WMA11 January 2020

3. WMA11/01 Edexcel IAL P1 January 2020, Q3 (Differentiation)

Figure 1 shows part of the curve with equation​​ y = x2 + 3x – 2​​ 

The point P(3,16) lies on the curve.​​ 

(a) Find the gradient of the​​ tangent to the curve at P.​​ 

(2)

The point Q with x coordinate 3 + h also lies on the curve.​​ 

(b) Find, in terms of h, the gradient of the line PQ.​​ 

Write your answer in simplest form.​​ 

(3)

(c) Explain briefly the relationship between the answer to (b) and​​ the answer to (a).​​ 

(1)

SOLUTION

a-​​ 

y=x2+3x -2

dydx=2x+3

Putting x=3.​​ 

dydx=23+3

dydx=9

Hence, the gradient of tangent at P is 9.​​ 

b- ​​ 

When x=3+h, y-coordinate is given as​​ 

y=3+h2+33+h-2

=9+6h+h2+9+3h-2

=h2+9h+16

The gradient, mPQ, where, point P (3,16) & Q(3+h,h2+9h+16) is​​ 

mPQ=h2+9h +16-163+h-3

mPQ=h2+9hh

mPQ=hh+9h

mPQ=h+9

mPQ=h+9

c-​​ 

The answer of part (a) gives the​​ gradient of curve at point P. Whereas, answer of part (b) gives the gradient of line PQ.​​ This means that as h approaches to 0, the gradient of curve at point P is equal to the chord length between P and Q. In other words, the answer of part (a) and (b) would be same as h approaches to 0.​​