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The paper specifies required materials (mathematical instruments only, no calculator), strict answer layout within provided boxes, and that working must be shown clearly for all calculations. A formulae sheet supports sphere and cone calculations, triangle area rules, quadratic solutions, and trigonometric identities, with a total of 70 marks.",{"@graph":69,"@context":116},[70,84,99],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/further-mathematics-paper-1-non-calculator-friday-14-june-2019/207490/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Grenda","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What tools and rules are required for this Non-Calculator paper?","Question",{"text":106,"@type":107},"Use mathematical instruments but do not use a calculator. Use black ink/ball-point pen, draw diagrams in pencil, and show working clearly for calculations.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"How must answers be presented?",{"text":111,"@type":107},"Answer all questions in the spaces provided and do not write outside the box. If extra space is needed, use the lined pages at the end and write the question number beside the answer.",{"name":113,"@type":104,"acceptedAnswer":114},"What topics and formulae are covered to help solve the questions?",{"text":115,"@type":107},"The paper includes coordinate geometry, inequalities, algebraic manipulation, transformation matrices, piecewise functions with graphing, factorisation, and cone/sphere/trigonometric formulae. A formulae sheet provides key identities and rules such as triangle area, sine/cosine rules, and the quadratic equation.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},207490,1788599762,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":133,"language":134,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":67,"update_tm":123,"read_time":138},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","| Please write clearly in block capitals. |  |  |  |\n| --- | --- | --- | --- |\n| Centre number |  | Candidate number |  |\n| Surname  \u003Cbr>Forename(s)  \u003Cbr>Candidate signature   |  |  |  |\n\nLevel 2 Certificate  \nFURTHER MATHEMATICS  \nPaper 1 Non-Calculator  \nFriday 14 June 2019 Afternoon Time allowed: 1 hour 30 minutes  \nMaterials  \nFor this paper you must have:  \n• mathematical instruments. You must not use a calculator.  \nInstructions  \n• Use black ink or black ball-point pen. Draw diagrams in pencil.  \n• Fill in the boxes at the top of this page.  \n• Answer all questions.  \n• You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages.  \n• If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s) .  \n• Do all rough work in this book. Cross through any work you do not want to be marked.  \n• In all calculations, show clearly how you work out your answer.  \nInformation  \n• The marks for questions are shown in brackets.  \n• The maximum mark for this paper is 70.  \n• You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer book.  \n\n| For Examiner’s Use |  |\n| --- | --- |\n| Pages | Mark |\n| 3 |  |\n| 4−5 |  |\n| 6−7 |  |\n| 8−9 |  |\n| 10−11 |  |\n| 12−13 |  |\n| 14−15 |  |\n| 16−17 |  |\n| 18−19 |  |\n| 20−21 |  |\n| TOTAL |  |\n\n\n| Formulae Sheet |\n| --- |\n| Volume of sphere = 43 πr3 Surface area of sphere = 4πr2\u003Cbr>Volume of cone = 13 πr2 h\u003Cbr>Curved surface area of cone = πrl\u003Cbr>In any triangle ABC\u003Cbr>Area of triangle = 12 ab sin C Sine rule sianA = si~~ ~~bnB = sicnC\u003Cbr>Cosine rule a 2 = b 2 + c 2 – 2bc cos Acos A = b2~~ ~~+c22bc−~~ ~~a~~ ~~2\u003Cbr>The Quadratic Equation\u003Cbr>The solutions of ax 2 + bx + c = 0, where a ≠ 0, are given by x = _~~ ~~b~~ ~~±~~  ~~(b22a~~ ~~_~~ ~~4ac)\u003Cbr>\u003Cbr>\u003Cbr>|\n| Trigonometric Identities\u003Cbr>tan θ ≡ scoinsθ~~θ ~~ sin 2 θ + cos2 θ ≡ 1 |\n\nDo not write outside the box  \n\n| Answer all questions in the spaces provided. | outside the box\u003Cbr>3 |\n| --- | --- |\n| 1 A straight line passes through the points (−2, 11) and (1, 2)\u003Cbr>Work out the equation of the line.