Powtórzenie klasa I – poziom podstawowy i rozszerzony</= title> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"metricconverter"/>  <style>  </style>  </head> <body lang=3DPL style=3D'tab-interval:35.4pt'> <div class=3DSection1> Powtórzenie klasa I = 211; poziom podstawowy i rozszerzony<o:p></o:p> <![if !vml]><img width=3D127 height=3D108 src=3D"powt_pliki/image036.jpg" v:shapes=3D"_x0000= _s1026"><![endif]>= <o:p></o:p> <o:p> </o:p></s= pan> <ol style=3D'margin-top:0cm' start=3D1 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Na rysunku przedstawiony jest zbiór= A – półpłaszczyzna bez brzegu i zbiór B – koło.<o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]>Opisz za pomocą nierówności oba zbiory,<o:p></o:p> <![if !supportLists]>b) </sp= an><![endif]>Wyznacz zbiór A\B</= span>. <o:p></o:p> <![if !supportLists]>2. &n= bsp; <![endif]>Dane s= 1; liczby a =3D 2,(12) i b =3D 0,(15). Oblicz a + b. Wynik przedstaw w postaci ułamka zwykłego.<o:p></o:p> <ol style=3D'margin-top:0cm' start=3D3 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Dane są liczby: <![if !vml]><img width=3D71 height=3D24 src=3D"powt_pliki/image004.gif" v:shapes=3D"_x0000_i1025"><![endif]></= sub> i <sub= ><![if !vml]><img width=3D69 height=3D24 src=3D"powt_pliki/image006.gif" v:shapes=3D"_x0000_i1026"><![endif]></= sub>. Wykonaj działania: <o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]><![if !vml]><img width=3D83 height=3D25 src=3D"powt_pliki/image008.gif" v:shapes=3D"_x0000_i1027"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1027" DrawAspect=3D"Content" ObjectID=3D"_1239435509"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>b) </sp= an><![endif]><![if !vml]><img width=3D33 height=3D21 src=3D"powt_pliki/image010.gif" v:shapes=3D"_x0000_i1028"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1028" DrawAspect=3D"Content" ObjectID=3D"_1239435510"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>c) </spa= n><![endif]><![if !vml]><img width=3D21 height=3D41 src=3D"powt_pliki/image012.gif" v:shapes=3D"_x0000_i1029"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1029" DrawAspect=3D"Content" ObjectID=3D"_1239435511"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>4. &n= bsp; <![endif]>Oceń wartość logiczną zdania i napisz zaprzeczenie:<o:p></o:p></s= pan> <![if !supportLists]>a) &n= bsp; <![endif]><![if !vml]><img width=3D148 height=3D131 src=3D"powt_pliki/image037.jpg"= v:shapes=3D"_x0000_s1027"><![endif]><![if !vml]><img width=3D104 height=3D21 src=3D"powt_pliki/image014.gif" v:shapes=3D"_x0000_i1030"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1030" DrawAspect=3D"Content" ObjectID=3D"_1239435512"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]><![if !vml]><img width=3D104 height=3D24 src=3D"powt_pliki/image018.gif" v:shapes=3D"_x0000_i1031"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1031" DrawAspect=3D"Content" ObjectID=3D"_1239435513"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>c) &n= bsp; <![endif]><![if !vml]><img width=3D153 height=3D25 src=3D"powt_pliki/image020.gif" v:shapes=3D"_x0000_i1032"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1032" DrawAspect=3D"Content" ObjectID=3D"_1239435514"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <ol style=3D'margin-top:0cm' start=3D5 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Na rysunku zaznaczony jest trójk= 61;t.