Cambridge International AS and A Level Mathematics Pure Mathematics 1

Answers

294

P1^

10 (i) ddyx = −^720 x

(ii) 0.8225 and −0.8225

(iii) x=^107

11 (i)

(ii) (−^12 , 0)

(iii) − x^12

(iv) − 4

12 (i) − x^83 + 1

(iii) 2

(v) 0

(vi) There is a minimum point at

(2, 3)

13 (i) y

x

y = –16x + 13

y = + 1

O

1

x^2

(iii) − (^) x^23 ; − 16
(iv) The line y = − 16 x + 13 is a
tangent to the curve
y = (^) x^12 + 1 at (0.5, 5)
14  (i)
(ii) ddyx= 21 x−^12
(iii) (^16)
15  (i)
(ii) ddyx=−x^83
(iii)  1
(iv) –1; the curve is symmetrical
about the y axis
16  (i) ddyx=+^12 x^22
(ii) x = 2, gradient = 1
17 4
(^18 38)
Exercise 5D (Page 142)
  1 (i) ddyx = 6 − 2 x
(ii) 4
(iii) y = 4 x + 1
  2 (i)
(ii) ddyx = 4 − 2 x
(iii) 2
(iv) y = 2 x + 1
  3 (i) ddyx = 3 x^2 − 8 x
(ii) − 4
(iii) y = − 4 x
(iv) (0, 0)
  4 (i)
(ii) At (−1, 5), ddyx = 2;
at (1, 5), ddyx = − 2
(iii) y = 2 x + 7, y = − 2 x + 7
(iv) (0, 7)
  5 (i)
(iii) y = 4 x is the tangent to the
curve at (2, 8).
   6 (i) y = 6 x + 28
(ii) (3, 45)
(iii) 6 y = −x + 273
  7  (i) ddyx = 3 x^2 − 8 x + 5
(ii) 4
(iii) 8
(iv) y = 8 x − 20
(v) 8 y = −x + 35
(vi) x = 0 or x = (^83)
  8 (i)
A(1, 0); B(2, 0) or vice versa
y
x
2
2
O
4

x
y
 
O
10
5
x
y
–3 3
y
O 4
4
x
y
O
6
x
y
2
8
x
4
O
y
1 2 x
2
O