Opiskelupolut LOPS 2016
Opiskelupolut
1.1 Peruskäsitteitä (1 h)
|
TASO 1 (AS 5-6) |
101 102 103 104 105 106 |
|
TASO 2 (AS 7-8) |
101 102 103 104 105 106 107 108 109 110 111 113 114 116 |
|
TASO 3 (AS 9-10) |
101 102 103 104 105 106 107 108 109 110 111 113 114 116 117 118 119 121 122 125 |
1.2 Yhdenmuotoisuus (1 h)
|
TASO 1 (AS 5-6) |
126 127 128 129 130 131 |
|
TASO 2 (AS 7-8) |
126 127 128 129 130 131 132 133 134 135 136 137 139 140 |
|
TASO 3 (AS 9-10) |
126 127 128 129 130 131 132 133 134 135 136 137 139 140 143 146 |
1.3 Pinta-alojen ja tilavuuksien suhteita (1 h)
|
TASO 1 (AS 5-6) |
149 150 151 152 153 154 |
|
TASO 2 (AS 7-8) |
149 150 151 152 153 154 155 156 157 158 160 161 163 164 |
|
TASO 3 (AS 9-10) |
149 150 151 152 153 154 155 156 157 158 160 161 163 164 |
2.1 Kolmio (1 h)
|
TASO 1 (AS 5-6) |
201 202 203 204 205 206 |
|
TASO 2 (AS 7-8) |
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 |
|
TASO 3 (AS 9-10) |
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 218 220 |
2.2 Pythagoraan lause (2 h)
|
TASO 1 (AS 5-6) |
223 224 225 226 227 228 |
|
TASO 2 (AS 7-8) |
223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 |
|
TASO 3 (AS 9-10) |
223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 240 242 |
2.3 Trigonometriaa (1-2 h)
|
TASO 1 (AS 5-6) |
245 246 248 249 250 251 |
|
TASO 2 (AS 7-8) |
245 246 247 248 249 250 251 252 253 254 256 258 |
|
TASO 3 (AS 9-10) |
245 246 247 248 249 250 251 252 253 254 256 258 259 263 265 267 |
2.4 Nelikulmio (1 h)
|
TASO 1 (AS 5-6) |
269 270 271 272 273 274 |
|
TASO 2 (AS 7-8) |
269 270 271 272 273 274 275 277 278 279 |
|
TASO 3 (AS 9-10) |
269 270 271 272 273 274 276 277 278 279 281 282 283 284 285 |
2.5 Muita monikulmioita (0-1 h)
|
TASO 1 (AS 5-6) |
288 289 290 291 |
|
TASO 2 (AS 7-8) |
288 289 290 291 292 293 294 |
|
TASO 3 (AS 9-10) |
288 289 290 291 292 293 294 296 297 299 |
3.1 Ympyrään liittyviä pituuksia (1 h)
|
TASO 1 (AS 5-6) |
301 302 303 304 305 306 |
|
TASO 2 (AS 7-8) |
301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 |
|
TASO 3 (AS 9-10) |
301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 318 319 321 323 |
3.2 Ympyrään liittyviä pinta-aloja (1 h)
|
TASO 1 (AS 5-6) |
326 327 328 329 330 331 |
|
TASO 2 (AS 7-8) |
326 327 328 329 330 331 332 333 334 335 336 337 339 342 |
|
TASO 3 (AS 9-10) |
326 327 328 329 330 331 332 333 334 335 336 337 339 342 344 346 349 |
3.3 Ympyrän tangentti (1 h)
|
TASO 1 (AS 5-6) |
351 352 353 354 355 |
|
TASO 2 (AS 7-8) |
351 352 353 354 355 356 357 359 361 362 363 365 366 |
|
TASO 3 (AS 9-10) |
351 352 353 354 355 356 357 359 361 362 363 365 366 367 369 372 |
4.1 Särmiö (1 h)
|
TASO 1 (AS 5-6) |
401 402 403 404 405 406 |
|
TASO 2 (AS 7-8) |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 |
|
TASO 3 (AS 9-10) |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 419 |
4.2 Ympyrälieriö (1 h)
|
TASO 1 (AS 5-6) |
422 423 424 425 426 |
|
TASO 2 (AS 7-8) |
422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 |
|
TASO 3 (AS 9-10) |
422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 439 441 |
4.3 Pyramidi (1 h)
|
TASO 1 (AS 5-6) |
442 443 444 445 446 447 |
|
TASO 2 (AS 7-8) |
442 443 444 445 446 447 448 450 451 453 454 |
|
TASO 3 (AS 9-10) |
442 443 444 445 446 447 449 450 451 453 454 456 457 459 |
4.4 Ympyräkartio (1 h)
|
TASO 1 (AS 5-6) |
460 461 462 463 464 |
|
TASO 2 (AS 7-8) |
460 461 462 463 464 465 466 467 468 469 471 472 473 |
|
TASO 3 (AS 9-10) |
460 461 462 463 464 465 466 467 469 471 472 473 475 476 477 479 |
TÄSTÄ ETEENPÄIN MUUTTAMATTA!!!
4.5 Pallo (1 h)
|
TASO 1 (AS 5-6) |
480 481 482 483 484 |
|
TASO 2 (AS 7-8) |
480 481 482 483 484 485 486 487 488 490 491 492 493 494 |
|
TASO 3 (AS 9-10) |
480 481 482 483 484 485 486 487 488 490 491 492 493 494 496 497 499 |