Solution Pearson Edexcel Level 3 GCE Wednesday 13 May 2020 Paper Reference 8MA0/01

Pearson Edexcel
Level 3 GCE
Wednesday 13 May 2020
Paper Reference 8MA0/01
Solved by shahbaz ahmed
November 2024




Mathematics

Advanced Subsidiary

Paper 1: Pure Mathematics


1. A curve has equation



y = 2x3 − 4x + 5

Find the equation of the tangent to the curve

at the point P (2, 13).

Write your answer in the form y = mx + c,
1

,where m and c are integers to be found

Solution



y = 2x3 − 4x + 5

dy d
= (2x3 − 4x + 5)
dx dx
dy d d d
= (2x3) − (4x) + (5)
dx dx dx dx
dy d dx d
= 2 (x3) − 4 + (5)
dx dx dx dx
dy
= 2(3x2) − 4 + 0 = 6x2 − 4
dx

Slope of the line at the point P (2, 13) = P (x, y)


dy
m= = 6(2)2 − 4 = 20
dx

Where m denotes the slope at the point P (2, 13)

Putting P (2, 13) = P (x, y) and m = 20 in :



y = mx + c

2

, 13 = 20 × 2 + c

13 = 40 + c

40 + c = 13

c = 13 − 40 = −27

Putting m=20, c=-27 , equation of tangent to the curve

at the point P(2,13)



y = mx + c = 20x − 27

Or



y = 20x − 27




3

, Graph of solution




............................................................................


Solution


(a) Calculate the bearing on which the boat is

moving.

To calculate the bearing, we first determine the dis-

placement vector. The displacement vector d is given

by:

d = final position − initial position.




4