2025 OCR A Level Law
H418/04 The nature of law and the law of contract
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Thursday 15 May 2025 – Afternoon
AS Level Mathematics A
H230/01 Pure Mathematics and Statistics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different degree
of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is needed
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [603/0933/7] OCR is an exempt Charity
DC (SL/SG) 350669/4 Turn over
, 2
Formulae
AS Level Mathematics A (H230)
Binomial series
^a + bhn = an + nC1 a n-1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
n n!
where nC = C = c m =
r n r r r!^n - rh!
Differentiation from first principles
f^x + hh - f^xh
f l^xh = lim
h "0 h
Standard deviation
f ^x
= 2 or =
n n
The binomial distribution
n
If X ~ B^n, ph then P^X = xh = c mpx^1 - phn -x , mean of X is np, variance of X is np^1 - ph
x
Kinematics
v = u + at
s = ut + 1 at2
2
s = 12^u + vht
v2 = u2 + 2as
s = vt - 12at2
© OCR 2025 H230/01 Jun25
, 3
Section A
Pure Mathematics
1 In this question you must show detailed reasoning.
Solve the following equations.
(a) 11 = 5 [2]
(b) y6 + 7y3 - 8 = 0 [4]
(c) 2 3z-10 = 16 [2]
5
2 It is given that y0 (ax2 - 2x + 4) d x = 45 , where a is a constant.
Determine the value of a. [3]
3 (a) Express x2 - 6x in the form (x + p) 2 + q, where p and q are constants. [2]
(b) Hence or otherwise determine the centre and radius of the circle with equation
x2 + y2 - 6x - 16 = 0. [3]
cos i 1
4 (a) Show that - / tan i (where i ! 90n° for any odd integer n). [3]
1 - sin i cos i
cos 3x 1
(b) Hence solve the equation - = 1 for 0 G x G 90°. [4]
1 - sin 3x cos 3x
5 (a) Find the coefficient of x7 in the expansion of (2x + 3) 9. [2]
(b) The following questions are about the binomial expansion of (1 + x) 21 in ascending powers
of x.
(i) Two consecutive terms have equal coefficients.
State the powers of x in these two terms. [1]
(ii) Given that the terms in xr and x r+5 have equal coefficients, find r. [2]
© OCR 2025 H230/01 Jun25 Turn over
, 4
6 In this question you must show detailed reasoning.
Solve the following equations.
(a) log3 (x + 32) - log3 (2x) +log3 2 = 2 [4]
1 3
(b) log y c m = – [3]
8 2
7 In this question you must show detailed reasoning.
B
C
c P
Q
A
a
O
The diagram shows a parallelogram OABC. The position vectors of A and C are a and c
respectively.
1
• The point P lies on AB such that AP = AB.
3
3
• The point Q lies on OP such that OQ = OP .
4
3 1
(a) Show that OQ = a + c. [4]
4 4
(b) Hence show that Q lies on AC. [3]
8 A curve with equation y = x3 + 3x2 - 9x - 12 has stationary points A and B.
Determine the coordinates of the point where the line through A and B meets the x-axis. [8]
© OCR 2025 H230/01 Jun25
H418/04 The nature of law and the law of contract
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Thursday 15 May 2025 – Afternoon
AS Level Mathematics A
H230/01 Pure Mathematics and Statistics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different degree
of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is needed
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [603/0933/7] OCR is an exempt Charity
DC (SL/SG) 350669/4 Turn over
, 2
Formulae
AS Level Mathematics A (H230)
Binomial series
^a + bhn = an + nC1 a n-1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
n n!
where nC = C = c m =
r n r r r!^n - rh!
Differentiation from first principles
f^x + hh - f^xh
f l^xh = lim
h "0 h
Standard deviation
f ^x
= 2 or =
n n
The binomial distribution
n
If X ~ B^n, ph then P^X = xh = c mpx^1 - phn -x , mean of X is np, variance of X is np^1 - ph
x
Kinematics
v = u + at
s = ut + 1 at2
2
s = 12^u + vht
v2 = u2 + 2as
s = vt - 12at2
© OCR 2025 H230/01 Jun25
, 3
Section A
Pure Mathematics
1 In this question you must show detailed reasoning.
Solve the following equations.
(a) 11 = 5 [2]
(b) y6 + 7y3 - 8 = 0 [4]
(c) 2 3z-10 = 16 [2]
5
2 It is given that y0 (ax2 - 2x + 4) d x = 45 , where a is a constant.
Determine the value of a. [3]
3 (a) Express x2 - 6x in the form (x + p) 2 + q, where p and q are constants. [2]
(b) Hence or otherwise determine the centre and radius of the circle with equation
x2 + y2 - 6x - 16 = 0. [3]
cos i 1
4 (a) Show that - / tan i (where i ! 90n° for any odd integer n). [3]
1 - sin i cos i
cos 3x 1
(b) Hence solve the equation - = 1 for 0 G x G 90°. [4]
1 - sin 3x cos 3x
5 (a) Find the coefficient of x7 in the expansion of (2x + 3) 9. [2]
(b) The following questions are about the binomial expansion of (1 + x) 21 in ascending powers
of x.
(i) Two consecutive terms have equal coefficients.
State the powers of x in these two terms. [1]
(ii) Given that the terms in xr and x r+5 have equal coefficients, find r. [2]
© OCR 2025 H230/01 Jun25 Turn over
, 4
6 In this question you must show detailed reasoning.
Solve the following equations.
(a) log3 (x + 32) - log3 (2x) +log3 2 = 2 [4]
1 3
(b) log y c m = – [3]
8 2
7 In this question you must show detailed reasoning.
B
C
c P
Q
A
a
O
The diagram shows a parallelogram OABC. The position vectors of A and C are a and c
respectively.
1
• The point P lies on AB such that AP = AB.
3
3
• The point Q lies on OP such that OQ = OP .
4
3 1
(a) Show that OQ = a + c. [4]
4 4
(b) Hence show that Q lies on AC. [3]
8 A curve with equation y = x3 + 3x2 - 9x - 12 has stationary points A and B.
Determine the coordinates of the point where the line through A and B meets the x-axis. [8]
© OCR 2025 H230/01 Jun25
