Version 1.0 Level Certificate in Further Mathematics Practice Paper Set 1 Paper 1 860/1 Mark Scheme
Mark Schemes Principal Examiners have prepared these mark schemes for practice papers. These mark schemes have not, therefore, been through the normal process of standardising that would take place for live papers. It is not possible to indicate all the possible approaches to questions that would gain credit in a live examination. The principles we work to are given in the glossary on page of this mark scheme. Evidence of any method that would lead to a correct answer, if applied accurately, is generally worthy of credit. Accuracy marks are awarded for correct answers following on from a correct method. The correct method may be implied, but in this qualification there is a greater expectation that method will be appropriate and clearly shown. Further copies of this Mark Scheme are available to download from the AQA Website: www.aqa.org.uk Copyright 011 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number 6447) and a registered charity (registered charity number 1074). Registered address: AQA, Devas Street, Manchester 5 6EX
AQA Level Certificate in Further Mathematics - 860/1 - Set 1 - Paper 1 - Practice Paper Glossary for Mark Schemes These examinations are marked in such a way as to award positive achievement wherever possible. Thus, for these papers, marks are awarded under various categories. M A B M Dep BDep ft SC oe Method marks are awarded for a correct method which could lead to a correct answer. Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous independent mark has been awarded. Follow through marks. Marks awarded following a mistake in an earlier step. Special case. Marks awarded within the scheme for a common misinterpretation which has some mathematical worth. Or equivalent. Accept answers that are equivalent. eg, accept 0.5 as well as 1
Practice Paper - Paper 1 - Set 1-860/1 - AQA Level Certificate in Further Mathematics Paper 1 - Non-Calculator 1(a) 6 0 (< x oe ) 4 5 6 A For any correct or all 4 correct with one incorrect 1(b)(i) Any value of n where 1 < n < B1 1(b)(ii) Any value of n where 0 < n < 1 B1 Condone (n =) 0 1(b)(iii) Any value of n where 1 < n < 0 B1 (a) Fully correct graph B B1 Straight line from (0, ) to (, ) 5 4 1 y B1 Straight line from (, ) to (4, 5) B1 Straight line from (4, 5) to (9, 0) 0 0 1 4 5 6 7 8 9 x (b) 0 y 5 B1ft ft Their graph in (a) 18 m (tan x) = = 0 65 65 m oe eg, = 0 18 18 m = 65 0 9 (65 0 =) 5 and their 9 and Yes B1ft 4
AQA Level Certificate in Further Mathematics - 860/1- Set 1 - Paper 1 - Practice Paper 4(a) 1 or or 4 48 1 48 48 48 1 or 4 4 or 4 1 1 48 4 4 or 48 4 or 48 1 is M 4 1 or 0.5 4(b) 6 6 (+ 6 6 ) oe eg, 6 4 4 5
Practice Paper - Paper 1 - Set 1-860/1 - AQA Level Certificate in Further Mathematics 5(a) Two correct sketches B B1 Circle, centre O radius 1 y B1 Straight line, gradient through (0, 1) - - -1 O 1 x -1 - - 5(b) Correct region shaded B1ft ft If two graphs attempted y in (a) 1 - - -1 O 1 x -1 - - 6
AQA Level Certificate in Further Mathematics - 860/1- Set 1 - Paper 1 - Practice Paper 6 1 ( 5 ) ( 5 ) + cos θ = 1 16 5 4 4 ft and 5 5 16 ft If both square roots of their 5 Alt 6 Right-angled triangle drawn with θ marked with opposite and hypotenuse 5, 4, 5 triangle indicated eg, by labelling other side 4 4 4 ft and 5 5 ft If their adj their hyp 7 Eliminate y from any of the equations 1 x + 11 = 1 x + 14 or 1 x + 11 = x 16 or 1 x + 14 = x 16 Manipulates their equation Allow one error x + 66 = x + 84 x + = 4x or or x + 4 = 6x 48 x = 18 y = 0 Checks their (18, 0) in third equation and yes ft B1ft 8 Angle BOC = x Angle at centre = angle at circumference Angle BCO = x Isosceles triangle x + x + x = 180 Angle sum of triangle = 180 x = 90 Isosceles triangle 7
Practice Paper - Paper 1 - Set 1-860/1 - AQA Level Certificate in Further Mathematics 9(a) (y =) 1 π x x B1 9(b) πx B1 9(c) π 5 75π ft 10 (x 7)( x ) B B1 For numerator (x )(x ) B1 For denominator (x + x =) x(x + ) B1 x (their fraction) x x x x 7 x or x 7x x 11 d y = x + 6x + dx M One term correct 1 + 6 1 + Allow these marks for showing () + 6 () + substitution into their dy dx Obtains 1 for both gradients 1 Multiplies throughout by x or y or or xy or x or y or xy 6x = 1y - xy Collects terms in x on one side from their equation eg, 6x + xy = 1y Factorises to x(..) eg, x(6 + y) = 1y x = 1y oe 6 y 8
AQA Level Certificate in Further Mathematics - 860/1- Set 1 - Paper 1 - Practice Paper 1 or a = or a 9 or x 9 or a b = 18 or 9 Find one linear factor (x 9)(x + ) Find another linear factor (x + )(x )(x + ) 14(a) Square drawn with vertices O (0, 0), A' (0, 1), B' (1, 1), C' (1, 0) B B1 Attempt at matrix multiplication to give one or more of the vertices A', B', C' or states reflection y = x or correct diagram not labelled correctly 14(b) 0 1 B B1 For each column 1 0 Their 0 0 0 1 Attempt at multiplying their two matrices 1 0 0 0 9
Practice Paper - Paper 1 - Set 1-860/1 - AQA Level Certificate in Further Mathematics 15(a) Shows 60 angle and a right-angled triangle (with right angle marked) and side 1 (cm) marked B B1 Any of the criteria shown Alt 15(a) = + cos60 oe 4 = 8 cos60 15(b) (x + 1) = (x + 4) + (x + ) (x + 4)(x + ) 1 4x + x + x + 1 = 4x + 8x + 8x + 16 + x + x + x + 9 (x + 4x + 6x + 1) 4x + x + x + 1 = 4x + 8x + 8x + 16 + x + x + x + 9 (x + 4x + 6x + 1) Any of the 4 term expansions or all four with errors All correct x 8x = 1 or x 8x 1 = 0 oe Must be simplified to terms their 8 (x ) their 8 = their 1 + ( or _ ( 8) _ ( _ 8) 1 4 1 1 ) oe Substitutes x = 4 + 7 in their equation x = 4 + 8 Must reject the other solution Shows substitution satisfies the correct equation. 10
AQA Level Certificate in Further Mathematics - 860/1- Set 1 - Paper 1 - Practice Paper 11
Practice Paper - Paper 1 - Set 1-860/1 - AQA Level Certificate in Further Mathematics 1