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9.4E: Mazoezi

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    176543

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    Mazoezi hufanya kamili

    Mazoezi 1 - 32: Tatua Ulinganifu wa Quadratic Kutumia Mfumo wa Quadratic

    Katika mazoezi yafuatayo, tatua kwa kutumia Mfumo wa Quadratic.

    1. \(4 m^{2}+m-3=0\)

    2. \(4 n^{2}-9 n+5=0\)

    3. \(2 p^{2}-7 p+3=0\)

    4. \(3 q^{2}+8 q-3=0\)

    5. \(p^{2}+7 p+12=0\)

    6. \(q^{2}+3 q-18=0\)

    7. \(r^{2}-8 r=33\)

    8. \(t^{2}+13 t=-40\)

    9. \(3 u^{2}+7 u-2=0\)

    10. \(2 p^{2}+8 p+5=0\)

    11. \(2 a^{2}-6 a+3=0\)

    12. \(5 b^{2}+2 b-4=0\)

    13. \(x^{2}+8 x-4=0\)

    14. \(y^{2}+4 y-4=0\)

    15. \(3 y^{2}+5 y-2=0\)

    16. \(6 x^{2}+2 x-20=0\)

    17. \(2 x^{2}+3 x+3=0\)

    18. \(2 x^{2}-x+1=0\)

    19. \(8 x^{2}-6 x+2=0\)

    20. \(8 x^{2}-4 x+1=0\)

    21. \((v+1)(v-5)-4=0\)

    22. \((x+1)(x-3)=2\)

    23. \((y+4)(y-7)=18\)

    24. \((x+2)(x+6)=21\)

    25. \(\dfrac{1}{4} m^{2}+\dfrac{1}{12} m=\dfrac{1}{3}\)

    26. \(\dfrac{1}{3} n^{2}+n=-\dfrac{1}{2}\)

    27. \(\dfrac{3}{4} b^{2}+\dfrac{1}{2} b=\dfrac{3}{8}\)

    28. \(\dfrac{1}{9} c^{2}+\dfrac{2}{3} c=3\)

    29. \(16 c^{2}+24 c+9=0\)

    30. \(25 d^{2}-60 d+36=0\)

    31. \(25 q^{2}+30 q+9=0\)

    32. \(16 y^{2}+8 y+1=0\)

    Jibu

    1. \(m=-1, m=\dfrac{3}{4}\)

    3. \(p=\dfrac{1}{3}, p=2\)

    5. \(p=-4, p=-3\)

    7. \(r=-3, r=11\)

    9. \(u=\dfrac{-7 \pm \sqrt{73}}{6}\)

    11. \(a=\dfrac{3 \pm \sqrt{3}}{2}\)

    13. \(x=-4 \pm 2 \sqrt{5}\)

    15. \(y=-\dfrac{2}{3}, y=-1\)

    17. \(x=-\dfrac{3}{4} \pm \dfrac{\sqrt{15}}{4} i\)

    19. \(x=\dfrac{3}{8} \pm \dfrac{\sqrt{7}}{8} i\)

    21. \(v=2 \pm 2 \sqrt{2}\)

    23. \(y=-4, y=7\)

    25. \(m=1, m=\dfrac{-4}{3}\)

    27. \(b=\dfrac{-2 \pm \sqrt{22}}{6}\)

    29. \(c=-\dfrac{3}{4}\)

    31. \(q=-\dfrac{3}{5}\)

    Mazoezi 33 - 36 Tumia Ubaguzi kutabiri Idadi ya Ufumbuzi halisi wa Equation ya Quadratic

    Katika mazoezi yafuatayo, tambua idadi ya ufumbuzi halisi kwa kila equation ya quadratic.

      1. \(4 x^{2}-5 x+16=0\)
      2. \(36 y^{2}+36 y+9=0\)
      3. \(6 m^{2}+3 m-5=0\)
      1. \(9 v^{2}-15 v+25=0\)
      2. \(100 w^{2}+60 w+9=0\)
      3. \(5 c^{2}+7 c-10=0\)
      1. \(r^{2}+12 r+36=0\)
      2. \(8 t^{2}-11 t+5=0\)
      3. \(3 v^{2}-5 v-1=0\)
      1. \(25 p^{2}+10 p+1=0\)
      2. \(7 q^{2}-3 q-6=0\)
      3. \(7 y^{2}+2 y+8=0\)
    Jibu

    33. a. hakuna ufumbuzi halisi b.\(1\) c.\(2\)

    35. a.\(1\) b. hakuna ufumbuzi halisi c.\(2\)

    Mazoezi 37 - 40: Tambua Njia sahihi zaidi ya Kutumia Kutatua Equation ya Quadratic

    Katika mazoezi yafuatayo, kutambua njia sahihi zaidi (Factoring, Square Root, au Quadratic Formula) kutumia kutatua kila equation quadratic. Je, si kutatua.

      1. \(x^{2}-5 x-24=0\)
      2. \((y+5)^{2}=12\)
      3. \(14 m^{2}+3 m=11\)
      1. \((8 v+3)^{2}=81\)
      2. \(w^{2}-9 w-22=0\)
      3. \(4 n^{2}-10=6\)
      1. \(6 a^{2}+14=20\)
      2. \(\left(x-\dfrac{1}{4}\right)^{2}=\dfrac{5}{16}\)
      3. \(y^{2}-2 y=8\)
      1. \(8 b^{2}+15 b=4\)
      2. \(\dfrac{5}{9} v^{2}-\dfrac{2}{3} v=1\)
      3. \(\left(w+\dfrac{4}{3}\right)^{2}=\dfrac{2}{9}\)
    Jibu

    Kipengele cha Mizizi ya mraba c Mfumo wa Quadratic

    39. a Mfumo wa Quadratic b Mizizi ya mraba c. sababu

    Mazoezi 41 - 42: Mazoezi ya kuandika
    1. Kutatua equation\(x^{2}+10 x=120\)
      1. kwa kukamilisha mraba
      2. kutumia Mfumo wa Quadratic
      3. Ni njia ipi unayopendelea? Kwa nini?
    2. Kutatua equation\(12 y^{2}+23 y=24\)
      1. kwa kukamilisha mraba
      2. kutumia Mfumo wa Quadratic
      3. Ni njia ipi unayopendelea? Kwa nini?
    Jibu

    41. Majibu yatatofautiana

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali hili linatoa orodha ya kutathmini ustadi wa malengo ya sehemu hii. Chagua jinsi gani unaweza kujibu kauli â € naweza kutatua equations quadratic kwa kutumia formula quadratic. € € â € kwa ujasiri, â € â € â € € € au â € hakuna, Mimi donâ €™ t kupata hiyo.â € Chagua jinsi gani unaweza kujibu kauli â € naweza kutumia ubaguzi kutabiri idadi ya ufumbuzi wa quadratic equation.â € € kwa ujasiri, â € € â € € na baadhi ya msaada, â € au †â hakuna, mimi donâ €™ t kupata hivyo.â € Chagua jinsi gani unaweza kujibu kauli â € naweza kutambua njia sahihi zaidi ya kutumia kutatua equadratic equation.â € € â € kwa ujasiri, â € â € â € â € â € kwa msaada fulani, â € au â € no, mimi donâ €™ Ili kupata hiyo.â €
    Kielelezo 9.3.87

    b Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?