Oxford Cambridge and RSA
*1335505743*
Tuesday 4 June 2025 – Afternoon
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 page 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 100.
• 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 2024 [603/1038/8] DC (PQ/FC) 339384/3
, H240/01 Mark Scheme June 2024
OCR is an exempt Charity
Turn over
Formulae
A Level Mathematics A (H240)
Arithmetic series
na l n d
Sn = 12 ^+=h "2a+ -^n 1h ,
Geometric series
Sn = a^11--rrnh
S3= 1-a r for r 1 1
Binomial series
^a+ = +bhnan nC1an-1b+ nC2an-2 2b + +f nCran r r- b + +f bn ^n !Nh
n! C C
JLnNOOP r n!^ - rh! where n r = = =n r KKr
^1+ = + +xhn 1 nx n n^ 2-! 1hx2+ +fn n^ -1hfr!^n- +r 1hxr +f ^ x 1 1,n !Rh
Differentiation
f^xh fl^xh
tankx ksec2kx
secx sec tanxx
cotx -cosec2x
2
, H240/01 Mark Scheme June 2024
cosecx -cosec cotx x
Quotient rule y = uv, ddyx = vdduxv-2uddxv
Differentiation from first principles flxh= hlim" f^x+ -hhh f^xh
^
d h
0 Integration c deffl^^xxh dx = ln f^xh +c
1
;fl^xhaf^xhkn dx = n+ 1af^xhkn+1+c
d d
Integration by parts ;u dvx dx = -uv ;v dux dx
Small angle approximations sini i. , cosi. 1- 12i2, tani i. where i is measured in radians Trigonometric identities
sin^A!Bh= sinAcosB!cosAsinB cos^A!Bh= cosAcosB"sinAsinB
tan A! tan B
tan^A!Bh= 1 "tan A tan B aA!B !^k+ hrk
Numerical methods
yb h y y 2 y y y b- a
Trapezium rule: a y xd . "^ 0+ + nh ^ 1+ + + 2 f h,, where h = n
n-1
The Newton-Raphson iteration for solving f^xh= 0: xn+1 = -xn fl^^xnnhh f x
3
, H240/01 Mark Scheme June 2024
Probability
B A B B
P^A, h= P^ h+P^ h-P^A+ h
P A + B
P^A+Bh= P^AhP^B Ah= P^BhP^A Bh or P^A Bh= ^ ^ h h
PB
Standard deviation
/^xn--xh2 = /nx2 --x2 or / f x^/-f -xh2 = //fxf2 --x2
The binomial distribution
then
If X + B^n p, h P^X = =xh JKKnxNOOPpx^1-phn-x, mean of X is np, variance of X is np^1-ph L
Hypothesis test for the mean of a normal distribution
J 2
N
v O -n
If X + N^n v, 2h then X + NKKLn, n O P and vX n + N^0 1, h
Percentage points of the normal distribution
If Z has a normal distribution with mean 0 and variance 1 then, for each value of p, the table gives the value of z such that P^Z G zh= p.
p 0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
z 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291
Kinematics
4
*1335505743*
Tuesday 4 June 2025 – Afternoon
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 page 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 100.
• 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 2024 [603/1038/8] DC (PQ/FC) 339384/3
, H240/01 Mark Scheme June 2024
OCR is an exempt Charity
Turn over
Formulae
A Level Mathematics A (H240)
Arithmetic series
na l n d
Sn = 12 ^+=h "2a+ -^n 1h ,
Geometric series
Sn = a^11--rrnh
S3= 1-a r for r 1 1
Binomial series
^a+ = +bhnan nC1an-1b+ nC2an-2 2b + +f nCran r r- b + +f bn ^n !Nh
n! C C
JLnNOOP r n!^ - rh! where n r = = =n r KKr
^1+ = + +xhn 1 nx n n^ 2-! 1hx2+ +fn n^ -1hfr!^n- +r 1hxr +f ^ x 1 1,n !Rh
Differentiation
f^xh fl^xh
tankx ksec2kx
secx sec tanxx
cotx -cosec2x
2
, H240/01 Mark Scheme June 2024
cosecx -cosec cotx x
Quotient rule y = uv, ddyx = vdduxv-2uddxv
Differentiation from first principles flxh= hlim" f^x+ -hhh f^xh
^
d h
0 Integration c deffl^^xxh dx = ln f^xh +c
1
;fl^xhaf^xhkn dx = n+ 1af^xhkn+1+c
d d
Integration by parts ;u dvx dx = -uv ;v dux dx
Small angle approximations sini i. , cosi. 1- 12i2, tani i. where i is measured in radians Trigonometric identities
sin^A!Bh= sinAcosB!cosAsinB cos^A!Bh= cosAcosB"sinAsinB
tan A! tan B
tan^A!Bh= 1 "tan A tan B aA!B !^k+ hrk
Numerical methods
yb h y y 2 y y y b- a
Trapezium rule: a y xd . "^ 0+ + nh ^ 1+ + + 2 f h,, where h = n
n-1
The Newton-Raphson iteration for solving f^xh= 0: xn+1 = -xn fl^^xnnhh f x
3
, H240/01 Mark Scheme June 2024
Probability
B A B B
P^A, h= P^ h+P^ h-P^A+ h
P A + B
P^A+Bh= P^AhP^B Ah= P^BhP^A Bh or P^A Bh= ^ ^ h h
PB
Standard deviation
/^xn--xh2 = /nx2 --x2 or / f x^/-f -xh2 = //fxf2 --x2
The binomial distribution
then
If X + B^n p, h P^X = =xh JKKnxNOOPpx^1-phn-x, mean of X is np, variance of X is np^1-ph L
Hypothesis test for the mean of a normal distribution
J 2
N
v O -n
If X + N^n v, 2h then X + NKKLn, n O P and vX n + N^0 1, h
Percentage points of the normal distribution
If Z has a normal distribution with mean 0 and variance 1 then, for each value of p, the table gives the value of z such that P^Z G zh= p.
p 0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
z 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291
Kinematics
4
