Cambridge International AS and A Level Mathematics Pure Mathematics 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