\u003Cbr>Give your answer in the form y = mx + c\u003Cbr>[3 marks]\u003Cbr>\u003Cbr>Answer  \u003Cbr>Turn over for the next question |  |\n\n2 Write  5  +  a  as a single fraction.  \n6a 4  \nGive your answer in its simplest form.  \n[2 marks]  \nAnswer    \nnot write outside the box  \n\n| 3 Work out the smallest integer value of x that satisfies the inequality 8 – 5x ˂ 26\u003Cbr>[2 marks]\u003Cbr>\u003Cbr>Answer  \u003Cbr>4 p(x – 1) + 2(3x + k) ≡ 4(x + 2) where p and k are integers.\u003Cbr>Work out the values of p and k.\u003Cbr>[4 marks]\u003Cbr>\u003Cbr>Answer p =   , k =   | box |\n| --- | --- |\n|  |  |\n|  | 8 |\n\n5 Solve 3 ( 2x −10) = 2  \n[3 marks]  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n\nx =    \n􀂧 2a b 􀂷  \n6 The transformation matrix 􀂩􀂨 −b −a 􀂹􀂸 maps the point (3, 4) onto the point (8, −7)  \nWork out the values of a and b.  \n[5 marks]  \nAnswer a =   , b =    \nnot write outside the box  \n7 A function is given by f(x) = −2x −1 ⩽ x ˂ 0 = x(4 – x) 0 ⩽ x ˂ 3  \n= 2x – 3 3 ⩽ x ⩽ 4  \nDraw the graph of y = f(x) on the grid.  \n[4 marks]  \nbox  \n\n|  |\n| --- |\n| 12 |\n\n8 ABC is a straight line.  \nA is the point (−4, 5) C is the point (20 , −7) AB : BC = 5 : 3  \nWork out the coordinates of B.  \n[4 marks]  \nAnswer (  ,  )  \nbox  \n9 y = 2x(x2 – 5x)  \nCircle the expression for ~~ ~~ddyx  \n[ 1 mark]  \n2(2x – 5) 6x2 – 20 3x2 – 10x 6x2 – 20x  \n10 Factorise fully 6x2 + 26xy – 20y2  \n[3 marks]  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n\nAnswer    \nTurn over for the next question  \noutside the box  \n\n|  |\n| --- |\n| 8 |\n\n11 A cone has base radius r cm, perpendicular height h cm and slant height l cm The curved surface area is 60π cm2  \nl = 3r  \nWork out the value of h.  \nGive your answer in the form a 10 where a is an integer greater than 1  \nYou must show your working.  \n[5 marks]  \n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n\nAnswer    \nbox","cbCaipSx3t2SYvJo","https://ap.wps.com/l/cbCaipSx3t2SYvJo","pdf",919022,28,"English","# Instructions and Information\n## Materials and Pen Requirements\n## Answer Layout Rules\n## Mark Scheme Overview\n# Formulae Sheet\n## Sphere and Cone\n## Triangle Area and Trig Identities\n## Quadratic Equation\n# Questions\n## Coordinate Geometry and Lines\n## Fractions and Simplification\n## Inequalities and Integer Solutions\n## Algebraic Equations and Parameters\n## Solving Linear/Proportional Equations\n## Transformation Matrices\n## Piecewise Functions and Graphing\n## Ratios on a Line Segment\n## Expanding and Selecting Expressions\n## Factorisation\n## Cone Geometry and Exact Form Answers","[{\"question\":\"What tools and rules are required for this Non-Calculator paper?\",\"answer\":\"Use mathematical instruments but do not use a calculator. Use black ink/ball-point pen, draw diagrams in pencil, and show working clearly for calculations.\"},{\"question\":\"How must answers be presented?\",\"answer\":\"Answer all questions in the spaces provided and do not write outside the box. If extra space is needed, use the lined pages at the end and write the question number beside the answer.\"},{\"question\":\"What topics and formulae are covered to help solve the questions?\",\"answer\":\"The paper includes coordinate geometry, inequalities, algebraic manipulation, transformation matrices, piecewise functions with graphing, factorisation, and cone/sphere/trigonometric formulae. A formulae sheet provides key identities and rules such as triangle area, sine/cosine rules, and the quadratic equation.\"}]","Further Mathematics - Paper 1 Non-Calculator - Friday 14 June 2019 | PDF",71]