<o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]>*Wykaż, że nie jest on prostokąt= ny.<o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]>Opisz trójkąt za pomocą uk = 2;adu nierówności. <o:p></o:p> <![if !supportLists]>6. &n= bsp; <![endif]>Śrubo= kręt i młotek kosztują tyle samo. Jeśli śrubokręt podrożeje o 5%, a młotek o 3%, to ile procent więcej należy zapłacić za zestaw siedmiu śrubokrętó= ;w i trzech młotków?<o:p></o:p> <![if !supportLists]>7. &n= bsp; <![endif]>Proporcja = liczby chłopców do liczby dziewcząt jest równa 3:4. Jeżeli chłopców jest o 17 więcej niż dziewcz= 1;t, to ile osób liczy ta grupa?<o:p></o:p> <![if !supportLists]>8. &n= bsp; <![endif]>Obwó= ;d czworokąta ABCD opisanego na okręgu jest równy 140. Bok AB jest o 60% krótszy od boku CD. Oblicz długości tych boków.<o:p></o:p> <![if !vml]><img width=3D124 height=3D103 src=3D"powt_pliki/image038.jpg"= v:shapes=3D"_x0000_s1028"><![endif]><o:p></o:p> <![if !supportLists]>9. </spa= n><![endif]>Dany jest wykres pewnej funkcji f(x). Opisz t&#= 281; funkcję za pomocą wzorów, podaj jej dziedzinę i zbiór wartości. <o:p></o:p> <o:p> </o:p>= <o:p> </= o:p> <![if !supportLists]>10. </sp= an><![endif]>Punkty A =3D (1-a, b) i B =3D (-2a, 3a) nale= 80;ą do wykresu funkcji f(x) =3D 2x – 1, x <![if !vml]><img width=3D13 height=3D13 src=3D"powt_pliki/image024.gif" v:shapes=3D"_x0000_i1033"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1033" DrawAspect=3D"Content" ObjectID=3D"_1239435515"> </o:OLEObject> </xml><![endif]-->R. Oblicz współrzędne tych punktó= w.<o:p></o:p> <![if !supportLists]>11. </sp= an><![endif]>Wyznacz zbiór: A =3D {x: x<![if !vml]><img width=3D13 height=3D13 src=3D"powt_pliki/image024.gif" v:shapes=3D"_x0000_i1034"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1034" DrawAspect=3D"Content" ObjectID=3D"_1239435517"> </o:OLEObject> </xml><![endif]-->R i x – 3 < 2x – 1 < x2}<o:p= ></o:p> <ol style=3D'margin-top:0cm' start=3D12 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'> </s= pan><o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]>*Udowodnij, że suma dowolnej liczby całkowitej i jej kwadratu jest parzysta.<o:p></o:p> <![if !supportLists]>b) </sp= an><![endif]>Uzasadnij, ze wyrażenie <![if !vml]><img width=3D75 height=3D41 src=3D"powt_pliki/image039.gif" v:shapes=3D"_x0000_i1035"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1035" DrawAspect=3D"Content" ObjectID=3D"_1239435518"> </o:OLEObject> </xml><![endif]--> przyjmuje t= ylko wartości dodatnie.<o:p></o:p> <ol style=3D'margin-top:0cm' start=3D13 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Oblicz obwód figury opisanej uk = 2;adem nierówności: <![if !vml]><img width=3D99 height=3D75 src=3D"powt_pliki/image040.gif" v:shapes=3D"_x0000_i1036"><![endif]></= sub>.<o:p></o:p></li> </ol> <![if !supportLists]>14. </sp= an><![endif]>Narysuj wykresy funkcji: f(x) =3D x2= – 2x – 3 i g(x) =3D x + <st1:metricconverter ProductID=3D"1, a" w:st=3D= "on">1, a</st1:metricconverter> następnie wyznacz zbiór argumentów x, dla których obie funkcje przyjmują wartości dodatnie.<o:p></o:p> <![if !supportLists]>15. </sp= an><![endif]>Wyznacz współczynniki trójmi= anu kwadratowego y =3D ax2 + bx + wiedz&= #261;c, że miejscem zerowym jest 3 i dla x =3D 1 przyjmuje maksimum równe 12.<o:p></o:p> <ol style=3D'margin-top:0cm' start=3D16 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'> </s= pan><o:p></o:p></li> </ol> <![if !supportLists]>a) &n= bsp; <![endif]>*Wykaż, że jeśli trójk= 61;t ma oś symetrii, to jest równoramienny.