1. Higher Supported Study
May 2015
Session 2
Paper 2

2. Question 1 A curve has equation (a) Express in the form where k > 0
and
(b) Hence find, in the interval , the x – coordinate of the
point on the curve where the gradient is 1.
06 December 2018

3. Question 2 F is the point (8, 4, 6). P divides AE in
The diagram shows a cuboid OABC, DEFG
F is the point (8, 4, 6). P divides AE in
the ratio 2:1 Q is the midpoint of CG
(a) State the coordinates of P and Q  
(b) Write down the components of PQ and PA
(c) Find the size of angle QPA    
06 December 2018

4. Question 3 The curve is such that
The curve passes through the point (-1,9).
Express y in terms of x
06 December 2018

5. Question 4 The curve with equation , where x > 1
cuts the x-axis at the point (a,0). Find the value of a or
06 December 2018

6. Question 5
Find the coordinates of the turning points of the curve with equation
and determine their nature.
When x = -1
When x = 3
and x -2 -1 3 4 _ + +
slope
Max TP
at (-1,17)
Min TP
at (3,-15)
06 December 2018

7. Question 6 The diagram shows the graph of a cubic
Function and its derived function
(a) Given that is of the form
(i) write down the values of a and b
(ii) find the value of k
(b) Find the equation of the graph of the
cubic function
06 December 2018

8. Question 7
Find the value of
06 December 2018

9. Question 8 Functions f , g and h are defined on suitable domains by
(a) Find expressions for
(b) Hence solve
06 December 2018

10. Question 9

11. Solve algebraically the equation
Question 10
Solve algebraically the equation

12. Question 11a
Kite ABCD has two of its vertices at A(3,8) and B(7,14) as shown.
Given that the equation of the longer diagonal BD is ,
find the equation of the short diagonal AC
A(3,8)
B(7,14) C D E O x y

13. Question 11b
(b) Find the coordinates of E, the point of intersection of the
two diagonals.

14. Question 11c (c) Hence establish the coordinates of C. A(3,8) E (5,6)

15. Question 12
For what values of x is the function
increasing?