Index Addition Law o Probabiliti Probabilities es addition o matrices 326–35 Associative Law 328 Commutative Law 328 addition principle 540–4 antidierentiation 432–6 applications 467–73
496–502
CAS calculator equations and unctions 16 indicial equations 237 modelling using 149 simultaneouss equations 21 simultaneou change, rates o see rates o change circles 208–12 arrangements in 559–61 complementary complementar y unctions 285 exact values 272 general equation o 209 quadrants 271–2 radians 276–9 symmetry 280–5 tangent 285 unit circle 271–6 circular unctions 267 column matrix 331 combinations using nCr 561–5 completing the square actorising by 53–6 solving quadratic equations 61–4 conditional probability 508–13 constant rates 363–8 continuous unctions, limits o 412 cosine and sine graphs 289–97 cubes dierence o two cubes 124–6 sum o two cubes 124–6 cubic unctions 109 domain 143–8 graphs in power unction orm 139–43 maximums 143–8 minimums 143–8 range 143–8 cubic graphs intercepts method 129–36 delta 70 diagonal matrix 331 diagrams lattice 491–6 tree 491–6 dierence nite dierences 152–8 two cubes, o 124–6 two squares, o (DOTS) 50 dierentiation 410 applications applicatio ns o 449
638
Index
rst principles, using 420–3 rules, nding derivatives by 423–32 discontinuous unctions, limits o 415 discriminant 70–5 distance two points, between 29–32, 36 division in index orm 227 domain 177–83 unction, o 143–8 equal matrices 331 equations CAS calculator 16 indicial 235–8 linear see linear equations matrix equations, solving 339–45 quadratic see quadratic equations rearrangement rearrangeme nt 6–11, 36 simultaneous see simultaneou simultaneouss equations straight line, o 25–8, 36 substitution 6–11, 36 trigonometric, trigonometr ic, solving 301–9 event space 486 reduced 508 expanding linear actors 109–11 experimental probability see probabilities experiments random outcome 483 exponential unctions 226 applications 253–8 graphs o 238–44 horizontal translatio translations ns 239 refections 239 vertical translations 239 x-axis, dilation rom 240 y-axis, dilation rom 240 actor theorem 118–21 actorials 548–50 actorising completing the square, by 53–6 denition 49 inspection, by 50 methods 50 polynomials 121–4 nite dieren dierences ces 152–8 xed point iteration 59 unctions 184 CAS calculator 16 evaluating 195 exponential 226 ully dening 196 unction notation 195–200 gradient see gradient unction inverse 206–8 linear see linear unctions modelling and 212–15
original see original unction rate o change 449–55 restriction o 201 types 200–6 gradient denition 11, 420 perpendicular lines 26, 36 rate o change o unction 449–55 straight line, o 11–15, 36 gradient unction denition 420 deriving original unction rom 437–41 original unction, relating to 387–9 graphs 173–7 exponential unctions, o 238–44 linear, sketching 16 logarithmic 251–3 motion 379–87 sine and cosine 289–97 stationary points, containing 455–62 tangent 297–301 velocity–time and position–time, relating 389–94 graphs o cubic unctions power unction orm 139–43 graphs o quadratic unctions intercepts method 80–91 power unctions (turning point orm) 75–9 highest common actor (HCF) 50 hybrid unctions 202–6, 396–7 limits o 415, 417–20 hyperbola 187–9 identities 285 independent events 520–6 index laws 227–32 indicial equations 235–8 inequations, linear see linear equations instantaneous rates 375–9 intercepts 140 intercepts method cubic graphs 129–36 graphs o quadratic unctions 80–91 quartic graphs 136–9 interval notation 178 inverse matrix 339 inverse relations and unctions 206–8 Karnaugh maps 502–7 kinematics 379–87 lattice diagrams 491–6 limit(s) concept o 410–12 continuous unctions, o 412 discontinuous unctions, o 415 hybrid unctions, o 415, 417–20 rational unctions, o 415 theorems on 412–13 line perpendicular 26 straight see straight line