<o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]>Udowodnij, że jeżeli ramię trape= zu równoramiennego, w który można wpisać okrąg ma długość m, to obwód trapezu jest równy 4m.<o:p= ></o:p> <![if !supportLists]>c) &n= bsp; <![endif]>Sprawd%= 8;, czy istnieje wielokąt, który ma tyle samo boków, co = ;przekątnych.<o:p></o:p> <![if !supportLists]>17. </sp= an><![endif]>W kwadracie ABCD dany jest wierzchołek A(1= , 0) i wektor <![if !vml]><img width=3D28 height=3D29 src=3D"powt_pliki/image041.gif" v:shapes=3D"_x0000_i1037"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1037" DrawAspect=3D"Content" ObjectID=3D"_1239435520"> </o:OLEObject> </xml><![endif]-->=3D [2, 6]. Wyznacz równania prostych zawieraj= 1;cych boki kwadratu.<o:p></o:p> <![if !supportLists]>18. </sp= an><![endif]>Wyznacz wartości <![if !vml]><img width=3D101 height=3D24 src=3D"powt_pliki/image042.gif" v:shapes=3D"_x0000_i1038"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1038" DrawAspect=3D"Content" ObjectID=3D"_1239435521"> </o:OLEObject> </xml><![endif]-->, dla których zachodzi równość: 2= cosx =3D -1.<o:p></o:p> <![if !supportLists]>19. </sp= an><![endif]>Dane są wierzchołki trójką= ;ta ABC: A =3D (1, 4), B =3D (0, -1), C =3D (2, -4). Punkty K =3D (-3, 2), L =3D (-9, -2), M =3D (-3, -4) są wierzchołkami trójkąta KLM. Sprawdź, czy trójkąty są podobne. Uzasadnij odpowiedź.<o:p></o:p><= /span> <ol style=3D'margin-top:0cm' start=3D20 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'> </s= pan><o:p></o:p></li> </ol> <![if !supportLists]>a) &n= bsp; <![endif]>Określ położenie okręg&oacu= te;w O1(A, r1), O2(B, r2) wiedząc, że = <![if !vml]><img width=3D31 height=3D27 src=3D"powt_pliki/image043.gif" v:shapes=3D"_x0000_i1039"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1039" DrawAspect=3D"Content" ObjectID=3D"_1239435522"> </o:OLEObject> </xml><![endif]-->=3D22, r1 =3D 15, r2 =3D 8.<o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]>Określ wzajemne położenie proste= j 2x – y =3D 5 i okręgu x2 + y2 =3D 5.<o:p></o:= p> <![if !supportLists]>21. </sp= an><![endif]>*Dany jest okrąg o równaniu x2= + y2 + 4x – 5 =3D 0. Wyznacz odległość punk= tu B =3D (2, 7) od okręgu.<o:p></o:p> <![if !supportLists]>22. </sp= an><![endif]>Różnica między długoś= ;ciami dłuższej i krótszej przekątnej sześciokąta foremnego jest równa d. Oblicz pole tego sześciokąta.<o:p>= </o:p> <![if !supportLists]>23. </sp= an><![endif]>Prosta 2x – y + 3 =3D 0 przecina parabol&= #281; y =3D 2x2 – 4x + 3 w punktach A i B. Wyznacz współrzędne tych punktów i narysuj w układzie współrzędnych wykresy funkcji.<o:p></o:p> <o:p> </o:p></s= pan> <o:p> </o:p> <o:p> </o:p> </div> </body> </html> ------=_NextPart_01C78B15.9FEA8770 Content-Location: file:///C:/2689CB54/powt_pliki/image036.jpg Content-Transfer-Encoding: base64 Content-Type: image/jpeg /9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIf IiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/wAALCABsAH8BAREA/8QAHwAAAQUBAQEB AQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1Fh ByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZ WmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXG x8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/9oACAEBAAA/APZaKKKKyPFHiO18K6FN q92jSRxMq+WhG5iWAwM/ifwrM+Isb3Xge7ERuAzBSPJdlIBPJIXlgASxAz06VB4FnOq32t6zFdTT 