Edexcel 9MA0/02 • Pure Mathematics 2
BEST GUESS PRACTICE PAPER 2A
ALevelMathsRevision.com
HOW TO USE THIS PAPER
This is not a prediction of what the real Paper 2 will look like — nobody can claim to know that. Treat
it instead as a diagnostic tool: it brings together the topics most worth practising for Paper 2 in one
place, so that working through it shows you where the gaps in your knowledge and understanding lie
and lets you direct your revision time where it will make the most difference.
Time: about 2 hours • 14 questions • 106 marks. Questions are in roughly increasing
order of difficulty. Give non-exact answers to 3 significant figures unless told otherwise.
Q1 Laws of logarithms & logarithmic equations • 7 marks
(a) Show that the equation 2 log2 (x + 15) − log2 x = 6 can be written as x2 − 34x + 225 = 0. (4)
(b) Hence solve the equation 2 log2 (x + 15) − log2 x = 6. (3)
Q2 Reduction to linear form • 4 marks
The variables x and y are related by y = axn , where a and n are constants. The straight-line graph
of log10 y against log10 x passes through the points (1, 5) and (5, 17).
(a) Find the value of n. (2)
(b) Find the value of a. (2)
Q3 Trapezium rule • 6 marks
(a) Use the trapezium rule, with 4 strips each of width 0.5, to find an approximate value for
Z 5
log10 (2 + x) dx,
3
giving your answer correct to 3 significant figures. (4)
(b) Use your answer to part (a) to deduce an approximate value for
Z 5 √
log10 2 + x dx,
3
showing your method clearly. (2)
Continue your A Level Maths journey at: SCAN FOR
© 2026 – ALevelMathsRevision.com
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, Edexcel 9MA0/02 • Pure Mathematics 2
BEST GUESS PRACTICE PAPER 2A
ALevelMathsRevision.com
Q4 Circles • 10 marks
Figure 1 shows a circle C. The points A(4, −2) and B(10, 6) are the ends of a diameter of C, and M
is the centre of C.
B(10, 6)
M
C
A(4, −2)
tangent at A
Figure 1
(a) Find the coordinates of M . (2)
(b) Show that the radius of C is 5. (2)
(c) Find an equation for C. (2)
(d) Find an equation of the tangent to C at the point A, giving your answer in the form ax+by+c = 0,
where a, b and c are integers. (4)
Q5 Arithmetic series • 11 marks
An arithmetic series has first term a and common difference d.
n
(a) Prove that the sum of the first n terms of the series is Sn = 2a + (n − 1)d .
(4)
2
A particular arithmetic sequence has its 10th term equal to twice its 4th term, and its 20th term equal
to 44.
(b) Find the value of a and the value of d. (5)
(c) For this sequence, find the sum of the first 50 terms. (2)
Q6 Vectors (Year 1 foundation) • 7 marks
Relative to a fixed origin, a = 2i + 6j and b = 2i − 4j.
(a) Given that pa + qb = 6i − 7j, find the value of p and the value of q. (4)
(b) Given that |a + kb| = 5, find the two possible values of the constant k. (3)
Continue your A Level Maths journey at: SCAN FOR
© 2026 – ALevelMathsRevision.com
ALevelMathsRevision.com/lessons PREDICTIONS PAGE
BEST GUESS PRACTICE PAPER 2A
ALevelMathsRevision.com
HOW TO USE THIS PAPER
This is not a prediction of what the real Paper 2 will look like — nobody can claim to know that. Treat
it instead as a diagnostic tool: it brings together the topics most worth practising for Paper 2 in one
place, so that working through it shows you where the gaps in your knowledge and understanding lie
and lets you direct your revision time where it will make the most difference.
Time: about 2 hours • 14 questions • 106 marks. Questions are in roughly increasing
order of difficulty. Give non-exact answers to 3 significant figures unless told otherwise.
Q1 Laws of logarithms & logarithmic equations • 7 marks
(a) Show that the equation 2 log2 (x + 15) − log2 x = 6 can be written as x2 − 34x + 225 = 0. (4)
(b) Hence solve the equation 2 log2 (x + 15) − log2 x = 6. (3)
Q2 Reduction to linear form • 4 marks
The variables x and y are related by y = axn , where a and n are constants. The straight-line graph
of log10 y against log10 x passes through the points (1, 5) and (5, 17).
(a) Find the value of n. (2)
(b) Find the value of a. (2)
Q3 Trapezium rule • 6 marks
(a) Use the trapezium rule, with 4 strips each of width 0.5, to find an approximate value for
Z 5
log10 (2 + x) dx,
3
giving your answer correct to 3 significant figures. (4)
(b) Use your answer to part (a) to deduce an approximate value for
Z 5 √
log10 2 + x dx,
3
showing your method clearly. (2)
Continue your A Level Maths journey at: SCAN FOR
© 2026 – ALevelMathsRevision.com
ALevelMathsRevision.com/lessons PREDICTIONS PAGE
, Edexcel 9MA0/02 • Pure Mathematics 2
BEST GUESS PRACTICE PAPER 2A
ALevelMathsRevision.com
Q4 Circles • 10 marks
Figure 1 shows a circle C. The points A(4, −2) and B(10, 6) are the ends of a diameter of C, and M
is the centre of C.
B(10, 6)
M
C
A(4, −2)
tangent at A
Figure 1
(a) Find the coordinates of M . (2)
(b) Show that the radius of C is 5. (2)
(c) Find an equation for C. (2)
(d) Find an equation of the tangent to C at the point A, giving your answer in the form ax+by+c = 0,
where a, b and c are integers. (4)
Q5 Arithmetic series • 11 marks
An arithmetic series has first term a and common difference d.
n
(a) Prove that the sum of the first n terms of the series is Sn = 2a + (n − 1)d .
(4)
2
A particular arithmetic sequence has its 10th term equal to twice its 4th term, and its 20th term equal
to 44.
(b) Find the value of a and the value of d. (5)
(c) For this sequence, find the sum of the first 50 terms. (2)
Q6 Vectors (Year 1 foundation) • 7 marks
Relative to a fixed origin, a = 2i + 6j and b = 2i − 4j.
(a) Given that pa + qb = 6i − 7j, find the value of p and the value of q. (4)
(b) Given that |a + kb| = 5, find the two possible values of the constant k. (3)
Continue your A Level Maths journey at: SCAN FOR
© 2026 – ALevelMathsRevision.com
ALevelMathsRevision.com/lessons PREDICTIONS PAGE
