數學 必修部分 試卷二 樣本試卷 - hkeaa.edu.hk · pdf file香港考試及評核局...

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數學 必修部分 試卷二 ( 樣本試卷 ) 考試時間:一小時十五分鐘 (一) 細讀答題紙上的指示,並於適當位置貼上電腦條碼及填上各項所需資料。 (二) 試場主任宣布開卷後,考生須檢查試題有否缺漏,最後一題之後應有「 試卷完」字樣。 (三) 本試卷各題佔分相等。 (四) 本試卷全部試題均須回答 為便於修正答案,考生宜用 HB 鉛筆把答案填畫在答題紙上。 錯誤答案可用潔淨膠擦將筆痕徹底擦去。 (五) 每題只可填畫 一個答案,若填畫多個答案,則該題 不給分(六) 答案錯誤,不另扣分。 考試結束前不可 將試卷攜離試場 HKDSE-MATH-CP 2 – 1 (樣本試卷) 33

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  • ()

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    HKDSE-MATH-CP 2 1 ( ) 33

  • 30 15

    31. (3a)2 a =

    A. 3a5

    B. 6a6

    C. 9a5

    D. 9a6

    2. 5 3m = 2n m =

    A. n

    B. 2n 3 5

    C. 2n3 + 5

    D. 2n3 +15

    2 23. a b + 2b 1 =

    A. (a b 1)(a + b 1)

    B. (a b 1)(a + b +1)

    C. (a b +1)(a + b 1)

    D. (a b +1)(a b 1)

    HKDSE-MATH-CP 2 2 () 34

  • 4. p q

    A. 25

    B. 10

    C. 3

    D. 5

    5)2)((5)(2 ++++ xxqp xx q =

    5. 372f ( ) 23 ++= xxxx

    A. 3

    B. 5

    C. 17

    D. 33

    f ( )x x + 2

    6. a )(1))(( axaxax =

    A. +1= ax

    B. + 2= ax

    C. ax = +1= ax

    D. ax = + 2= ax

    7. k

    A. k < 7

    B. k > 7

    C. k < 11

    D. k > 11

    kxx = 262

    HKDSE-MATH-CP 2 3 () 35

  • 8. y = f (x) L A(1, k) B(7 , k)

