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The document specifies required stationery, black ink/pen rules, diagram and working conventions, and instructions to answer all questions within provided spaces. Questions cover coordinate distance, algebraic manipulation, rate of change from expressions, domain and range of functions, inverse functions, sequences and limits, trigonometric equations, inequalities, and expansion/simplification. It also includes quadratic sequences, matrix identities, and circle geometry with tangent-related equations.",{"@graph":69,"@context":109},[70,84,100],{"@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/june-2021-qp-level-2-certificate-further-mathematics-paper-1-non-calculator/207489/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":94,"encodingFormat":92,"isAccessibleForFree":95,"interactionStatistic":96},"DigitalDocument",{"name":87,"@type":88},"Mimi","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-06","2026-09-05",true,{"@type":97,"interactionType":98,"userInteractionCount":8},"InteractionCounter",{"@type":99},"ViewAction",{"@type":101,"mainEntity":102},"FAQPage",[103],{"name":104,"@type":105,"acceptedAnswer":106},"What topics are covered in the questions?","Question",{"text":107,"@type":108},"Topics include distance between points, rate of change from algebraic expressions, sketching/graph interpretation for linear equations, functions (domain, range, inverse), sequences (values of n and limiting values), trigonometry, inequalities, expansion and simplification, quadratic sequences, matrices, and circle geometry with tangents.","Answer","https://schema.org",{"og:url":83,"og:type":111,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":113,"canonical":83},"index,follow",{"doc_id":115,"site_id":62},207489,1788599761,{"code":4,"msg":5,"data":118},{"doc_id":115,"user_id":119,"nickname":87,"user_avatar":120,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":121,"file_id":122,"file_url":123,"file_type":124,"file_size":125,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":126,"language":127,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":128,"faqs":129,"seo_title":130,"seo_description":67,"update_tm":116,"read_time":131},2336477974920,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","| Please write clearly in block capitals. |  |  |  |\n| --- | --- | --- | --- |\n| Centre number |  | Candidate number |  |\n| Surname  \u003Cbr>Forename(s)  \u003Cbr>Candidate signature  \u003Cbr>I declare this is my own work. |  |  |  |\n\nLevel 2 Certificate  \nFURTHER MATHEMATICS  \nPaper 1 Non-Calculator  \nTime allowed: 1 hour 45 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 80.  \n• You may ask for more 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| 2–3 |  |\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| 22–23 | |\n| TOTAL |  |\n\n\n| Answer all questions in the spaces provided. |  |\n| --- | --- |\n| 1\u003Cbr>2 | Work out the distance between the points A (–3, 7) and B (5, 1)\u003Cbr>[2 marks] |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n|  | Answer   units\u003Cbr>y = x(2x4 – 7x3)\u003Cbr>Work out an expression for the rate of change of y with respect to x.\u003Cbr>[3 marks] |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n|  | Answer   |\n\noutside the box  \n3 Here are four sketch graphs.  \nCircle the letter of the sketch graph that represents 3x + 2y = 5  \n[1 mark]  \nbox  \n\n|  |\n| --- |\n| 6 |\n\n4 (a) The function f is given by f(x) = 3x – 5  \nThe range is 13 \u003C f(x) \u003C 19  \nWork out the domain of the function.  \n[1 mark]  \nAnswer    \n4 (b) The function g is given by g(x) = x2 – 4 with domain –1 \u003C x \u003C 3  \nWork out the range of the function.  \n[2 marks]  \nAnswer    \n4 (c) The function h is given by h(x) = 3~~ ~~+2~~ ~~x  \nWork out h–1(x)  \n[2 marks]  \nh–1(x) =    \nbox  \n5 The nth term of a sequence is ~~ ~~2nn417  \n5 (a) A term of the sequence has a value of 5  \nWork out the value of n.  \n[2 marks]  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n\nAnswer    \n5 (b) Write down the limiting value of the sequence as n → ∞  \n[1 mark]  \nAnswer    \nbox  \n\n|  |\n| --- |\n| 8 |\n\n6 Here is a sketch of y = sin x for 0 ° ⩽ x ⩽ 360 °  \nYou are given that sin 220 ° = –k  \nWork out the two values of x for 0° ⩽ x ⩽ 360° for which y = k  \n[2 marks]  \nAnswer   and    \n7 Solve 2x2 + 4 > (2x – 3)(x + 1)  \n[3 marks]  \nAnswer    \nbox  \n8 Simplify 3 ( 75 + 48 ) writing your answer as an integer.  \n[2 marks]  \n|  |\n| --- |\n|  |\n|  |\n|  |\n\nAnswer    \n9 Expand and simplify fully (2x – 5)(3x – 4)(x + 2)  \n[3 marks]  \nAnswer    \noutside the box  \n\n|  |\n| --- |\n| 10 |\n\n10 The first four terms of a quadratic sequence are  \n0 1 0 –3  \nWork out an expression for the nth term.  \n[3 marks]  \n\n|  |\n| --- |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n|  |\n\nAnswer    \nbox  \n11 􀂧􀂩􀂨 20 13􀂷􀂹􀂸 􀂨􀂧􀂩a0 0b4􀂷􀂹􀂸 = k I where k is a constant and I is the identity matrix.  \nWork out the values of a and b.  \n[4 marks]  \nAnswer a =   b =    \noutside the box  \n\n|  |\n| --- |\n| 7 |\n\n12 A circle, centre C (4,–2), passes through the origin and point A (8, 0) on the x-axis. The tangent at A is shown.  \n12 (a) Work out the equation of the circle.  \n[2 marks]  \n\n|  |\n| --- |\n|  |\n\nAnswer    \nbox","cbCaip9afVG48Oxh","https://ap.wps.com/l/cbCaip9afVG48Oxh","pdf",415501,28,"English","# Instructions\n## Materials and pen rules\n## Answer layout and rough work\n# Questions\n## Distance and coordinate geometry\n## Algebra: rate of change and expressions\n## Sketch graphs and equations\n## Functions: domain, range, inverse\n## Sequences: nth term and limits\n## Trigonometry: sin graph and solving for angles\n## Inequalities and simplification\n## Expanding products and quadratic sequences\n## Matrices and identity matrix\n## Circle equation and tangent","[{\"question\":\"What topics are covered in the questions?\",\"answer\":\"Topics include distance between points, rate of change from algebraic expressions, sketching/graph interpretation for linear equations, functions (domain, range, inverse), sequences (values of n and limiting values), trigonometry, inequalities, expansion and simplification, quadratic sequences, matrices, and circle geometry with tangents.\"}]","June 2021 QP - Level 2 Certificate Further Mathematics Paper 1 Non-Calculator | PDF",71]