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Page 1

General Certificate of Secondary Education
2012

Paper 1

G0301
Pure Mathematics
[G0301]

MONDAY 28 MAY, MORNING

TIME
2 hours.

INSTRUCTIONS TO CANDIDATES
Write your Centre Number and Candidate Number on the Answer Booklet and the Supplementary
At the conclusion of this…

Page 2

1(i)Using the axes and scales in Fig. 1 in your Supplementary Answer Booklet, sketch the
graph of y tan x for 75° x 75°.[2]

(ii)Hence, using the axes and scales in Fig. 2 in your Supplementary Answer Booklet,
1
sketch the graph of y tan (…

Page 3

dy 3 1
4(a)Find if y x6 - + 2 [3]
dx 2 2 x3

6 3

(b) Find
7x 3 dx
x
[3]

5 (i) Find the equation of the tangent to the curve y 6x3 2x4 at the point (1, 4). [3]

(ii) Find the coordinates of P,…

Page 4

6(i)Show that

5x + 1 3x ­ 7
­
2x + 3 1­ x

can be written as

11x 2 ­ 9 x ­ 22
[4]
2x 2 x ­ 3

(ii)Hence, or otherwise, solve the equation

5x 1 3x ­ 7
­ 4 [4]
2x 3 1­ x

7(a)Solve…

Page 5

8 Two cowboys, Frank and Jesse, were riding along separate straight trails towards a ranch R,
passing over flat terrain.

Frank crossed over a straight railway line PQ at a point X and continued on to the ranch R,
where XR = 4.50km.

^ X is 60°, as
A station…

Page 6

9 Carly noted the cost C (in pounds) and the age A (in months) of five FAYE laptops. The data
are given in Table 1.

Table 1

Age Cost
A (months) £C

5 206.54

9 139.78

14 101.69

23 71.13

34 53.68

She believes that a relationship of the form…

Page 7

10 Matthew, Emma and Simon decided to invest some money in low, medium and high risk
accounts.

Matthew invested £5000, £3000 and £2000 in the low, medium and high risk accounts
respectively, and his expected interest after one year is £500.

Let x, y and z represent the percentage interest…

Page 8

11 A curve is defined by the equation

y 2x3 3x2 5x

(i) Find the coordinates of the points where this curve crosses the x-axis. [3]

(ii) Find the coordinates of the turning points of this curve. Give your answers to 2 decimal
places. [5]

(iii)Identify each turning point as…

Page 9

Centre Number

71

Candidate Number

General Certificate of Secondary Education
2012

Paper 1

G0301
Pure Mathematics
[G0301]

MONDAY 28 MAY, MORNING

SUPPLEMENTARY

7251.02

Page 10

1 (i)Sketch the graph of y = tan x, for 75° x 75°, on the axes in Fig. 1 below.

y
4

2

­75° ­60° ­45° ­30° ­15° 15° 30° 45° 60° 75° x

­2

­4

Fig. 1

(ii)Sketch the graph of y tan ( 1 x), for 150° x…

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