1. Higher Supported Study
May 2015
Session 2
Paper 1

2. Question 1 Solve the equation for rearrange to = 0 factorise
solve equations
23 April 2017

3. Question 2
D, E and F have coordinates (10,- 8, -15), (1,-2,-3) and (-2,0,1) respectively.
(a) (i) Show that D, E and F are collinear.
(ii) Find the ratio in which E divides DF
(b) G has coordinates (k,1,0). Given that DE is perpendicular to GE,
find the value of k.   
so EF and DE are parallel
E is a common point
so D, E and F are collinear  
23 April 2017

4. Question 3 The diagram shows a sketch of the function y = f (x)
Copy the diagram and on it sketch
the graph of y = f (2x)
(b) On a separate diagram sketch
the graph of y = 1 - f (2x).
23 April 2017

5. Question 4 Two variables, x and y, are connected by the law log 4 y
The graph of log 4 y against x
is a straight line passing through
the origin and the point A(6,3).
Find the value of a
A(6,3) O x
23 April 2017

6. Question 5a The diagram shows a sketch of
and the tangent to the curve at x = 2
Show that the equation of the tangent to the
curve at x = 2 is y = 5x - 8

7. Question 5a
Find algebraically the coordinates of the point where this tangent
meets the curve again 2 1 -2 -4 8
- 8

8. Question 6a Angle x is acute and is such that
(a) Show clearly that the exact value of is

9. Question 6b
(b) Hence show that

10. Question 7 Two identical circles touch at the point P(9,3)
as shown in the diagram.
 One of the circles has equation
Find the equation of the other circle. x y O
P (9, 3)
23 April 2017

11. Question 8
Solve the equation
23 April 2017

12. Question 9 y x y x
(–4, 0)
(12, 0)

13. Question 10 -1 1
-13
-12 12
remainder = 0
so x + 1 is a factor

14. Question 11

15. Question 12

16. Question 13

17. Question 14
Sketch the graph of