2EtwttYmR2IMcShSwBOOWzzjJxzXY0UUUUUUUUUVFc3MNpbvcTuEiQZZiOlUPEWtr4e0sahLCZYV 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MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C78B15.9FEA8770" Ten dokument to jednoplikowa strona sieci Web nazywana również plikiem archiwum sieci Web. Jeżeli widzisz ten komunikat, przeglądarka lub edytor nie obsługują plików archiwum sieci Web. Pobierz przeglądarkę obsługującą archiwa sieci Web, na przykład przeglądarkę Microsoft Internet Explorer. ------=_NextPart_01C78B15.9FEA8770 Content-Location: file:///C:/2689CB54/powt.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Powtórzenie klasa I – poziom podstawowy i rozszerzony</= title> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"metricconverter"/>  <style>  </style>  </head> <body lang=3DPL style=3D'tab-interval:35.4pt'> <div class=3DSection1> Powtórzenie klasa I = 211; poziom podstawowy i rozszerzony<o:p></o:p> <![if !vml]><img width=3D127 height=3D108 src=3D"powt_pliki/image036.jpg" v:shapes=3D"_x0000= _s1026"><![endif]>= <o:p></o:p> <o:p> </o:p></s= pan> <ol style=3D'margin-top:0cm' start=3D1 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Na rysunku przedstawiony jest zbiór= A – półpłaszczyzna bez brzegu i zbiór B – koło.<o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]>Opisz za pomocą nierówności oba zbiory,<o:p></o:p> <![if !supportLists]>b) </sp= an><![endif]>Wyznacz zbiór A\B</= span>. <o:p></o:p> <![if !supportLists]>2. &n= bsp; <![endif]>Dane s= 1; liczby a =3D 2,(12) i b =3D 0,(15). Oblicz a + b. Wynik przedstaw w postaci ułamka zwykłego.<o:p></o:p> <ol style=3D'margin-top:0cm' start=3D3 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Dane są liczby: <![if !vml]><img width=3D71 height=3D24 src=3D"powt_pliki/image004.gif" v:shapes=3D"_x0000_i1025"><![endif]></= sub> i <sub= ><![if !vml]><img width=3D69 height=3D24 src=3D"powt_pliki/image006.gif" v:shapes=3D"_x0000_i1026"><![endif]></= sub>. Wykonaj działania: <o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]><![if !vml]><img width=3D83 height=3D25 src=3D"powt_pliki/image008.gif" v:shapes=3D"_x0000_i1027"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1027" DrawAspect=3D"Content" ObjectID=3D"_1239435509"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>b) </sp= an><![endif]><![if !vml]><img width=3D33 height=3D21 src=3D"powt_pliki/image010.gif" v:shapes=3D"_x0000_i1028"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1028" DrawAspect=3D"Content" ObjectID=3D"_1239435510"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>c) </spa= n><![endif]><![if !vml]><img width=3D21 height=3D41 src=3D"powt_pliki/image012.gif" v:shapes=3D"_x0000_i1029"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1029" DrawAspect=3D"Content" ObjectID=3D"_1239435511"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>4. &n= bsp; <![endif]>Oceń wartość logiczną zdania i napisz zaprzeczenie:<o:p></o:p></s= pan> <![if !supportLists]>a) &n= bsp; <![endif]><![if !vml]><img width=3D148 height=3D131 src=3D"powt_pliki/image037.jpg"= v:shapes=3D"_x0000_s1027"><![endif]><![if !vml]><img width=3D104 height=3D21 src=3D"powt_pliki/image014.gif" v:shapes=3D"_x0000_i1030"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1030" DrawAspect=3D"Content" ObjectID=3D"_1239435512"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]><![if !vml]><img width=3D104 