    I. f (x) > k x < 1 x > 7 II. f (x) = k 1 7 III. y = f (x) x = 3

    A. I II y

    B. I III

    y = f (x) C. II III

    D. I II III LA B

    xO

    9. 325 x +

    A. x > 2

    B. x > 1

    C. x > 1

    D. 12

  • 11. an n a1 = 4 a2 = 5 n an+2 = an + an+1 =a10

    A. 13

    B. 157

    C. 254

    D. 411

    12. 20% x% 50% x =

    A. 20

    B. 25

    C. 30

    D. 35

    13. x y z 2x = 3y x = 2z (x + z) : (x + y) =

    A. 3 : 5

    B. 6 : 7

    C. 9 : 7

    D. 9 :10

    14. z x y x = 3 y = 4 z =18 x = 2 z = 8 y =

    A. 1

    B. 3

    C. 6

    D. 9

    HKDSE-MATH-CP 2 5 () 37

  • 15. 15 cm 24 cm 25 cm cm 0.1%

    A. 0.8%

    B. 2.3%

    C. 4.7%

    D. 6.3%

    16. O C D OBC BAD OC = 20 cm

    OA = AB = 10 cm BCD cm2

    2 D A. 214 cm

    2 B. 230 cm

    2 C. 246 cm

    2 D. 270 cm

    C B

    AO

    17. a cm2 b cm2 c cm2

    r

    r 2

    r

    r

    A. a < b < c

    B. a < c < b

    C. c < a < b

    D. c < b < a

    2r

    r

    HKDSE-MATH-CP 2 6 () 38

  • C

    18. ABCD T AB DT AB CD = 9 cm AT :TB = 1: 2 ABCD 36 cm2 ABCD

    A. 26 cm D

    B. 28 cm

    C. 30 cm A B

    D. 32 cm T

    sin cos(270 )19. + = cos 60 tan 45

    A. sin

    B. 3sin

    C. 2sin cos

    D. 2sin + cos

    20. AB =1 cm BC = CD = DE = 2 cm EF = 3 cm A F 0.1 cm

    A. 7.2 cm A B

    B. 7.4 cm

    DC C. 8.0 cm

    D. 8.1 cm E F

    21. ABCD BC = CD ADC =

    A. 118

    B. 121

    C. 124

    D. 126

    A

    D 28

    B

    HKDSE-MATH-CP 2 7 () 39

    C

  • 22. O ABCDE ABE = 30 CDE = 105 AOC =

    A. 120

    24. ABC BD = CD

    A. 8 cm

    B. 13 cm

    C. 14 cm

    D. 15 cm

    C A

    AD BF CD

    cm10=BA BC cm

    2040

    D

    O

    105

    C A

    E D

    B

    30

    A D

    CB

    E

    F

    B

    B. 135

    C. 150

    D. 165

    23. ABCD F E CD : DE = 2 :1 AF : BC =

    A. 1: 2

    B. 2 : 3

    C. 3 : 4

    D. 8 : 9

    HKDSE-MATH-CP 2 8 () 40

  • 25.

    A.

    B.

    C.

    D.

    26. ( 4,3) 180

    A. (3, 4)

    B. (3 , 4)

    C. (4, 3)

    D. (4 , 3)

    27.

    30 40 50 60 70 80 90

    50

    A. 25%

    B. 50%

    C. 70%

    D. 75%

    HKDSE-MATH-CP 2 9 () 41

  • 28. 23 cm

    15 3 3 4 5 6 7 9 16 1 2 2 3 5 6 6 8 17 1 2 6 7 9 18 2 6 7

    A. 164 cm

    B. 165 cm

    C. 165.5 cm

    D. 166 cm

    29. { a 7 , a 1 , a , a + 2 , a + 4 , a + 8 } { a 9 , a 2 , a 1 , a + 3 , a + 4 , a + 6 }

    I. II. III.

    A. I

    B. II

    C. I III

    D. II III

    30. 950

    I. II. III.

    A. I II

    B. I III

    C. II III

    D. I II III

    HKDSE-MATH-CP 2 10 () 42

  • 1 x 131. + = 2 x (x 2)2

    A. (2 3

    x)2

    B. (2

    1 x)2

    C. (22 x

    x

    )32

    +

    D. (22x x)3

    2

    32. x log5 y y = abx a =

    A. 1 log5 y

    B. 2

    C. 52

    D. 25

    O x

    33. 10100100010012 =

    A. 212 + 210 +137

    B. 212 + 210 + 273

    C. 213 + 211 +137

    D. 213 + 211 + 273

    34. k 4k 6 + ki = i

    A. 3k + 6i

    B. 3k 6i

    C. 5k + 6i

    D. 5k 6i

    HKDSE-MATH-CP 2 11 () 43

  • 0 x 6 35.

    0 y 3 x 2y

    A. OAC y

    B. OBD F D3 C. OCE

    2 E D. ODF

    1

    B xO 1 2 3 4 5 6

    A

    C

    36. 3 6 18 6 2

    A. 8

    B. 10

    C. 26

    D. 34

    37. y = f (x) y = g(x)

    A. g(x) = f (x 2) 3 y

    B. g(x) = f (x 2) + 3 y = f (x)

    C. g(x) = f (x + 2) 3 y = g(x)

    xO D. g(x) = f (x + 2) + 3

    (2, 3)

    38. y =

    A. x sin 77 sin 56

    x sin 47 B. sin 56

    56

    47

    y x

    C. x sin 56 sin 77

    x sin 77 D. sin 47

    HKDSE-MATH-CP 2 12 () 44

  • 39. $P 6% $10 000 P

    A. 806.63

    B. 829.19

    C. 833.33

    D. 882.18

    40. ABCDEFGH ACE ABCD tan =

    E H A. 2

    B. 3 F

    6 cm2

    C. 5 2

    C

    D. 125

    A

    G

    D

    3 cm

    B4 cm

    41. A B C TA A CBT TA BC = 6 cm 0.1 cm

    T A. 3.2 cm

    20

    B

    B. 3.9 cm

    A C C. 4.2 cm

    D. 4.7 cm

    42. a 90 < b < 90 y = a cos(x + b)

    A. a = 3 b = 40 y

    3

    B. a = 3 b = 40

    C. a = 3 b = 40 O x140

    D. a = 3 b = 40

    HKDSE-MATH-CP 2 13 () 45

  • 43. A 2 3 4 B 2 3 4

    A. 13 81

    29 B. 81

    C. 52 81

    D. 68 81

    44. 2 5

    1 A. 7

    2 B. 7

    6 C. 7

    1 D. 21

    45. 32 27 25 3

    A. 64 60 50

    B. 70 60 100

    C. 70 54 50

    D. 70 54 100

    HKDSE-MATH-CP 2 14 () 46