Opiskelupolut
Opiskelupolut
Opiskelupolut
Juuri 8 Juuri- ja trigonometriset funktiot
Opiskelijapolut
Suositeltavia tehtäviä, saa ja voi laskea tietenkin muitakin tehtäviä.
1.1 Potenssi ja verrannollisuus (2 h)
|
TASO 1 (AS 5-6) |
101 102 103 104 105 |
|
TASO 2 (AS 7-8) |
101 102 103 104 105 106 107 108 109 110 111 112 113 115 |
|
TASO 3 (AS 9-10) |
101 102 103 104 105 106 107 108 109 110 111 112 113 115 117 118 120 |
1.2 Funktion potenssin derivaatta (2 h)
|
TASO 1 (AS 5-6) |
121 122 123 124 125 126 127 |
|
TASO 2 (AS 7-8) |
121 122 123 124 125 126 127 128 129 130 133 134 |
|
TASO 3 (AS 9-10) |
121 122 123 124 125 126 127 128 129 130 133 134 135 136 138 139 |
1.3 Murtopotenssi (1 h)
|
TASO 1 (AS 5-6) |
141 142 143 144 145 |
|
TASO 2 (AS 7-8) |
141 142 143 144 145 146 147 148 149 150 151 152 153 154 |
|
TASO 3 (AS 9-10) |
141 142 143 144 145 146 147 148 149 150 151 152 153 154 157 158 159 161 |
2.1 Juurifunktio ja -yhtälö (2 h)
|
TASO 1 (AS 5-6) |
201 202 203 204 205 206 207 208 |
|
TASO 2 (AS 7-8) |
201 202 203 204 205 206 207 208 209 210 211 212 213 215 216 217 219 222 224 |
|
TASO 3 (AS 9-10) |
201 202 203 204 205 206 207 208 209 210 211 212 213 215 216 217 219 221 222 223 224 225 228 229 231 |
2.2 Juurifunktion derivaatta ja kulun tutkiminen (2 h)
|
TASO 1 (AS 5-6) |
232 233 234 235 236 237 238 |
|
TASO 2 (AS 7-8) |
232 233 234 235 236 237 238 239 240 241 242 244 245 248 250 251 252 |
|
TASO 3 (AS 9-10) |
232 233 234 235 236 237 238 239 240 241 242 243 246 247 249 251 252 253 254 255 257 258 259 |
2.3 Sovelluksia (1 h)
|
TASO 1 (AS 5-6) |
262 263 264 265 |
|
TASO 2 (AS 7-8) |
262 263 264 265 266 267 268 269 270 271 272 274 |
|
TASO 3 (AS 9-10) |
262 263 264 265 266 267 268 269 270 271 272 274 275 276 277 |
3.1 Eksponentiaalinen muutos (1 h)
|
TASO 1 (AS 5-6) |
301 302 303 304 305 |
|
TASO 2 (AS 7-8) |
301 302 303 304 305 306 307 309 310 311 312 313 |
|
TASO 3 (AS 9-10) |
301 302 303 304 305 306 307 308 310 311 312 313 315 316 317 320 |
3.2 Neperin luku ja eksponenttifunktion derivaatta (2 h)
|
TASO 1 (AS 5-6) |
321 322 323 324 325 326 327 |
|
TASO 2 (AS 7-8) |
321 322 323 324 325 326 327 328 329 330 331 332 333 335 337 338 339 |
|
TASO 3 (AS 9-10) |
321 322 323 324 325 326 327 328 329 330 331 332 333 335 337 338 339 341 342 343 344 346 347 348 |
4.1 Logaritmi (1 h)
|
TASO 1 (AS 5-6) |
401 402 403 404 405 |
|
TASO 2 (AS 7-8) |
401 402 403 404 405 406 407 408 409 410 411 412 414 415 |
|
TASO 3 (AS 9-10) |
401 402 403 404 405 406 407 408 409 410 411 412 414 415 417 419 420 |
4.2 Luonnollinen logaritmi (1 h)
|
TASO 1 (AS 5-6 ) |
422 423 424 425 426 427 428 |
|
TASO 2 (AS 7-8) |
422 423 424 425 426 427 428 429 430 431 432 434 435 436 |
|
TASO 3 (AS 9-10) |
422 423 424 425 426 427 428 429 430 431 432 434 435 436 437 438 439 440 442 445 447 448 |
4.3 Logaritmifunktio ja -yhtälö (1 h)
|
TASO 1 (AS 5-6) |
451 452 453 454 455 |
|
TASO 2 (AS 7-8) |
451 452 453 454 455 456 457 458 459 461 462 464 |
|
TASO 3 (AS 9-10) |
451 452 453 454 455 456 457 458 459 461 462 464 465 468 469 471 |
4.4 Logaritmifunktion derivaatta (1 h)
|
TASO 1 (AS 5-6) |
472 473 474 475 476 |
|
TASO 2 (AS 7-8) |
472 473 474 475 476 477 478 479 480 481 482 483 487 |
|
TASO 3 (AS 9-10) |
472 473 474 475 476 477 478 479 480 481 482 483 484 487 488 490 491 492 |