href="http://nrich.maths.org/5869">Impossible Square?</a> B <a href="http://nrich.maths.org/5923">Impossible Triangles?</a> B Finding solutions of sin(kx)=c, cos(kx)=c, tan(kx)=c and equations which can be reduced to these forms within a specified interval. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Inverse trigonomic relations sin-1, cos -1, tan-1, and their graphs on an appropriate domain. Properties of sec, cosec and cot. Solving equations using: sec2 ? = 1+ tan2 ? cosec2 ? = 1 + cot2 ? expansions of sin(A+B), cos(A+B), tan(A+B) formulae for sin 2A, cos 2A, tan 2A <a href="http://nrich.maths.org/7050">Trig Identity</a> W expression of a sin ? + b cos ? in the form Rsin(?+?) and Rcos(?+?) <a href="http://nrich.maths.org/2693">Loch Ness</a> B </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Definition of sinh, cosh, tanh, sech, cosech and coth in terms of ex. Graphs of simple hyperbolic functions. cosh 2x ? sinh 2x = 1, sinh 2x = 2 sinh x cosh x, etc. Expressing in terms of logarithms the inverse hyperbolic relations sinh-1x, cosh-1x, tanh-1x. </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Sequences and Series </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Definitions such as un=n2 or un+1=2un, and deducing simple properties from such definitions. ? notation Arithmetic and geometric progressions, finding the sum of an AP or GP, including the formula ½n(n+1) for the sum of the first n natural numbers. <a href="http://nrich.maths.org/6333">Direct Logic</a> A <a href="http://nrich.maths.org/7097">AP Train</a> W <a href="http://nrich.maths.org/7054">Prime APs</a> W <a href="http://nrich.maths.org/7056">Mad Robot</a> W <a href="http://nrich.maths.org/7315">Medicine Half Life</a> W Sum to infinity of a GP with |r|<1. <a href="http://nrich.maths.org/262">Circles Ad Infinitum</a> B Expansion of (a+b)n where n is a positive integer. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Expansion of (1+x)n where n is a rational number and |x|<1 </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> ?r, ?r2, ?r3 and related sums. Summing finite series using the method of differences. Recognising when a series is convergent, finding the sum to infinity. </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Algebra and functions </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Factor Theorem and Remainder Theorem. <a href="http://nrich.maths.org/7066">Cubic Roots</a> W Algebraic division of polynomials by a linear polynomial. Sketching y=ax where a>0 Relationship between logarithms and indices. Laws of logarithms. <a href="http://nrich.maths.org/6159">Power Match</a> C <a href="http://nrich.maths.org/6169">Extreme Dissociation</a> B, S Solving ax=b using logarithms. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Simplifying rational functions. Algebraic division of polynomials by a linear or quadratic polynomial. Expressing rational functions using partial fractions. <a href="http://nrich.maths.org/6960">Rational Request</a> A <a href="http://nrich.maths.org/6959">Inverting Rational Functions</a> A Identifying domain and range. Composition of functions. One-one functions, finding inverses. Graphical illustration of the relation between a one-one function and its inverse. Exponential and logarithmic functions ex and ln x, and their graphs. Exponential growth and decay. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Partial fractions with (x2+a2) in the denominator, and where the numerator is of higher degree than the denominator. Determining asymptotic behaviour for rational functions. Relationship between graphs of y=f(x) and y2=f(x) </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Numerical methods </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Locating roots by graphical considerations or sign-change <a href="http://nrich.maths.org/7038">Solve Me!</a> W <a href="http://nrich.maths.org/5876">Root Hunter</a> B Simple iterative methods, xn+1=F(xn), relating such an iterative formula to the equation being solved. <a href="http://nrich.maths.org/7291">Archimedes Numerical Roots</a> W Numerical integration: Simpson's rule. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Staircase and cobweb diagrams. Properties of successive errors in a converging iteration. Newton-Raphson method for finding roots. </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Differential Equations </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Forming differential equations from situations involving rate of change First order differential equations with separable variables: general form, and particular solutions from initial conditions. Interpreting solutions to differential equations within the context of a problem being modelled. <a href="http://nrich.maths.org/5874">It's only a minus sign</a> B </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Integrating factors for first order differential equations Reducing a first order differential equation to linear form or variable-separable using substitution. Complementary functions, particular integrals and general solutions of differential equations. Finding particular solutions using initial conditions, interpreting solutions in the context of a problem modelled by a differential equation. <a href="http://nrich.maths.org/4752">Out