iGCSE Further Maths Specimen Assessment Material - AQA

56 Pages·2013·1.24 MB·English

AQA Level 2 Certificate in
AQA Certificate in Further Mathematics (Level 2) Further Mathematics
from 2011 onwards
Specimen Assessment Materials 8360
Qualification Accreditation Number: TBC
Please note that where candidates enter for more than one qualification with the same accreditation number only one
For exams June 2012 onwards
grade will count towards School and College Performance Tables. As a result, some schools and colleges regard the
candidate as having only achieved one of the two qualifications. For certification June 2012 onwards
The same view may be taken if candidates take two qualifications that have a significant overlap of content.
Candidates with any doubts about their subject combinations should check with their chosen centre prior to starting
their programmes.
In the case of a candidate taking two qualifications with the same accreditation number that are of the same size
and level, eg, two full course GCSEs, the higher grade will count.
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aqa.org.uk/igcsemaths
Copyright © 2011 AQA and its licensors. All rights reserved.
The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales
(company number 3644723) and a registered charity (registered charity number 1073334).
Registered address: AQA, Devas Street, Manchester M15 6EX.
Version 1.0 MSD1233.11
AQALevel 2 CertificateinFurther Mathematics - May2011
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Contents
Background Information 4
Introduction 4
Paper1(Non-Calculator) 5
MarkScheme 19
Paper2(Calculator) 29
MarkScheme 45
Page 3
Background Information
Introduction
This Level 2 Certificate in Further Mathematics Thespecificationcontent is set out insix distinct
qualification fillsthegapfor high achieving topic areas althoughquestions will be askedthat
students by assessing their higher order range across thesetopics.
mathematicalskills, particularly in algebraic
Number
reasoning, ingreater depth without infringing upon
Algebra
AS Level mathematics,thus preparing themfully to
maximise their potential infurther studies at Level Co-ordinateGeometry (2dimensions only)
3. It offers theopportunity for stretchand challenge
Calculus
that builds onthe Key Stage4 curriculum and is
Matrix Transformations
intended as an additionalqualification totheGCSE
Mathematics, rather thanas areplacement. Geometry
Thecontent assumes prior knowledge of the Key
Papers
Stage4Programme of Study and covers the areas
Thesespecimenpapers have been designedto
of algebraandgeometry, which are crucial to
exemplify thequestion papers, tobesetfor our
further study inthe subject, ingreater depth and
Level 2 Certificatein Further Mathematics
breadth. This newqualification places anemphasis
Specification, forfirstqualification inJune 2012.
on higher order technical proficiency, rigorous
Theassociatedmark schemefollows each paper.
argument andproblem solving skills. It alsogives
an introductionto calculus andmatrices and Thequestionpapers should be readin conjunction
develops further skills intrigonometry,functions with AQA Level 2 Certificate in Further
andgraphs. Mathematics Specification 2011 onwards.This
specification is available on thewebsite
TheAQALevel 2 Certificate in Further
http://web.aqa.org.uk/qual/igcse/maths.php
Mathematics is an untiered Level 2 linear
qualification for learners who Thequestionpapers areintended torepresent the
lengthand balanceof the papers that will be set for
either already have, or are expectedto
achieve grades A andA* in GCSE the examination andtoindicate thetypes of
mathematics questions that will be used. It must be emphasised,
however, that thequestions have not been
are likely toprogress toA-Level study in
subjectedtotherigorous reviewthat would take
mathematics and possibly further
place with questions before usein examination.
mathematics.
It will be graded onafive-gradescale: A* with Markschemes
Distinction (A^), A*, A, Band C.
Principal Examiners have preparedthesemark
Thequalification is designed tobe assessed as a schemesfor specimen papers.Thesemark
full Level 2 mathematics qualification inits own schemes have not, therefore, beenthroughthe
right andis thereforenotdependent onGCSE normal process of standardising that would take
mathematics. placefor live papers.
Thereforethereareno prior learning requirements
but thereis the expectation that candidates have
some assumedknowledge.
Page 4
CentreNumber CandidateNumber
ForExaminer’sUse
Surname
OtherNames Examiner’sInitials
CandidateSignature
Pages Mark
Certificate in Further Mathematics
3
Level 2
4 -5
6 -7
Further Mathematics 8360/1
8 - 9
Level 2
10 - 11
Specimen Paper 1
12 - 13
Non-Calculator
TOTAL
Forthispaperyoumusthave:
 mathematicalinstruments.
Youmaynotuseacalculator.
Youmayuseacalculator.
Time allowed
1 hour 30 minutes
Instructions
 Use black ink or black ball-point pen. Drawdiagrams inpencil.
 Fill in the boxes at thetop of this page.
 Answer all questions.
 You must answer thequestions inthe space provided. Do not write outside the
box around eachpage or on blank pages.
 Do all rough work inthis book. Cross throughany work that you do not want to
be marked.
 In all calculations, showclearly howyou work out your answer.
Information
 Themarksfor questions are shown in brackets.
 Themaximum mark for this paper is 70.
 You may ask for moreanswer paper,graphpaper andtracing paper.
Thesemust betagged securely tothis answer booklet.
8360/1
Page 5
FormulaeSheet
4
Volume of sphere = r3 r
3
Surface area of sphere = 4r2
Volume of cone = 1r2h
3
Curved surface areaof cone = rl l
h
r
In anytriangle ABC
C
1
Area of triangle = ab sin C
2 b a
a b c A B
Sine rule = = c
sinA sinB sinC
Cosine rule a2 = b2 +c2 – 2bccos A
b2  c2  a2
cos A =
2bc
The Quadratic Equation
_ _
b (b2 4ac)
Thesolutions of ax2 + bx+ c = 0, where a 0, aregiven by x =
2a
TrigonometricIdentities
sinθ
tan  sin2  + cos2   1
cosθ
Page 6 8360/2
3
Donotwrite
outsidethe
box
Answer all questions in the spaces provided.
1 (a) Solve 7(3x 1) + 2(x +7) = 3(6x1)
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Answer x= ................................................................. (4marks)
1 (b) Solve 3x  10 = 4
….…………………………………………………………………………………………….
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….…………………………………………………………………………………………….
Answer x= ................................................................. (2marks)
Turn over for the next question
6
Turn over 
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4
Donotwrite
outsidethe
2 (a) Thenthterms of two sequences are 4n + 13 and 6n 21 box
Whichterm has thesame value in each sequence?
………….…………………………………………………………………………………….
………….…………………………………………………………………………………….
…………….………………………………………………………………………………….
Answer ..................................................................... (3marks)
2 (b) Thefirst five terms of aquadratic sequence are 4 10 18 28 40
Work out an expressionfor the nthterm.
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Answer ..................................................................... (5marks)
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5
Donotwrite
outsidethe
box
3 (a) Onthe axes belowsketch thegraphof y= x2 9
Label clearly any points of intersection with the x-axis.
y
x
O
(2marks)
3 (b) Writedown all the integer solutions to x2 9 0
…….………………………………………………………………………………………….
…….………………………………………………………………………………………….
Answer ..................................................................... (2marks)
Turn over for the next question
12
Turn over 
Page 9
8360/1
6
Donotwrite
outsidethe
box
4 Afunctionf(x) is definedas
f(x) =3x 0  x 1
= 3 1 x 3
= 12  3x 3 x 4
Calculate the areaenclosed by thegraphof y =f(x) andthe x-axis.
y
4
3
2
1
0
x
0 1 2 3 4
…….………………………………………………………………………………………….
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…….………………………………………………………………………………………….
Answer ...........................................................units2 (5marks)
Page 10
8360/1