height=3D24 src=3D"powt_pliki/image018.gif" v:shapes=3D"_x0000_i1031"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1031" DrawAspect=3D"Content" ObjectID=3D"_1239435513"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <![if !supportLists]>c) &n= bsp; <![endif]><![if !vml]><img width=3D153 height=3D25 src=3D"powt_pliki/image020.gif" v:shapes=3D"_x0000_i1032"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1032" DrawAspect=3D"Content" ObjectID=3D"_1239435514"> </o:OLEObject> </xml><![endif]--><o:p></o:p> <ol style=3D'margin-top:0cm' start=3D5 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Na rysunku zaznaczony jest trójk= 61;t.<o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]>*Wykaż, że nie jest on prostokąt= ny.<o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]>Opisz trójkąt za pomocą uk = 2;adu nierówności. <o:p></o:p> <![if !supportLists]>6. &n= bsp; <![endif]>Śrubo= kręt i młotek kosztują tyle samo. Jeśli śrubokręt podrożeje o 5%, a młotek o 3%, to ile procent więcej należy zapłacić za zestaw siedmiu śrubokrętó= ;w i trzech młotków?<o:p></o:p> <![if !supportLists]>7. &n= bsp; <![endif]>Proporcja = liczby chłopców do liczby dziewcząt jest równa 3:4. Jeżeli chłopców jest o 17 więcej niż dziewcz= 1;t, to ile osób liczy ta grupa?<o:p></o:p> <![if !supportLists]>8. &n= bsp; <![endif]>Obwó= ;d czworokąta ABCD opisanego na okręgu jest równy 140. Bok AB jest o 60% krótszy od boku CD. Oblicz długości tych boków.<o:p></o:p> <![if !vml]><img width=3D124 height=3D103 src=3D"powt_pliki/image038.jpg"= v:shapes=3D"_x0000_s1028"><![endif]><o:p></o:p> <![if !supportLists]>9. </spa= n><![endif]>Dany jest wykres pewnej funkcji f(x). Opisz t&#= 281; funkcję za pomocą wzorów, podaj jej dziedzinę i zbiór wartości. <o:p></o:p> <o:p> </o:p>= <o:p> </= o:p> <![if !supportLists]>10. </sp= an><![endif]>Punkty A =3D (1-a, b) i B =3D (-2a, 3a) nale= 80;ą do wykresu funkcji f(x) =3D 2x – 1, x <![if !vml]><img width=3D13 height=3D13 src=3D"powt_pliki/image024.gif" v:shapes=3D"_x0000_i1033"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1033" DrawAspect=3D"Content" ObjectID=3D"_1239435515"> </o:OLEObject> </xml><![endif]-->R. Oblicz współrzędne tych punktó= w.<o:p></o:p> <![if !supportLists]>11. </sp= an><![endif]>Wyznacz zbiór: A =3D {x: x<![if !vml]><img width=3D13 height=3D13 src=3D"powt_pliki/image024.gif" v:shapes=3D"_x0000_i1034"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1034" DrawAspect=3D"Content" ObjectID=3D"_1239435517"> </o:OLEObject> </xml><![endif]-->R i x – 3 < 2x – 1 < x2}<o:p= ></o:p> <ol style=3D'margin-top:0cm' start=3D12 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'> </s= pan><o:p></o:p></li> </ol> <![if !supportLists]>a) </sp= an><![endif]>*Udowodnij, że suma dowolnej liczby całkowitej i jej kwadratu jest parzysta.<o:p></o:p> <![if !supportLists]>b) </sp= an><![endif]>Uzasadnij, ze wyrażenie <![if !vml]><img width=3D75 height=3D41 src=3D"powt_pliki/image039.gif" v:shapes=3D"_x0000_i1035"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1035" DrawAspect=3D"Content" ObjectID=3D"_1239435518"> </o:OLEObject> </xml><![endif]--> przyjmuje t= ylko wartości dodatnie.<o:p></o:p> <ol style=3D'margin-top:0cm' start=3D13 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'>Oblicz obwód figury opisanej uk = 2;adem nierówności: <![if !vml]><img width=3D99 height=3D75 src=3D"powt_pliki/image040.gif" v:shapes=3D"_x0000_i1036"><![endif]></= sub>.