https://peda.net/id/4fa9f4ce32e 2023-08-04T19:16:47+03:00 https://peda.net/:static/548/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license noopener" href="https://peda.net/info" target="_blank">Peda.net-yleislisenssi</a></div> https://peda.net/id/4faa57f332e 2024-03-18T11:02:02+02:00 <br/> <div class="main"> <div class="messages"> <p class="message success"><a class="close message" href="https://peda.net/siilinjarvi/siilinjarvenlukio/opiskelu/oppiaineet/pitk%C3%A4-matematiikka/lyhyt-matematiikka/mab3/opiskelupolut?session-tdid=66fc265c-36c3-478e-ada4-43a1db9d8ab0#" aria-hidden="true" target="_blank" rel="noopener"></a>Muutokset tallennettu.</p> </div> <h1><a href="https://peda.net/siilinjarvi/siilinjarvenlukio/opiskelu/oppiaineet/pitk%C3%A4-matematiikka/lyhyt-matematiikka/mab3/opiskelupolut/opiskelupolut#top" rel="nofollow ugc noopener" target="_blank">Opiskelupolut</a></h1> <a class="menutoggle" href="https://peda.net/siilinjarvi/siilinjarvenlukio/opiskelu/oppiaineet/pitk%C3%A4-matematiikka/lyhyt-matematiikka/mab3/opiskelupolut?session-tdid=66fc265c-36c3-478e-ada4-43a1db9d8ab0#" aria-haspopup="menu" aria-expanded="false" target="_blank" rel="noopener"><span>Valikko</span></a> <div class="main"> <div class="content enclose"> <p><strong>1.1 Peruskäsitteitä</strong><strong><span> </span>(1 h)<br/> </strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>101 <b>102</b> 103 104 105 106 107 <b>108</b> <b>109</b></p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>101 102 103 104 105 106 107 108 109 110 111 <b>112</b> <b>113</b> 114 <b>115</b> 116 119 <b>121</b></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p>101 102 103 104 105 106 107 108 109 110 111 <b>112</b> <b>113</b> 114 <b>115</b> 116 119 <b>121 </b>123 <b>125</b></p> </td> </tr> </tbody> </table> <p><strong>1.2 Kolmio </strong><strong>(1 h)<br/> </strong></p> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p><span>127 128 129 <b>130</b> 131 <b>132</b> 133 <b>134</b></span></p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p><span>127 128 129 130 131 132 133 134 135 <b>136</b> 137 138 139 140 <b>141</b> 143</span></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p><span>127 128 129 130 131 132 133 134 135 <b>136</b> 137 138 139 140 <b>141</b> 143 146 <b>148</b></span></p> </td> </tr> </tbody> </table> <div class="tablewrap"> </div> <p><strong>1.3 Pythagoraan lause (3 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p><span>150 151 <b>152</b> <b>153</b> 154 <b>155</b> 156 157 158 </span></p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p><span>150 151 152 153 154 155 156 157 158 <b>159</b> 160 <b>161</b> <b>163</b> 164 165 166 <b>168</b></span></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p><span>150 151 152 153 154 155 156 157 158 159 160 161 163 164 165 166 167 170 171 172 </span></p> </td> </tr> </tbody> </table> </div> </div> <p><strong><br/> 2.1 Yhdenmuotoisuus</strong><strong><span> </span>(1 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>201 <b>202</b> 203 <b>204 205</b> 206 <b>207</b> 208 </p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>201 202 203 204 205 206 207 208 209 <b>210</b> <b>211</b> 212 213 <b>214 </b> 217 <b>218</b></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p>201 202 203 204 205 206 207 208 209 210 211 212 213 215 217 218 <b>221 222</b> 223</p> </td> </tr> </tbody> </table> </div> <p><strong><br/> 2.2 Trigonometriaa (1 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>226 227 228 229 230 231 232</p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>226 227 228 229 230 231 232 233 234 236 237 239 241 245</p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p>226 227 228 229 230 231 232 233 234 236 237 239 241 242 244 245 246 250 </p> </td> </tr> </tbody> </table> <br/> <p><strong>2.3 Nelikulmio (1 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p><b>251</b> 252 <b>253</b> 254 255 <b>256 