Opiskelupolut LOPS2016
Opiskelupolut
Opiskelupolut
Juuri 3 Geometria
Opiskelijapolut
Suositeltavia tehtäviä, saa ja voi laskea tietenkin muitakin tehtäviä.
1.1 Erilaisia kulmia (1 h)
|
TASO 1 (AS 5-6) |
101 102 103 104 105 |
|
TASO 2 (AS 7-8) |
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 |
|
TASO 3 (AS 9-10) |
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 117 118 120 |
1.2 Pythagoraan lause ja kolmion pinta-ala (1 h)
|
TASO 1 (AS 5-6) |
122 123 124 125 126 |
|
TASO 2 (AS 7-8) |
122 123 124 125 126 127 128 129 130 131 132 133 134 136 |
|
TASO 3 (AS 9-10) |
122 123 124 125 126 127 128 129 130 131 132 133 134 136 137 139 140 |
1.3 Monikulmioita (1 h)
|
TASO 1 (AS 5-6) |
142 143 144 145 146 |
|
TASO 2 (AS 7-8) |
142 143 144 145 146 147 148 149 150 151 152 153 154 156 |
|
TASO 3 (AS 9-10) |
142 143 144 145 146 147 148 149 150 151 152 153 154 156 158 160 162 |
1.4 Yhdenmuotoisuus ja yhtenevyys (2 h)
|
TASO 1 (AS 5-6) |
163 164 165 166 167 168 169 |
|
TASO 2 (AS 7-8) |
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 179 180 183 186 |
|
TASO 3 (AS 9-10) |
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 179 180 182 183 184 186 187 188 189 19 |
2.1 Suorakulmaisen kolmion trigonometriaa (1 h)
|
TASO 1 (AS 5-6) |
201 202 203 204 205 |
|
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) |
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 219 220 |
2.2 Tylppäkulmaisen kolmion trigonometriaa (1 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) |
223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 244 |
TÄHÄN asti päivitetty 18.12.2017
Päivittämättä 2.3-3.3
2.3 Sinilause (1 h)
|
TASO 1 (AS 5-6) |
223 224 225 226 227 228 |
|
TASO 2 (AS 7-8) |
223 224 225 226 227 228 232 233 234 235 236 237 238 239 240 241 242 244 245 248 250 251 252 |
|
TASO 3 (AS 9-10) |
223 224 225 226 227 228 232 233 234 235 236 237 238 239 240 241 242 243 246 247 249 251 252 253 254 255 257 258 259 |
2.4 Kosinilause
(1 h)
|
TASO 1 (AS 5-6) |
223 224 225 226 227 228 |
|
TASO 2 (AS 7-8) |
223 224 225 226 227 228 232 233 234 235 236 237 238 239 240 241 242 244 245 248 250 251 252 |
|
TASO 3 (AS 9-10) |
223 224 225 226 227 228 232 233 234 235 236 237 238 239 240 241 242 243 246 247 249 251 252 253 254 255 257 258 259 |
3.1 Ympyrä (1 h)
|
TASO 1 (AS 5-6) |
301 302 303 304 305 |
|
TASO 2 (AS 7-8) |
301 302 303 304 305 306 307 308 310 311 313 |
|
TASO 3 (AS 9-10) |
301 302 303 304 305 306 307 308 310 311 312 313 316 317 320 |
3.2 Ympyrään liittyviä kulmia (1 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 |
3.3 Kolmion merkilliset pisteet (1 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 |
Päivitetty 4. luku 17.1.18
4.1 Avaruusgeometrian peruskäsitteitä (1 h)
|
TASO 1 (AS 5-6) |
401 402 403 404 405 |
|
TASO 2 (AS 7-8) |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 |
|
TASO 3 (AS 9-10) |
401 402 403 404 405 406 407 408 409 410 412 413 416 417 418 420 |
4.2 Lieriö (1 h)
|
TASO 1 (AS 5-6 ) |
421 422 423 424 425 |
|
TASO 2 (AS 7-8) |
421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 |
|
TASO 3 (AS 9-10) |
421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 440 |
4.3 Kartio (1 h)
|
TASO 1 (AS 5-6) |
441 442 443 444 445 |
|
TASO 2 (AS 7-8) |
441 442 443 444 445 446 447 448 449 450 451 452 453 454 |
|
TASO 3 (AS 9-10) |
441 442 443 444 445 446 447 448 449 450 451 452 453 454 456 457 458 (yhdessä) 459 |
4.4 Pallo (1 h)
|
TASO 1 (AS 5-6) |
461 462 463 464 465 |
|
TASO 2 (AS 7-8) |
461 462 463 464 465 466 467 468 469 470 471 472 |
|
TASO 3 (AS 9-10) |
461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 |