SUMMER 2026
PREDICTED PAPER
GCE
Mathematics A
H240/03: Pure Mathematics and Mechanics
A Level
Mark Scheme
for more: tyrionpapers.com
,1 Calculate the values of x and y in the triangle below. Giving your answers to 3 significant
figures.
(4 marks)
,2 (a) Show that x 2 + y 2 + 5x − 2y − 5 = 0 can be written in the form (x − a ) 2 + (y − b ) 2 = r 2 ,
where a , b and r are constants to be found.
(2 marks)
(b) Hence write down the centre and radius of the circle with equation
x 2 + y 2 + 5x − 2y − 5 = 0 .
, (2 marks)
3 The line y + 2x = 11 meets the circle with equation x 2 + y 2 + 6x − 14y = − 38 .
(i) Show that the line and circle meet at one point only.
(ii) Find the coordinates of the point of intersection.
(4 marks)
4 Solve the equation
4x + 2 = 5 .
PREDICTED PAPER
GCE
Mathematics A
H240/03: Pure Mathematics and Mechanics
A Level
Mark Scheme
for more: tyrionpapers.com
,1 Calculate the values of x and y in the triangle below. Giving your answers to 3 significant
figures.
(4 marks)
,2 (a) Show that x 2 + y 2 + 5x − 2y − 5 = 0 can be written in the form (x − a ) 2 + (y − b ) 2 = r 2 ,
where a , b and r are constants to be found.
(2 marks)
(b) Hence write down the centre and radius of the circle with equation
x 2 + y 2 + 5x − 2y − 5 = 0 .
, (2 marks)
3 The line y + 2x = 11 meets the circle with equation x 2 + y 2 + 6x − 14y = − 38 .
(i) Show that the line and circle meet at one point only.
(ii) Find the coordinates of the point of intersection.
(4 marks)
4 Solve the equation
4x + 2 = 5 .
