Exam (elaborations)
ACTUAL OCR AS LEVEL 2024 WITH MARK SCHEME MATHS A H230 PAPER 1
ACTUAL OCR AS LEVEL 2024 WITH MARK SCHEME MATHS A H230 PAPER 1
[Show more]
Content preview
Oxford Cambridge and RSAThursday 16 May 2024 – Afternoon
AS Level Mathematics A
H230/01 Pure Mathematics and Statistics
Time allowed: 1 hour 30 minutes
* 1 3 3 4 8 1 9 0 4 9 *
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 2024 [603/0933/7] OCR is an exempt Charity
DC (LK) 335474/2 Turn over
, 2
Formulae
AS Level Mathematics A (H230)
Binomial series
^a + bhn = a n + n C1 a n - 1 b + n C2 a n - 2 b 2 + f + n Cr a n - r b r + f + b n ^n ! Nh,
n
where n C r = n C r = c m =
n!
r r! ^n - rh !
Differentiation from first principles
f ^x + hh - f ^xh
f l^xh = lim
h"0 h
Standard deviation
/^x - x h2 / x2 / f ^x - x h2 / fx 2
= - x 2 or = / f -x
2
n n /f
The binomial distribution
If X + B ^n, ph then P ^X = xh = c m p x ^1 - ph , mean of X is np, variance of X is np ^1 - ph
n n-x
x
Kinematics
v = u + at
s = ut + 12 at 2
s = 12 ^u + vh t
v 2 = u 2 + 2as
s = vt - 12 at 2
© OCR 2024 H230/01 Jun24
, 3
Section A
Pure Mathematics
1 In this question you must show detailed reasoning.
Solve the equation ln `x 3j - ln `5x 2j = ln 2 , where x 2 0 . [3]
2 Points A and B have position vectors OA = 2 i + 3j and OB =- i + 5j, respectively, where O is the
origin.
(a) Find the position vector of the midpoint of AB. [1]
(b) Find the exact magnitude of the vector AB. [3]
(c) Find the angle between the vector OA and the positive x-axis. [2]
3 In the triangle ABC, AB = 3, AC = 5 and angle BAC = a.
5
The area of the triangle is .
2
Determine the two possible values of cos a . Give your answers in exact form. [5]
4 (a) Write down the term in b 5 in the expansion of (a + b) 12 . [1]
(b) A variable X has a binomial distribution such that P(X = 5) is given by the term in part (a).
(i) State a condition that must be satisfied by a and b. [1]
(ii) State the distribution of X. Give the values of any parameters. [2]
1
5 A curve has equation y = 4x 2 + .
x
(a) Determine the coordinates of the stationary point on the curve. [5]
d2y
(b) Use to determine whether this turning point is a maximum or a minimum. [2]
d x2
(c) Find the values of x for which the curve is increasing. [2]
6 A curve has the following properties:
dy
• The gradient of the curve is given by d x =-2x .
• The curve passes through the point (4, - 13) .
Determine the coordinates of the points where the curve meets the line y = 2x . [7]
© OCR 2024 H230/01 Jun24 Turn over
, 4
7 In this question you must show detailed reasoning.
(a) Show that (x + 2) 4 - 6 (x + 2) 2 - 16 / x 4 + 8x 3 + 18x 2 + 8x - 24 . [1]
(b) Hence solve the equation x 4 + 8x 3 + 18x 2 + 8x - 24 = 0 . [4]
8 A circle, C, has equation x 2 - 6x + y 2 = 16 .
A second circle, D, has the following properties:
• The line through the centres of circle C and circle D has gradient 1.
• Circle D touches circle C at exactly one point.
• The centre of circle D lies in the first quadrant.
• Circle D has the same radius as circle C.
Find the coordinates of the centre of circle D. [5]
7 5
a2 - a2
9 Express 3 in the form a m + a n , where m and n are integers and a ! 0 or 1. [5]
a2 - a
© OCR 2024 H230/01 Jun24
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller chillzonetyrion. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £6.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
64438 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now