linear equations denition 1 general orm 16 simultaneous quadratic equations and 95–101 solving 1–8, 36 linear actors expanding 109–11 linear unctions sketching 16–21, 36 linear inequations solving 1–8, 36 linear modelling 32–5, 36 local maximum turning point 456 local minimum turning point 455–6 logarithmic equations, solving 248–51 logarithmic unctions, applications 253–8 logarithmic graphs 251–3 logarithms 244–8 base 10, to 248 common 248 laws 245 long division actorising polynomials 121–5 polynomials, o 111–15 many-to-many relations 183 many-to-one relations 183 Markov chains 513–20 matrices 326 addition 326–35 Associative Law or addition 328 Commutative Law or addition 328 elements 327 inverse 339 multiplication 335–9 multiplication by a scalar 332 multiplicative identity matrix 339 subtraction 326–35 transormations and 345–50 transition matrices 513–20 types 330–2 matrix equations, solving 339–45 maximum problems, solving 462–7 midpoint o a segment 29–32, 36 minimum problems, solving 462–7 modelling CAS calculator, using 149 unctions and 212–15 technology, using 148–52 motion graphs 379–87 multiplication index orm, in 227 matrices 335–9 matrix, o, by a scalar 332 multiplication principle 540–4 negative powers 232–5 normals 427 Null Factor Law 56–61 one-to-many relations 183 one-to-one unctions 200–1 one-to-one relations 183
Index
639
original unction gradient unction, deriving rom 437–41 relating to gradient unction 387–9 perect squares 50 permutations 544–8 grouped objects 556 identical objects 555 n Pr , using 550–4 restrictions, involving 555–8 perpendicular lines 26, 36 polynomials 43–6 cubic 109 actorising 121–4 long division 111–15 polynomial values 115–17 quartics 109 rates o change 394–401 solving polynomial equations 126–9 value o 44 position–time graphs velocity–time graphs, relating to 389–94 power unctions 187–95 powers negative 232–5 rational 233–5 probabilities addition law o 496–502 applications 566–71 calculating 486–91 conditional probability 508–13 denition 566 event space 486 experimental 482–6 introduction 482–6 probability tables 502–7 range o 488 subjective 482 products 227 Pythagoras’ theorem 29 Pythagorean identity 285 quadrants 271–2 quadratic equations completing the square 61–4 denition 46 discriminant 70–5 examples 46 expanding 46–9 actorising 49–53 xed point iteration 59 graphs o see graphs o quadratic unctions Null Factor Law 56–61 power unctions, as 75–8 simultaneous linear equations and 95–101 solving 56–64 technology, using 91–5 quadratic ormula 65–70 quadratic trinomials 50 quartic unctions 109 quartic graphs intercepts method 136–9 quotients 227
640
Index
radians 276–9 raising to a power 227 raising to the power o zero 227 random outcome experiments 483 range 177–83 unction, o 143–8 rates constant 363–8 identiying 360–3 instantaneous 375–9 variable 368–70 rates o change average 370–5 unction, o 449–55 polynomials, o 394–401 rational unctions, limits o 415 rational powers 233–5 rearrangement o equations 6–11, 36 relations 173–7 inverse 206–8 types 183–7 remainder theorem 118–21 row matrix 331 segment, midpoint o 29–32, 36 set notation 170–3 sets o numbers 171 short division actorising polynomials 121 simulation 526–30 simultaneous equations algebraic solution 22 CAS calculator 21 denition 21 graphical solution 21 solving 21–2, 36 use o matrices to solve 340 using, to nd a polynomial model sine and cosine graphs 289–97 square matrix 331 square root unction 192–5 stationary points graphs containing 455–62 infection, o 456 straight line equation, nding 25–8, 36 gradient 11–15, 36 substitution o equations 6–11, 36 subtraction o matrices 326–35 sum o two cubes 124–6 symmetry in unit circles 280–5
155–7
tangent graphs 297–301 tangents 427 technology modelling using 148–52 quadratic equations, solving 91–5 transormations and matrices 345–50 transition matrices 513–20 tree diagrams 491–6 trigonometric equations, solving 301–9 trigonometric unctions, applications 309–13 trigonometric ratio revision 267–70
truncus 189–92 turning point (TP) local maximum 456 local minimum 455–6 quadratic unctions 75–9 turning point coordinates 80 two points distance between 29–32, 36
variable rates 368–70 velocity–time graphs position–time graphs, relating to Venn diagrams 502 vertical line test 184 x-intercepts y-intercept
unit circle 271–6 unit matrix 331
zero matrix
389–94
80 80 331
Index
641