in Space</a> B <a href="http://nrich.maths.org/5875">Differential Equation Matcher</a> C </td> </tr> <tr style="height:1.0pt"> <td colspan="2" style="width:530.65pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="708"> Vectors </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Vectors and Matrices </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Addition and subtraction of vectors, multiplication of a vector by a scalar, geometrical interpretation of these. Unit vectors, position vectors, displacement vectors <a href="http://nrich.maths.org/6572">Vector Walk</a> B <a href="http://nrich.maths.org/6632">Polygon Walk</a> B Magnitude of a vector Scalar product of two vectors; determining the angle between two vectors <a href="http://nrich.maths.org/439">Flexi Quads</a> A Equation of a straight line in the form r = a + tb Angle between straight lines, point of intersection of straight lines, parallel or skew lines. </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Matrix addition, subtraction and multiplication. Singular and non-singular matrices, finding determinants and inverses. 2x2 matrices as transformations in the x-y plane. Solving linear simultaneous equations using matrices. <a href="http://nrich.maths.org/6875">Square Pair</a> B <a href="http://nrich.maths.org/6876">Matrix Meaning</a> B <a href="http://nrich.maths.org/6877">Nine Eigen</a> B <a href="http://nrich.maths.org/2370">Limiting Probabilities</a> B Equation of a line in the form (x-a)/p = (y-b)/q = (z-c)/r Equation of a plane in the form ax + by + cz = d or (r ? a).n=0 or r = a + ?b + ?c Vector product of two vectors <a href="http://nrich.maths.org/6576">Cross with the Scalar Product</a> B <a href="http://nrich.maths.org/6575">Fix Me or Crush Me</a> B Determining whether a line is in a plane, parallel to a plane or intersects a plane, finding point of intersection. Line of intersection of two planes Perpendicular distance from point to plane or line Angle between two planes or a line and a plane Shortest distance between skew lines </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Complex Numbers </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Real and imaginary parts, modulus and argument, complex conjugate. Addition, subtraction, multiplication, division, square roots of complex numbers x + iy Conjugate pairs of roots of a polynomial Complex conjugates and addition/subtraction of complex numbers on an Argand diagram, loci of simple equations and inequalities. <a href="http://nrich.maths.org/2374">Thousand Words</a> B Multiplication and division of complex numbers in polar form. de Moivre's theorem sin ? and cos ? in terms of ei? nth roots of unity. </td> </tr> <tr style="height:1.0pt"> <td colspan="3" style="width:796.0pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="1061"> Proof by Induction </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Establishing a given result using induction. Making conjectures based on some trial cases, then proving the conjectures using induction. </td> </tr> <tr style="height:1.0pt"> <td colspan="2" style="width:530.65pt;border:solid windowtext 1.0pt; border-top:none;background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="708"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; background:#FF99CC;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Groups </td> </tr> <tr style="height:1.0pt"> <td style="width:265.3pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> </td> <td style="width:265.35pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:1.0pt" valign="top" width="354"> Definition of a group Establishing whether a structure is or is not a group <a href="http://nrich.maths.org/2681">Group of Sets</a> A <a href="http://nrich.maths.org/7446">Poison, Antidote, Water</a> C Order of group, order of elements in a group. Subgroups Lagrange's theorem Cyclic groups Isomorphic groups <a href="http://nrich.maths.org/7005">Rose</a> B </td> </tr> </tbody> </table></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="width:100.0%;border-collapse:collapse;border:none" width="100%"> <tbody> <tr style="height:20.25pt"> <td style="width:16.08%;border:solid windowtext 1.0pt; border-right:none;background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt;height:20.25pt" valign="top" width="16%"> Year 7? </td> <td style="width:16.08%;border-top:solid windowtext 1.0pt; border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none; background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt;height:20.25pt" valign="top" width="16%"> ? </td> <td style="width:16.08%;border-top:solid windowtext 1.0pt; border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none; background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt;height:20.25pt" valign="top" width="16%"> ? </td> <td style="width:18.12%;border-top:solid windowtext 1.0pt; border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none; background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt;height:20.25pt" valign="top" width="18%"> ? </td> <td style="width:17.28%;border-top:solid windowtext 1.0pt; border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none; background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt;height:20.25pt" valign="top" width="17%"> ?Year 11 </td> <td