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The assessment covers algebraic manipulation and factorisation of polynomial expressions, geometric and trigonometric problem-solving in triangles, and sector-based mensuration using radians. The paper specifies clear working requirements and prohibits writing on the formulae page, with answers entered in provided 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is the examination date and paper reference shown on the document?","Question",{"text":106,"@type":107},"The paper is dated Monday 17 June 2019 and shows Paper Reference 4PM1/01 for International GCSE Further Pure Mathematics Paper 1.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"What key rule is stated about writing on the formulae page?",{"text":111,"@type":107},"Nothing should be written on the formulae page; any writing there gains no credit.",{"name":113,"@type":104,"acceptedAnswer":114},"What types of topics are included in the questions?",{"text":115,"@type":107},"The questions include polynomial factorisation and manipulation, triangle trigonometry and area calculations, and mensuration involving a circle sector and shaded regions using 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surname   | Other names   |\n| --- | --- |\n\nMonday 17 June 2019      \n\n| Afternoon(Time:2 hours)   | Paper Reference 4PM1/01   |\n| --- | --- |\n| Further Pure Mathematics  \u003Cbr>Paper 1   |  |\n\nCalculators may be used.Total Marks  \n# Instructions\n\n● Use black ink or ball-point pen.  \n● Fill in the boxes at the top of this page with your namecentre number and candidate number.  \n● Answer all questions.  \n● Without sufficient working,correct answers may be awarded no marks.  \n● Answer the questions in the spaces provided-there may be more space than you need.  \n● You must NOT write anything on the formulae page.Anything you write on the formulae page will gain NO credit.  \n# Information\n\n● The total mark for this paper is 100.  \n● The marks for each question are shown in brackets-use this as a guide as to how much time to spend on each question.  \n# Advice\n\n● Read each question carefully before you start to answer it.  \n● Check your answers if you have time at the end.  \n# International GCSE in Further Pure Mathematics Formulae sheet\n\n\n| Mensuration   |\n| --- |\n| Surface area of sphere=4πr²  \u003Cbr>Curved surface area of cone =πr×slant height   |\n| Series   |\n| Arithmetic series  \u003Cbr>Sum to n terms,  \u003Cbr>Geometric series  \u003Cbr>Sum to n terms,  \u003Cbr>Binomial series  \u003Cbr>for |\u003C1,neQ   |\n| Calculus   |\n| Quotient rule (differentiation)   |\n| Trigonometry   |\n| Cosine rule  \u003Cbr>In triangle ABC:a²=b²+c²-2bccos A  \u003Cbr>sin(A+B)=sin A cos B+cos A sin B  \u003Cbr>sin(A-B)=sin A cos B-cos A sin B  \u003Cbr>cos(A+B)=cos A cos B-sin A sin B  \u003Cbr>cos(A-B)=cos A cos B+sin A sin B   |\n| Logarithms   |\n|  |\n\nDO NOTWRITEINTHIS AREA  \nAnswer all ELEVEN questions.  \nWrite your answers in the spaces provided.  \nYou must write down all the stages in your working.  \n1f(x)=x³+2x²-5x-6  \n(a)Factorise x²-x-2  \n(1)  \n(b)Hence,or otherwise,show that(x²-x-2)is a factor of f(x).  \n(3)  \n-                  -                                       -                   -                    -                        (Total for Question 1 is 4marks)     \nP 5  8  2  8  6 A 0  3  3  6  \n2 Given thatcan be writen i the formwhere a and b are integersand c is prime,find the value of a,the value of b and the value of c.  \nShow your working clearly.  \n(3)  \nDO NOT WRITEIN THIS AREA  \nDO NOT WRITEIN THIS AREA  \nDO NOT WRITEINTHIS AREA  \nP58286A 0436  \nDO NOTWRITE IN THIS AREA  \nDO NOT WRITE IN THIS AREA  \nDO NOT WRITE IN THIS AREA  \n# Question 2 continued\n\n ، ٠ ،  ،  ٠ ، ، ٠ ء٠ ٠ ٠، ، ٠ ٠  ،  ٠ ٠٠ ، ، ء =  ٠ ٠ ء  ٠ ٠  ء ٠٠  ، ء ٠ ٠  ، ء ٠، ،  ٠٠ ٠  ، ء٠ه  ، ٠٠ ٠ ٠  ء٠،  ، ٠ ٠٠  ، ء ٠ ، ،  ٠٠ و ٠ و ١ ١ ؛  ٦ و١Y ٠١١١;ة;١١ ؛٠و١١١ةو١٥ ؟ةو١١؛ة٦١١٠ة١١١?٦ و3 ؟ ة ١ ١ ١ ؟ةو١١ ؟ةو١١ ؟ق١١و ؟ةو١١؟وو١١ ؟ة١١١؟٩و١١ »٦١١١؟٥١١و ٍةو١١ ٣ ٠ ، ، ، ء٠ ، ،، ء ٠ ،  ، ء ٠، ، ، ء٠، ، ، ءە، ،ء٠، ، ، ٠٠، ، ،ء٠، ، ٠٠، ،،ء٠، ، ، ٠ە، ،  ، ، ، ء٠ ، ، ،ء٠ه ،  ، ٠ ، ، ، ء ٠ ، ، ، ء ٠٠ ،  ءە ، ، ، ء ٠، ، ، ء٠٠٠٠٠٠٠٠٠ ٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠٠ ١ ١ ة و ١ ١ و ة و ١ ١ Y ق ١ ١١١ق و ١١  ةو١١١ ق١١١؛ق١١١و ةو١١Yق١١١١ق3١١ ؟ة١١١١ ق١                       (Total for Question 2 is 3marks)     \nP58286A0536  \n3 In triangle ABC,AC=7cm,BC=10cm and angle BAC=65°  \n(a)Find,to the nearest 0.1°,the size of angle ABC.  \n(b)Find,in cm²to 3 significant figures,the area of triangle ABC.  \n……………          …  ………………  …  …      ………………  \nP58286A 0636  \n(3)  \n(3)  \nDO NOT WRITEIN THIS AREA  \nDO NOT WRITEIN THIS AREA  \nDO NOT WRITEINTHIS AREA  \nDO NOTWRITE IN THIS AREA  \nDO NOT WRITE IN THIS AREA  \nDO NOT WRITE IN THIS AREA  \n# Question 3 continued\n\n ، ٠ ،  ،  ٠ ، ، ٠ ء٠ ٠ ٠، ، ٠ ٠  ،  ٠ ٠٠ ، ، ء =  ٠ ٠ ء  ٠ ٠  ء ٠٠  ، ء ٠ ٠  ، ء ٠، ،  ٠٠ ٠  ، ء٠ه  ، ٠٠ ٠ ٠  ء٠،  ، ٠ ٠٠  ، ء ٠ ، ،  ٠٠ و ٠ و ١ ١ ؛  ٦ و١Y ٠١١١;ة;١١ ؛٠و١١١ةو١٥ ؟ةو١١؛ة٦١١٠ة١١١?٦ و3 ؟ ة ١ ١ ١ ؟ةو١١ ؟ةو١١ ؟ق١١و ؟ةو١١؟وو١١ ؟ة١١١؟٩و١١ »٦١١١؟٥١١و ٍةو١١ ٣ ٠ ، ، ، ء٠ ، ،، ء ٠ ،  ، ء ٠، ، ، ء٠، ، ، ءە، ،ء٠، ، ، ٠٠، ، ،ء٠،","cbCaidPpBmWFVPtI","https://ap.wps.com/l/cbCaidPpBmWFVPtI","pdf",2463815,36,"English","# Instructions\n## Answering guidance\n# Information\n## Marks and time guidance\n# Formulae sheet\n## Mensuration\n## Series\n## Calculus\n## Trigonometry\n## Logarithms\n# Questions\n## Question 1\n## Question 2\n## Question 3\n## Question 4","[{\"question\":\"What is the examination date and paper reference shown on the document?\",\"answer\":\"The paper is dated Monday 17 June 2019 and shows Paper Reference 4PM1/01 for International GCSE Further Pure Mathematics Paper 1.\"},{\"question\":\"What key rule is stated about writing on the formulae page?\",\"answer\":\"Nothing should be written on the formulae page; any writing there gains no credit.\"},{\"question\":\"What types of topics are included in the questions?\",\"answer\":\"The questions include polynomial factorisation and manipulation, triangle trigonometry and area calculations, and mensuration involving a circle sector and shaded regions using radians.\"}]","June 2019 QP - International GCSE Further Pure Mathematics (Paper 1) | PDF",91]