Cambridge International AS and A Level Mathematics Pure Mathematics 1

Achilles and the tortoise 94

addition

of vectors 263–4

see also sum; summation

algebraic expressions, manipulating

1

angles

between two vectors 271–2,

273–5

of elevation and depression 216

measuring 235

of a polygon 6–7

positive and negative 220

in three dimensions 274–5

arc of a circle, length 238

area

below the x axis 193–6

between a curve and the y axis

202–3

between two curves 197

as the limit of a sum 182–5

of a sector of a circle 238

of a trapezium 10

under a curve 179–82

arithmetic progressions 77–84

asymptotes 69, 228

bearings 216, 255

binomial coefficients

notation 97

relationships 101

sum of terms 101

symmetry 97, 101

tables 96–7

binomial distribution 102

binomial expansions, of

(1 + x)n 100–1

binomial expansions 95–104

binomial theorem 102–4

brackets, removing 1–2

calculus

fundamental theorem 180

importance of limits 126

notation 129, 131

see also differentiation;

integration

Cartesian system 38

centroid of a triangle 59

chain rule 167–71

changing the subject of a formula

10–11

Chinese triangle see Pascal’s triangle

chords, approaching the tangent

126

Chu Shi-kie 96

circle

arc 238

equation 69

properties 238–44

sectors 239

circular measure 235–8

common difference 77

completing the square 21–4

complex numbers 27

constant, arbitrary 173

co-ordinates

and distance between two points

41–2

and gradient of a line 39–40

of the mid-point of a line 42–3

plotting, sketching and drawing

39

of a point 258

in two and three dimensions 38

cosine (cos) 217, 223

graphs 226–7

cosine rule 240, 271

cubic polynomial, curve and

stationary points 64–5

curves

continuous and discontinuous

69

drawing 63

of the form y =^1

xn

68–9

gradient 123–6, 134–9

normal to 140–1

d (δ), notation 129

degrees 235

depression, angle 216

Descartes, René 58

difference of two squares 16

differential equations 173–4

general solution 174

particular solution 174

differentiation

of a composite function 167–8

from first principles 126–7, 131

and gradient of curves 134–9

with respect to different variables

169–70

reversing 173

using standard results 131–2

discriminant 27

displacement vector 260

distance between two points,

calculating 41–2

division, by a negative number 34

domain

of a function 108

of a mapping 106

drawing

co-ordinates 39

curves 63

a line, given its equation 47–9

elevation, angle 216

equations

of a circle 69

graphical solution 20–1

linear 6, 13

solving 7–8

of a straight line 46–54

of a tangent 140

see also differential equations;

quadratic equations;

simultaneous equations

expansion of (1 + x)n 100–1

factorials 97

factorisation 2

quadratic 13–17

Fermat, Pierre de 126

Index

Index

Index

P1^