style="width:16.36%;border:solid windowtext 1.0pt; border-left:none;background:#33CCCC;padding:0cm 5.4pt 0cm 5.4pt;height:20.25pt" valign="top" width="16%"> Extension </td> </tr> <tr style="height:22.5pt"> <td colspan="6" style="width:100.0%;border:solid windowtext 1.0pt; border-top:none;background:#66CCFF;padding:0cm 5.4pt 0cm 5.4pt;height:22.5pt" valign="top" width="100%"> Numbers and the number system </td> </tr> <tr style="height:12.75pt"> <td colspan="6" style="width:100.0%;border:solid windowtext 1.0pt; border-top:none;background:#FF99FF;padding:0cm 5.4pt 0cm 5.4pt;height:12.75pt" valign="top" width="100%"> Place value, ordering and rounding </td> </tr> <tr style="height:84.85pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:84.85pt" valign="top" width="16%"> understand and use decimal notation and place value; multiply and divide integers and decimals by 10, 100, 1000, and explain the effect <a href="http://nrich.maths.org/6606">Dicey Operations</a>* ü </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:84.85pt" valign="top" width="16%"> read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01 </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:84.85pt" valign="top" width="16%"> extend knowledge of integer powers of 10; recognise the equivalence of 0.1, 1/10 and 10-1; multiply and divide by any integer power of 10 </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:84.85pt" valign="top" width="18%"> express numbers in standard index form, both in conventional notation and on a calculator display </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:84.85pt" valign="top" width="17%"> <a href="http://nrich.maths.org/6349">A Question of Scale</a> ü </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:84.85pt" valign="top" width="16%"> </td> </tr> <tr style="height:72.0pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:72.0pt" valign="top" width="16%"> compare and order decimals in different contexts; know that when comparing measurements the units must be the same <a href="http://nrich.maths.org/6605">Nice and Nasty</a> ü </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:72.0pt" valign="top" width="16%"> order decimals </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:72.0pt" valign="top" width="16%"> </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:72.0pt" valign="top" width="18%"> convert between ordinary and standard index form representations </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:72.0pt" valign="top" width="17%"> use standard index form to make sensible estimates for calculations involving multiplication and/or division </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:72.0pt" valign="top" width="16%"> </td> </tr> <tr style="height:70.95pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:70.95pt" valign="top" width="16%"> round positive whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:70.95pt" valign="top" width="16%"> round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:70.95pt" valign="top" width="16%"> use rounding to make estimates and to give solutions to problems to an appropriate degree of accuracy </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:70.95pt" valign="top" width="18%"> round to a given number of significant figures; use significant figures to approximate answers when multiplying or dividing large numbers </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:70.95pt" valign="top" width="17%"> understand how errors can be compounded in calculations </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:70.95pt" valign="top" width="16%"> understand upper and lower bounds </td> </tr> <tr style="height:12.75pt"> <td colspan="6" style="width:100.0%;border:solid windowtext 1.0pt; border-top:none;background:#FF99FF;padding:0cm 5.4pt 0cm 5.4pt;height:12.75pt" valign="top" width="100%"> Integers powers and roots </td> </tr> <tr style="height:76.5pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:76.5pt" valign="top" width="16%"> understand negative numbers as positions on a number line; order, add and subtract integers in context <a href="http://nrich.maths.org/public/viewer.php?obj_id=5865">First Connect Three</a> ü </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:76.5pt" valign="top" width="16%"> add, subtract, multiply and divide integers <a href="http://nrich.maths.org/public/viewer.php?obj_id=5864">Playing Connect Three</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=5958">Weights</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=5868">Consecutive Negative Numbers</a>ü Article: <a href="http://nrich.maths.org/public/viewer.php?obj_id=5947">Adding & Subtracting Negative Numbers</a> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:76.5pt" valign="top" width="16%"> </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:76.5pt" valign="top" width="18%"> </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:76.5pt" valign="top" width="17%"> </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:76.5pt" valign="top" width="16%"> <a href="http://nrich.maths.org/public/viewer.php?obj_id=5798">Difference Sudoku</a> </td> </tr> <tr style="height:127.5pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:127.5pt" valign="top" width="16%"> recognise and use multiples, factors, primes (less than 100), common factors, highest common factors and lowest common multiples in simple cases; use simple tests of divisibility <a href="http://nrich.maths.org/7520">Sieve of Eratosthenes</a> ü <a href="http://nrich.maths.org/6650">How much can we spend?