Mathematics > Higher Education > Monday 18 October 2021 – Afternoon A Level Mathematics A H240/03 Pure Mathematics and Mechanics. L (All)

Monday 18 October 2021 – Afternoon A Level Mathematics A H240/03 Pure Mathematics and Mechanics. Latest Revision Guide. Graded A+

Document Content and Description Below

Formulae A Level Mathematics A (H240) Arithmetic series S n a l n a 2 1 n d n 2 1 12 = + ^ ^ h h = + " - , Geometric series S r a r 11 n n = - - ^ h S r a 3 = 1- for r 1 1 Binomi... al series a b n a a n nC C n n b an n b a C b b n N r n r r n 1 1 2 2 2 ^ ^ + = h h + + - - + + f f - + + ! , where ! ! n ! r r n r n nC C r n r = = = c m ^ - h x nx ! ! , n n x r n n n r 1 1 x x n 2 1 1 1 ^ + = hn + + ^ ^ - h h 2 + + f - - f^ + h r +f ^ 1 1 ! Rh Differentiation tankx k k sec2 x sec t x x an -cosec2x -cosec c x x ot sec x cot x cosec x f^xh f l^xh Quotient rule y uv = , yx v v ux u vx dd dd dd = 2 - Differentiation from first principles x lim h x h x f f f h 0 = + - " l^ h ^ ^ h h Integration ln xx x x c ff d f = + c l dde ^^ ^ hh h x x x n x c 1 1 f f d f n n 1 = + + + ; l^ h h a ^ k a ^ hk Integration by parts u vx x uv v ux x dd d dd ; ; = - d Small angle approximations sin i i . , Section A: Pure Mathematics Answer all the questions. 1 Show in a sketch the region of the x-y plane within which all three of the following inequalities hold. y x 2 H , x y + G 2, x H 0. You should indicate the region for which the inequalities hold by labelling the region R. [3] 2 A B C 60° (4 +h) cm (4 –h) cm The diagram shows triangle ABC in which angle A is 60° and the lengths of AB and AC are ( ) 4 c +h m and ( ) 4 c -h m respectively. (a) Show that the length of BC is pcm where p h 2 2 = + 16 3 . [2] (b) Hence show that, when h is small, p h . 4+ + m n 2 4 h , where m and n are rational numbers whose values are to be determined. [4] 3 An arithmetic progression has first term 2 and common difference d, where d ! 0. The first, third and thirteenth terms of this progression are also the first, second and third terms, respectively, of a geometric progression. By determining d, show that the arithmetic progression is an increasing sequence. [5]5 © OCR 2021 H240/03 Oct21 Turn over 4 (a) Sketch, on a single diagram, the following graphs. • y x = -1 • y kx = , where k is a negative constant [2] (b) Hence explain why the equation x x- = 1 k has exactly one real root for any negative value of k. [1] (c) Determine the real root of the equation x x- = 1 6 - . [2] 5 A particle P moves along a straight line in such a way that at time t seconds P has velocity vm s-1, where v t = + 12 cos s 5 in t. (a) Express v in the form R t cos( ) - a , where R 2 0 and 0 1 1 a r 2 1 . Give the value of a correct to 4 significant figures. [3] (b) Hence find the two smallest positive values of t for which P is moving, in either direction, with a speed of 3m s-1. [3] 6 The equation 6 2 arcsin( ) x x - - 1 0 2 = has exactly one real root. (a) Show by calculation that the root lies between 0.5 and 0.6. [2] In order to find the root, the iterative formula x p n n +1 = +q r sin( ) x2 , with initial value x 0 5 . 0 = , is to be usedcos 1 i i . - 2 1 2, tan i i . where i is meas [Show More]

Last updated: 2 years ago

Preview 1 out of 12 pages

Buy Now

Instant download

We Accept:

We Accept
document-preview

Buy this document to get the full access instantly

Instant Download Access after purchase

Buy Now

Instant download

We Accept:

We Accept

Reviews( 0 )

$12.00

Buy Now

We Accept:

We Accept

Instant download

Can't find what you want? Try our AI powered Search

113
0

Document information


Connected school, study & course


About the document


Uploaded On

Jun 28, 2022

Number of pages

12

Written in

Seller


seller-icon
SupremeDocs

Member since 3 years

25 Documents Sold

Reviews Received
1
0
0
1
1
Additional information

This document has been written for:

Uploaded

Jun 28, 2022

Downloads

 0

Views

 113

Document Keyword Tags


$12.00
What is Scholarfriends

In Scholarfriends, a student can earn by offering help to other student. Students can help other students with materials by upploading their notes and earn money.

We are here to help

We're available through e-mail, Twitter, Facebook, and live chat.
 FAQ
 Questions? Leave a message!

Follow us on
 Twitter

Copyright © Scholarfriends · High quality services·