Cambridge International AS and A Level Mathematics Pure Mathematics 1

Index

P1^

quadratic equations 12–18

completing the square 21–2

graphical solution 20–1, 229–33

that cannot be factorised 20–2

quadratic factorisation 13–17

quadratic formula 25–7

quadratic inequalities 35

quadratic polynomial, curve and

stationary point 64–5

quartic equation, rewriting as a

quadratic 17–18

quartic polynomial, curve and

stationary points 64–5

radians 235, 237

range, of a mapping 106

real numbers 27, 107, 108, 115

reflections, of trigonometrical

functions 246

reverse chain rule 203–6

roots

of a quadratic equation 17

real 26, 27, 28

rotational solids 209–11

Sawyer, W.W. 138

scalar, definition 254

scalar product (dot product) 271–4

second derivative 154–8

sectors of a circle, properties

239–41

selections 102

sequences

definition and notation 76

infinite 76

series

convergent 88, 89

definition 76

divergent 89

infinite 76

simplification 1

simultaneous equations 29–33

graphical solution 31

linear 30–1

non-linear 32

substitution 31

sine rule 240

sine (sin) 217, 223

graphs 226–7

sketching co-ordinates 39

snowflakes 94

speed of an oscillating point,

formula 11

square

completing 21–4

perfect 16

square root

of –1 27

of a negative number 27

stationary points 63–4

using the second derivative

154–8

see also maximum and minimum

points

straight line see line

stretches, one-way, of

trigonometrical functions

246–7

substitution, in simultaneous

equations 31, 32

subtraction, of vectors 264–5

sum

of binomial coefficients 102

of a sequence 76

of the terms of an arithmetic

progression 79–81

of the terms of a geometric

progression 86–90

summation

of a series 76

symbol 102

symmetry, of binomial coefficients

101

tangent

equation 140

to a curve 123, 126, 140

tangent (tan) 217, 223

graph 228

terms

collecting 1

like and unlike 1

of a sequence 76

translations, of trigonometrical

functions 244–5

trapezium, area 10

triangle

properties 59

see also Pascal’s triangle

trigonometrical functions 217–19

for angles of any size 222

inverse 229

transformations 244–52

turning points of a graph 63

see also stationary points

unit vectors 255, 258, 267–8

variables 6

vector product 273

vectors

adding 263–4

angle between 271–2, 273–5

calculations 262–70

components 255

definition 254

equal 259

length 260–1

magnitude–direction (polar) form

254–7

modulus 256

multiplying by a scalar 262

negative of 262–3

notation 254–6

perpendicular 272

in representation of geometrical

figures 265–7

scalar product (dot product)

271–4

subtracting 264–5

in three dimensions 258–62,

274–5

in two dimensions 254–7

see also unit vector

vertex, of a parabola 22, 23

volume

finding by integration 208–14

of rotation 209

Wallis’s rule 129, 130

Yang Hui 96