257</b></p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>251 252 253 254 255 256 257 258 <b>259</b> <b>260 261</b> 263 <b>265</b> <b>266</b> 268</p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p>251 252 253 254 255 256 257 258 259 260 261 263 265 266 268 <b>269</b> 272</p> </td> </tr> </tbody> </table> </div> <div class="tablewrap"><br/> <strong>2.4 Monikulmio ja pinta-alojen suhde</strong><strong> (1 h)</strong></div> </div> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p><b>274</b> <b>275</b> 276 <b>277</b> <b>278 279</b> 280 281 282 </p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>274 275 276 277 278 279 280 281 <b>282 283</b> <b>284</b> 285 286 <b>287 288</b></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p>274 275 276 277 278 279 280 281 282 283 284 286 287 288 290 <b>291 293</b> 295</p> </td> </tr> </tbody> </table> </div> <p><strong>Tähän asti päivitetty 28.2.2024<br/> <br/> 3.1 Ympyrään liittyviä pituuksia ja kulmia</strong><strong> (1 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>301 302 303 304 305 306 307 308</p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p><span>301 302 303 304 305 306 307 308 309 310 311 312 313 314 315</span></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td> <p><span>301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 318 319 321 323</span></p> </td> </tr> </tbody> </table> <br/> <strong>3.2 Ympyrään liittyviä pinta-aloja (1 h)</strong></div> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>325 326 327 328 329 330 331</p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p><span>325 326 327 328 329 330 331 332 333 334 336 337 339 342</span></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td><span>325 326 327 328 329 330 331 332 333 334 335 336 337 339 342 344 346</span></td> </tr> </tbody> </table> <br/> <strong>3.3 Ympyrän tangentti (1 h)</strong></div> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>349 350 <b>351</b> 352 <b>353 354</b> 355</p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p><span>349 350 3</span><span>51</span><span> 3</span><span>52</span><span> 3</span><span>53</span><span> 3</span><span>54</span><span> 3</span><span>55 <b>356 357</b> 359 361 <b>362 363</b> 365 366 367</span></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td><span>349 350 3</span><span>51</span><span> 3</span><span>52</span><span> 3</span><span>53</span><span> 3</span><span>54</span><span> 3</span><span>55 356 357 359 361 362 363 365 366 <b>368</b> <b>369</b> 372</span></td> </tr> </tbody> </table> <strong><br/> 4.1 Lieriö (1 h)</strong></div> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p><b>401 402</b> 403 404 <b>405</b> 406 <b>407</b></p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p><span>401 402 403 404 405 406 407 408 409 410 411 412 413 414 416</span></p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td><span>401 402 403 404 405 406 407 408 409 410 411 412 414 415 416 418 421 </span></td> </tr> </tbody> </table> </div> <p><strong>4.2 Kartio (1 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>427 <b>428</b> 429 <b>430</b> 431 <b>432</b> 433 434</p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>427 428 429 430 431 432 433 434 436 437 439 442 443 </p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td>427 428 429 430 431 432 433 434 436 437 439 442 443 443 447 449</td> </tr> </tbody> </table> </div> <p><strong>4.3 Pallo ja tilavuuksien suhde (2 h)</strong></p> <div class="tablewrap"> <table> <tbody> <tr> <td> <p>TASO 1 (AS 5-6)</p> </td> <td> <p>455 456 457 458 459 460 461</p> </td> </tr> <tr> <td> <p>TASO 2 (AS 7-8)</p> </td> <td> <p>455 456 457 458 459 460 461 462 463 464 466 467 468 470 471 </p> </td> </tr> <tr> <td> <p>TASO 3 (AS 9-10)</p> </td> <td>455 456 457 458 459 460 461 462 463 464 466 467 468 470 471 472 479</td> </tr> </tbody> </table> </div> <br/> <div class="tablewrap"> </div> </div> </div> </div> 2023-08-04T19:16:47+03:00