11 -19 PROGRESSIONEdexcel AS and A level MathematicsPure MathematicsYear 1/ASSeries Editor:Harry SmithAuthors:Greg Attwood,Jack Barraclough,lan Bettison,Alistair Macpherson,Bronwen Moran,Su Nicholson,Diane Oliver,Joe Petran,Keith Pledger,Harry Smith,Geoff Staley,Robert Ward-Penny,Dave Wilkins个PearsonContentsContentsOverarching themesiv4.6Stretching graphs75Extra online contentvi4.7Transforming functions79Mixed exercise 4821Algebraic expressions11.1Index laws2Review exercise 1851.2Expanding brackets41.3Factorising65Straight line graphs891.4Negative and fractional indices95.1y=mx+c901.5Surds125.2Equations of straight lines931.6Rationalising denominators135.3Parallel and perpendicular lines97Mixed exercise 1155.4Length and area1005.5Modelling with straight lines103Quadratics18Mixed exercise 51082.1 Solving quadratic equations192.2Completing the square226Circles1132.3Functions256.1Midpoints and perpendicular2.4Quadratic graphs27bisectors1142.5The discriminant306.2Equation of a circle1172.6Modelling with quadratics326.3Intersections of straight linesMixed exercise 235and circles1216.4Use tangent and chord properties1233Equations and inequalities386.5Circles and triangles1283.1Linear simultaneous equations39Mixed exercise 61323.2Quadratic simultaneous equations413.3Simultaneous equations on graphs427Algebraic methods1373.4Linear inequalities467.1Algebraic fractions1383.5Quadratic inequalities487.2Dividing polynomials1393.6Inequalities on graphs517.3The factor theorem1433.7Regions537.4Mathematical proof146Mixed exercise 3567.5Methods of proof150Mixed exercise 71544Graphs and transformations594.1Cubic graphs608The binomial expansion1584.2Quartic graphs648.1Pascal's triangle1594.3Reciprocal graphs668.2Factorial notation1614.4Points of intersection688.3The binomial expansion1634.5Translating graphs718.4Solving binomial problems165Contents8.5Binomial estimation16712.5 Differentiating functions with twoMixed exercise 8169or more terms26612.6 Gradients,tangents and normal2689Trigonometric ratios17312.7 Increasing and decreasing functions 2709.1The cosine rule17412.8 Second order derivatives2719.2The sine rule17912.9 Stationary points2739.3Areas of triangles18512.10 Sketching gradient functions2779.4Solving triangle problems18712.11 Modelling with differentiation2799.5Graphs of sine,cosine and tangent192Mixed exercise 122829.6Transforming trigonometric graphs194Mixed exercise 919813Integration28728810Trigonometric identities and13.2 Indefinite integrals290equations20213.3 Finding functions29310.1 Angles in all four quadrants20313.4 Definite integrals29510.2 Exact values of trigonometrical ratios 20813.5 Areas under curves29710.3 Trigonometric identities20913.6 Areas under the x-axis30010.4 Simple trigonometric equations21313.7 Areas between curves and lines30210.5 Harder trigonometric equations217Mixed exercise 1330610.6 Equations and identities219Mixed exercise 1022214Exponentials and logarithms31114.1 Exponential functions312Review exercise 222614.2y=er31414.3 Exponential modelling31711 Vectors23014.4 Logarithms31911.1 Vectors23114.5 Laws of logarithms32111.2 Representing vectors23514.6 Solving equations using logarithms32411.3 Magnitude and direction23914.7 Working with natural logarithms32611.4 Position vectors24214.8 Logarithms and non-linear data32811.5 Solving geometric problems244Mixed exercise 1433411.6 Modelling with vectors248Mixed exercise 11251Review exercise 333812Differentiation255Practice exam paper34212.1 Gradients of curves25612.2 Finding the derivative259Answers34512.3 Differentiating x"26212.4 Differentiating quadratics264Index399