WMA11 October 2021

9. WMA11/01​​ Edexcel​​ IAL P1 Oct 2021,​​ Q9​​ (Graphs​​ & Transformations and Algebraic Expressions:​​ Simplifying Surds)

In this question you must show all stages of your working.

Solutions relying on calculator​​ technology are not acceptable.

Figure 5 shows a sketch of the curve with equation y = f(x) where​​ 

f(x) =x                  x > 0 

The point P(9, 3) lies on the curve and is shown in Figure 5.​​ 

On the next page there is a copy of Figure 5 called Diagram 1.​​ 

(a) On Diagram 1, sketch and​​ clearly label the graphs of​​ 

y = f(2x) and y = f(x) + 3 

Show on each graph the coordinates of the point to which P is transformed.​​ 

(3)

The graph of y = f(2x) meets the graph of y = f(x) + 3 at the point Q.​​ 

(b) Show that the x coordinate of Q is the solution of​​ 

x = 3 2+1

(3)

(c) Hence​​ find, in simplest form, the coordinates of Q.​​ 

(3)

SOLUTION

a-

b-​​ To find the x-corrdinate of Q, we need to solve the following expression.​​ 

2x=x +3

2x= x+3

2x- x=3

x2-1=3

x=32-1

Rationalising the denominator.​​ 

x=32-1 ×2+12+1

x=32+12-1

x=32+1

Hence, shown.

c-​​ 

x=32+1

x=9 2+12

x= 9 2+22+1

x=93+22

y= x+3

Now, substituting the value of​​ x=32+1​​ in the above​​ expression.​​ 

y=(32+3)+3

y=32+6

Hence, the coordinates of Q are

Q27+182,32+6