Cambridge International AS and A Level Mathematics Pure Mathematics 1

(Michael S) #1
Answers

302

P1^


11  4.5 square units

12 (i) ddyx = 6 x − 6 x^2 − 4 x^3
(ii) 4 x + y − 4 = 0
(iv) 8.1 square units
13 (i) ddyx = 4 − 3 x^2 ; 8x + y − 16 = 0
(ii) (−4, 48)
(iii) 108 square units
14 1023 square units
15 (i) A: (1, 4); B: (3, 0)
(ii) 3 y = x + 4
(iii) 1712 square units

Exercise 6E (Page 203)
  1  6 square units
  2 623 square units
  3  4 square units

  4 823 square units

  5 615 square units

  6  20 square units

Activity 6.3 (Page 203)
(i) (a) 4(x − 2)^3
(b) 14(2x + 5)^6
(c) –
(– )

6
21 x^4
(d) –





4
18 x
(ii) (a) (x − 2)^4 + c
(b) 14 (x − 2)^4 + c
(c) 12 (2x + 5)^7 + c
(d) 2(2x + 5)^7 + c

(e) (^) (– 21 x–^1 ) 3 + c
(f) –
(– )
1
62 x 13



  • c
    (g) (^) (– 18 x) + c
    (h) (^) –( 21 –) 8 x + c
    Exercise 6F (Page 205)
      1 (i) 15 (x + 5)^5 + c
    (ii) 19 (x + 7)^9 + c
    (iii) –
    (–)
    1
    52 x^5

  • c
    (iv) 23 (x − 4)
    (^32)

  • c
    (v) 121 (3x − 1)^4 + c
    (vi) 351 (5x − 2)^7
    (vii) 14 (2x − 4)^6 + c
    (viii) 16 (4x − 2)
    3
    (^2) + c
    (ix) (^) 8–^4 x + c
    (x) (^32) x– 1 + c
      2 (i) (^513)
    (ii) 60
    (iii) 205
    (iv) 336
    (v) (^513)
    (vi) (^523)
      3 (i) 4
    (ii) –4; the graph has rotational
    symmetry about (2, 0).
      4 (i) 5.2 square units
    (ii) 1.6 square units
    (iii) 6.8 square units
    (iv) Because region B is below
    the x axis, so the integral for
    this part is negative.
      5 (i) 4 square units
    (ii) 223 square units
      6 (i) 3 y + x = 29
    (ii) y = 4 32 x−+ 1
      7 (i) (8.5, 4.25)
    (ii) y = 16 − 4 62 − x
    Activity 6.4 (Page 206)
    (i) (a) 21
    (b) (^23)
    (c) 0.9
    (d) 0.99
    (e) 0.9999
    (ii)  1
    ●?^ (Page^ 207)
    1
    a;
    1
    0 x^2 x

    ∫ d
    does not exist since^10 is
    undefined.
    Exercise 6G (Page 208)
      1 2
    (^2 12)
      3 2
      4 – (^14)
      5 –1
    x
    y
    O
    2
    y =^3 x
    x
    y
    2
    O
    –
    y = x – 
    x
    y
    2
    1
    O
    y =^4 x
    x
    y
    1
    –1
    –2
    O
    y^3 x–2

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