</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=559&part=index&refpage=monthindex.php">Dozens</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=5468&part=index&refpage=monthindex.php">Factors and Multiples Game</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=5448">Factors and Multiples Puzzle</a>ü Article: <a href="http://nrich.maths.org/public/viewer.php?obj_id=1308">Divisibility Tests</a> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:127.5pt" valign="top" width="16%"> use multiples, factors, common factors, highest common factors, lowest common multiples and primes; find the prime factor decomposition of a number, e.g. 8000 = 26 × 53 <a href="http://nrich.maths.org/6966">Counting Cogs</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=2669&refpage=titlesearch.php">Stars</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=6401">Power Mad!</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=480">14 Divisors</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=1866&part=index&refpage=monthindex.php">Take Three from Five</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=602">Differences</a> ü </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:127.5pt" valign="top" width="16%"> use the prime factor decomposition of a number <a href="http://nrich.maths.org/public/viewer.php?obj_id=4903&part=index&refpage=monthindex.php">Product Sudoku</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=740&part=index&refpage=monthindex.php">Funny Factorisation</a> </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:127.5pt" valign="top" width="18%"> <a href="http://nrich.maths.org/7547">Filling the Gaps</a> ü <a href="http://nrich.maths.org/public/viewer.php?obj_id=796&part=index&refpage=monthindex.php">American Billions</a> ü </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:127.5pt" valign="top" width="17%"> </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:127.5pt" valign="top" width="16%"> <a href="http://nrich.maths.org/public/viewer.php?obj_id=582">Expenses</a> </td> </tr> <tr style="height:89.25pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:89.25pt" valign="top" width="16%"> recognise the first few triangular numbers; recognise the squares of numbers to at least 12 × 12 and the corresponding roots </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:89.25pt" valign="top" width="16%"> use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers <a href="http://nrich.maths.org/public/viewer.php?obj_id=1163">Sissa's Reward</a> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:89.25pt" valign="top" width="16%"> use ICT to estimate square roots and cube roots </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:89.25pt" valign="top" width="18%"> <a href="http://nrich.maths.org/7282">Generating Triples</a> ü </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:89.25pt" valign="top" width="17%"> </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:89.25pt" valign="top" width="16%"> </td> </tr> <tr style="height:96.4pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:96.4pt" valign="top" width="16%"> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:96.4pt" valign="top" width="16%"> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:96.4pt" valign="top" width="16%"> use index notation for integer powers; know and use the index laws for multiplication and division of positive integer powers </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:96.4pt" valign="top" width="18%"> use index notation with negative and fractional powers, recognising that the index laws can be applied to these as well </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:96.4pt" valign="top" width="17%"> use inverse operations, understanding that the inverse operation of raising a positive number to power n is raising the result of this operation to power 1/n <a href="http://nrich.maths.org/6448">Power Countdown</a> ü </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:96.4pt" valign="top" width="16%"> understand and use rational and irrational numbers </td> </tr> <tr style="height:51.0pt"> <td style="width:16.08%;border-top:none;border-left: solid windowtext 1.0pt;border-bottom:solid windowtext 1.0pt;border-right: none;padding:0cm 5.4pt 0cm 5.4pt;height:51.0pt" valign="top" width="16%"> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:51.0pt" valign="top" width="16%"> </td> <td style="width:16.08%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:51.0pt" valign="top" width="16%"> </td> <td style="width:18.12%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:51.0pt" valign="top" width="18%"> know that n½ = ?n and n?= 3?n for any positive number n </td> <td style="width:17.28%;border:none;border-bottom: solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:51.0pt" valign="top" width="17%"> </td> <td style="width:16.36%;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt;height:51.0pt" valign="top" width="16%"> </td> </tr> </tbody> </table></mdoxml> 2 3 0 0 0 0 0 Mapping Docs Dev