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2011年臺(tái)灣省大學(xué)入學(xué)學(xué)科能力測(cè)驗(yàn)考試數(shù)學(xué)試卷

發(fā)布:2024/4/20 14:35:0

一、解答題(共13小題,滿分0分)

  • 1.有一箱子,內(nèi)有3黑球與2白球.有一游戲,從箱子中任取出一球.假設(shè)每一顆球被取出的機(jī)率都相同,若取出黑球可得獎(jiǎng)金50元,而取出白球可得獎(jiǎng)金100元,則下列哪一個(gè)選項(xiàng)是此游戲的獎(jiǎng)金期望值?
    (1)70元  (2)75元  (3)80元  (4)85元  (5)90元.

    組卷:50引用:1難度:0.9
  • 2.多項(xiàng)式4(x2+1)+(x+1)2(x-3)+(x-1)3等于下列哪一個(gè)選項(xiàng)?
    (1)x(x+1)2(2)2x(x-1)2(3)x(x-1)(x+1)
    (4)2(x-1)2(x+1)(5)2x(x-1)(x+1)

    組卷:28引用:1難度:0.9
  • 3.設(shè)
    a
    n
    +
    1
    2
    =
    1
    10
    a
    n
    2
    ,n為正整數(shù),且知an皆為正.令bn=lgan,則數(shù)列b1,b2,b3,…為
    (1)公差為正的等差數(shù)列
    (2)公差為負(fù)的等差數(shù)列
    (3)公比為正的等比數(shù)列
    (4)公比為負(fù)的等比數(shù)列
    (5)既非等差亦非等比數(shù)列.

    組卷:93引用:1難度:0.5
  • 4.坐標(biāo)平面上滿足方程式
    x
    2
    5
    2
    +
    y
    2
    4
    2
    x
    2
    3
    2
    -
    y
    2
    4
    2
    =
    0
    的點(diǎn)(x,y)所構(gòu)成的圖形為
    (1)只有原點(diǎn)
    (2)橢圓及原點(diǎn)
    (3)兩條相異直線
    (4)橢圓及雙曲線
    (5)雙曲線及原點(diǎn).

    組卷:167引用:1難度:0.9
  • 5.請(qǐng)問(wèn)下面哪一個(gè)選項(xiàng)是正確的?
    (1)37<73
    (2)510<105
    (3)2100<1030
    (4)log23=1.5
    (5)log211<3.5.

    組卷:129引用:1難度:0.7
  • 6.根據(jù)臺(tái)灣壽險(xiǎn)業(yè)的資料,男性從0歲、1歲、…到60歲各年齡層的死亡率
    (單位:%)依序?yàn)?br />1.0250,0.2350,0.1520,0.1010,0.0720,0.0590,0.0550,0.0540,0.0540,0.0520,
    0.0490,0.0470,0.0490,0.0560,0.0759,0.1029,0.1394,0.1890,0.2034,0.2123,
    0.2164,0.2166,0.2137,0.2085,0.2019,0.1948,0.1882,0.1830,0.1799,0.1793,
    0.1813,0.1862,0.1941,0.2051,0.2190,0.2354,0.2539,0.2742,0.2961,0.3202,
    0.3472,0.3779,0.4129,0.4527,0.4962,0.5420,0.5886,0.6346,0.6791,0.7239,
    0.7711,0.8229,0.8817,0.9493,1.0268,1.1148,1.2139,1.3250,1.4485,1.5851,
    1.7353.
    經(jīng)初步整理后,已知61個(gè)資料中共有24個(gè)資料小于0.2.請(qǐng)問(wèn)死亡率資料的中位數(shù)為下列哪一個(gè)選項(xiàng)?
    (1)0.2034   (2)0.2164   (3)0.2137   (4)0.2085   (5)0.2019.

    組卷:60引用:1難度:0.7

二、填空題(共7小題,每小題3分,滿分21分)

  • 19.設(shè)E1
    x
    2
    a
    2
    +
    y
    2
    b
    2
    =
    1
    (其中a>0)為焦點(diǎn)在(3,0),(-3,0)的橢圓;E2:焦點(diǎn)在(3,0)且準(zhǔn)線為x=-3的拋物線.已知E1,E2的交點(diǎn)在直線x=3上,則a=

    組卷:400引用:1難度:0.5
  • 20.H:x-y+z=2為坐標(biāo)空間中一平面,L為平面H上的一直線.已知點(diǎn)P(2,1,1)為L(zhǎng)上距離原點(diǎn)O最近的點(diǎn),則
    為L(zhǎng)的方向向量.

    組卷:464引用:1難度:0.5
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