Write down two equations relating p and q.

Find the value of p and of q.

Write down the equation of the horizontal asymptote to the graph of f (x).

p + q = 6     (A1)

0.5p + q = 4     (A1)     (C2)

Note: Accept correct equivalent forms of the equations.

[2 marks]

p = 4, q = 2     (A1)(A1)(ft)     (C2)

Notes: If both answers are incorrect, award (M1) for attempt at solving simultaneous equations.

[2 marks]

y = 2     (A1)(A1)(ft)     (C2)

Notes: Award (A1) for “y = a constant”, (A1)(ft) for 2. Follow through from their value for q as long as their constant is greater than 2 and less than 6.

An equation must be seen for any marks to be awarded.

[2 marks]

A significant number of candidates found it difficult to identify and write two equations that relate p and q. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of p and q in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote x = 2 or only 2 instead of y = 2.

A significant number of candidates found it difficult to identify and write two equations that relate p and q. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of p and q in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote x = 2 or only 2 instead of y = 2.

A significant number of candidates found it difficult to identify and write two equations that relate p and q. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of p and q in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote x = 2 or only 2 instead of y = 2.