<o:p></o:p></li> </ol> <![if !supportLists]>14. </sp= an><![endif]>Narysuj wykresy funkcji: f(x) =3D x2= – 2x – 3 i g(x) =3D x + <st1:metricconverter ProductID=3D"1, a" w:st=3D= "on">1, a</st1:metricconverter> następnie wyznacz zbiór argumentów x, dla których obie funkcje przyjmują wartości dodatnie.<o:p></o:p> <![if !supportLists]>15. </sp= an><![endif]>Wyznacz współczynniki trójmi= anu kwadratowego y =3D ax2 + bx + wiedz&= #261;c, że miejscem zerowym jest 3 i dla x =3D 1 przyjmuje maksimum równe 12.<o:p></o:p> <ol style=3D'margin-top:0cm' start=3D16 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'> </s= pan><o:p></o:p></li> </ol> <![if !supportLists]>a) &n= bsp; <![endif]>*Wykaż, że jeśli trójk= 61;t ma oś symetrii, to jest równoramienny.<o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]>Udowodnij, że jeżeli ramię trape= zu równoramiennego, w który można wpisać okrąg ma długość m, to obwód trapezu jest równy 4m.<o:p= ></o:p> <![if !supportLists]>c) &n= bsp; <![endif]>Sprawd%= 8;, czy istnieje wielokąt, który ma tyle samo boków, co = ;przekątnych.<o:p></o:p> <![if !supportLists]>17. </sp= an><![endif]>W kwadracie ABCD dany jest wierzchołek A(1= , 0) i wektor <![if !vml]><img width=3D28 height=3D29 src=3D"powt_pliki/image041.gif" v:shapes=3D"_x0000_i1037"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1037" DrawAspect=3D"Content" ObjectID=3D"_1239435520"> </o:OLEObject> </xml><![endif]-->=3D [2, 6]. Wyznacz równania prostych zawieraj= 1;cych boki kwadratu.<o:p></o:p> <![if !supportLists]>18. </sp= an><![endif]>Wyznacz wartości <![if !vml]><img width=3D101 height=3D24 src=3D"powt_pliki/image042.gif" v:shapes=3D"_x0000_i1038"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1038" DrawAspect=3D"Content" ObjectID=3D"_1239435521"> </o:OLEObject> </xml><![endif]-->, dla których zachodzi równość: 2= cosx =3D -1.<o:p></o:p> <![if !supportLists]>19. </sp= an><![endif]>Dane są wierzchołki trójką= ;ta ABC: A =3D (1, 4), B =3D (0, -1), C =3D (2, -4). Punkty K =3D (-3, 2), L =3D (-9, -2), M =3D (-3, -4) są wierzchołkami trójkąta KLM. Sprawdź, czy trójkąty są podobne. Uzasadnij odpowiedź.<o:p></o:p><= /span> <ol style=3D'margin-top:0cm' start=3D20 type=3D1> <li class=3DMsoNormal style=3D'mso-list:l2 level1 lfo1;tab-stops:list 36.0= pt'> </s= pan><o:p></o:p></li> </ol> <![if !supportLists]>a) &n= bsp; <![endif]>Określ położenie okręg&oacu= te;w O1(A, r1), O2(B, r2) wiedząc, że = <![if !vml]><img width=3D31 height=3D27 src=3D"powt_pliki/image043.gif" v:shapes=3D"_x0000_i1039"><![endif]><= !--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1039" DrawAspect=3D"Content" ObjectID=3D"_1239435522"> </o:OLEObject> </xml><![endif]-->=3D22, r1 =3D 15, r2 =3D 8.<o:p></o:p> <![if !supportLists]>b) &n= bsp; <![endif]>Określ wzajemne położenie proste= j 2x – y =3D 5 i okręgu x2 + y2 =3D 5.<o:p></o:= p> <![if !supportLists]>21. </sp= an><![endif]>*Dany jest okrąg o równaniu x2= + y2 + 4x – 5 =3D 0. Wyznacz odległość punk= tu B =3D (2, 7) od okręgu.<o:p></o:p> <![if !supportLists]>22. </sp= an><![endif]>Różnica między długoś= ;ciami dłuższej i krótszej przekątnej sześciokąta foremnego jest równa d. Oblicz pole tego sześciokąta.<o:p>= </o:p> <![if !supportLists]>23. </sp= an><![endif]>Prosta 2x – y + 3 =3D 0 przecina parabol&= #281; y =3D 2x2 – 4x + 3 w punktach A i B. 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