GCE AS Mathematics
GCE AS Mathematics (8MA0) – Paper 1
Pure Mathematics
Summer 2019 student-friendly mark scheme
Please note that this mark scheme is not the one used by
examiners for making scripts. It is intended more as a guide to
good practice, indicating where marks are given for model
solutions. As such, it doesn’t show follow-through marks (marks
that are awarded despite errors being made) or special cases.
It should also be noted that for many questions, there may be
alternative methods of finding correct solutions that are not
shown here – they will be covered in the formal mark scheme.
Guidance on the use of codes within this document
M1 – method mark. This mark is generally given for an appropriate method in the
context of the question. This mark is given for showing your working and may be
awarded even if working is incorrect.
A1 – accuracy mark. This mark is generally given for a correct answer following
correct working.
B1 – working mark. This mark is usually given when working and the answer cannot
easily be separated.
Some questions require all working to be shown; in such questions, no marks will
be given for an answer with no working (even if it is a correct answer).
, GCE AS Mathematics
Question 1 (Total 4 marks)
Part Working or answer an examiner might Mark Notes
expect to see
1 3 M1 This mark is given for a method to
(a) y=– x+
2 4 rearrange to find an equation for l1 in
terms of y =
m=2 A1 This mark is given for deducing the
gradient of the perpendicular line l2
(b) Substituting y = 2x + 7 into 2x + 4y – 3 = 0 M1 This mark is given for a method to
gives substitute to form and solve an equation
2x + 4(2x + 7) – 3 = 0 in a single variable.
10x + 25 A1 This mark is given for solving to find
x = –2.5 the value of the x-coordinate of the
point P.
Question 2 (Total 8 marks)
Part Working or answer an examiner might Mark Notes
expect to see
(i) 2 16a 2 M1 This mark is given for a method to find
16a = 2a so =1 an equation to solve with the terms in a
1
2a 2 on one side
3 3
8a 2 = 1 so a 2= 1
8
3
M1 This mark is given for finding a way to
1 2 deal with the indices when solving the
a = 8
equation
1 A1 This mark is given for finding one
a=
4 correct solution to the equation
a = 0 is also a solution B1 This mark is given for deducing that
a = 0 is also a solution
(ii) b4 + 7b2 – 18 = 0 factorises to M1 This mark is given for factorising the
equation given
(b + 9)(b – 2) = 0
2 2
b2 = –9, 2 A1 This mark is given for finding two
correct solutions for b2
For real solutions, b2 = 2 only M1 This mark is given for recognising that
b = –9 is not a real solution
b = 2, –2 A1 This mark is given for finding the two
real solutions to the equation
2
GCE AS Mathematics (8MA0) – Paper 1
Pure Mathematics
Summer 2019 student-friendly mark scheme
Please note that this mark scheme is not the one used by
examiners for making scripts. It is intended more as a guide to
good practice, indicating where marks are given for model
solutions. As such, it doesn’t show follow-through marks (marks
that are awarded despite errors being made) or special cases.
It should also be noted that for many questions, there may be
alternative methods of finding correct solutions that are not
shown here – they will be covered in the formal mark scheme.
Guidance on the use of codes within this document
M1 – method mark. This mark is generally given for an appropriate method in the
context of the question. This mark is given for showing your working and may be
awarded even if working is incorrect.
A1 – accuracy mark. This mark is generally given for a correct answer following
correct working.
B1 – working mark. This mark is usually given when working and the answer cannot
easily be separated.
Some questions require all working to be shown; in such questions, no marks will
be given for an answer with no working (even if it is a correct answer).
, GCE AS Mathematics
Question 1 (Total 4 marks)
Part Working or answer an examiner might Mark Notes
expect to see
1 3 M1 This mark is given for a method to
(a) y=– x+
2 4 rearrange to find an equation for l1 in
terms of y =
m=2 A1 This mark is given for deducing the
gradient of the perpendicular line l2
(b) Substituting y = 2x + 7 into 2x + 4y – 3 = 0 M1 This mark is given for a method to
gives substitute to form and solve an equation
2x + 4(2x + 7) – 3 = 0 in a single variable.
10x + 25 A1 This mark is given for solving to find
x = –2.5 the value of the x-coordinate of the
point P.
Question 2 (Total 8 marks)
Part Working or answer an examiner might Mark Notes
expect to see
(i) 2 16a 2 M1 This mark is given for a method to find
16a = 2a so =1 an equation to solve with the terms in a
1
2a 2 on one side
3 3
8a 2 = 1 so a 2= 1
8
3
M1 This mark is given for finding a way to
1 2 deal with the indices when solving the
a = 8
equation
1 A1 This mark is given for finding one
a=
4 correct solution to the equation
a = 0 is also a solution B1 This mark is given for deducing that
a = 0 is also a solution
(ii) b4 + 7b2 – 18 = 0 factorises to M1 This mark is given for factorising the
equation given
(b + 9)(b – 2) = 0
2 2
b2 = –9, 2 A1 This mark is given for finding two
correct solutions for b2
For real solutions, b2 = 2 only M1 This mark is given for recognising that
b = –9 is not a real solution
b = 2, –2 A1 This mark is given for finding the two
real solutions to the equation
2
