IndexP1^
formula
binomial coefficients 97–9
changing the subject 10–11
definition 10
for momentum after an impulse
11
quadratic 25–7
for speed of an oscillating point
11
fractions 3–4
functions
composite 112–13, 167
domain 108
graphical representation 108–10
increasing and decreasing 150–3
inverse 115–17
notation 113
as one-to-one mappings 108
order 113–14
range 108
sums and differences 132–3
fundamental theorem of calculus
180
Gauss, Carl Friederich 79
geometrical figures, vector
representation 265–7
geometric progressions 84–94
infinite 88–90
grade, for measuring angles 235
gradient
at a maximum or minimum point
146–50
of a curve 123–6, 134–9
fixed 46
of a line 39–40
gradient function 127–9
second derivative 155
graphical solution
of equations 20–1, 229–33
of simultaneous equations 31
graphs
of a function 108
of a function and its inverse
117–18
maximum and minimum points
146
of quadratic functions 22–5
of trigonometrical functions
226–35
heptagon 6
i (square root of –1) 27
identities
how they differ from equations
7, 223
involving sin, cos and tan 223–6
image (output) 106, 109
inequalities 34–6
linear and quadratic 35
input 106, 109
integrals
definite 186–7
improper 206–8
indefinite 188
integral sign 185
integration 173–9
notation 184–5
of xn 175
intersection
of a line and a curve 70–3
of two straight lines 56–8
inverse function 115–20Leibniz, Gottfried 131
length
of an arc of a circle 238
of a vector 260–1
limits
of an integral 185
importance in calculus 126
of a series 76
lines
drawing, given its equation 46–9
equation 46–54
gradient 39–40
intersection 56–8
mid-point 42–3
parallel 40–1
perpendicular 40–1
line segment 260
line of symmetry 22, 23, 62, 217
locus, of a circle 69mappings
definition 106
mathematical 107–11
one-to-one or one-to-many 106
maximum and minimum points
146–50
see also stationary points
maximum and minimum values,
finding 160–6median of a triangle 59
mid-point of a line 42–3
modulus of a vector 256
momentum after an impulse,
formula 11
multiplication
of algebraic expressions 3
by a negative number 35
of a vector by a scalar 262negative number
multiplying or dividing by 35
square root 27, 108, 114
Newton, Sir Isaac 131
normal to a curve 140–1object (input) 106, 109parabola
curve of a quadratic function 22
vertex and line of symmetry 22,
23
parallel lines 40–1
Pascal, Blaise 96
Pascal’s triangle (Chinese triangle)
95, 98, 101
perfect square 16
periodic function 226
perpendicular lines 40–1
plotting co-ordinates 39
points, three-dimensional
co-ordinates 258
points of inflection 153–4
polygons, sum of angles 6
polynomials
behaviour for large x (positive
and negative) 65
curves 63
dominant term 65
intersections with the x and y axes
65–7
position–time graph, velocity and
acceleration 161
position vectors 259–60
principal values
of graphs of trigonometrical
functions 229–30
in a restricted domain 117
Pythagoras’ theorem, alternative
proof 44