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The questions require all working to be shown, prohibit the use of a calculator, and instruct students to state units where appropriate and use blue or black ink. Topics include algebraic expansion and simplification, functions and solving for inputs, indices and radicals, statistics with median and interquartile range, trigonometry ordering and justification, geometry and sine rule relationships, coordinate geometry, scatter graphs with line of best fit, and analytic geometry with parabolas and circle geometry.",{"@graph":69,"@context":122},[70,84,105],{"@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/n5-essential-skills-national-5-mathematics-practice-exam-2026-paper-1-non-calculator/458839/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/n5-essential-skills-national-5-mathematics-practice-exam-2026-paper-1-non-calculator/458839.png","ImageObject",300,407,{"name":92,"@type":93},"gewufjwa","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Is a calculator allowed for this exam paper?","Question",{"text":112,"@type":113},"No calculator is allowed. Answers must be completed without a calculator.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What do students need to include to earn full marks?",{"text":117,"@type":113},"Students must show their working, state units where appropriate, and attempt all questions.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of topics are covered in Paper 1?",{"text":121,"@type":113},"The paper covers algebraic manipulation and functions, surds and radicals, statistics (median and interquartile range), trigonometry, and geometry/graph questions including a scatter graph and a parabola.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},458839,1791438777,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":46},3985747882900,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","N5  \nEssential Skills National 5  \nMathematics  \nPractice Exam 2026  \n| Paper 1 | (Non-calculator) |\n| --- | --- |\n| Time | 1 hour |\n\nTotal marks – 40  \nAttempt ALL questions.  \nYou may NOT use a calculator.  \nTo earn full marks, you must show your working in your answers.  \nState the units for your answer where appropriate.  \nUse blue or black ink.  \nMarks available are harsh but I wanted as much course coverage as possible.  \nFORMULAE LIST  \nThe roots of  \nSine rule  \nCosine rule  \nArea of a triangle  \nVolume of a sphere  \nVolume of a cone  \nVolume of a pyramid  \nStandard deviation:  \nor  \n􀜽􀝔2 + 􀜾􀝔 + 􀜿 = 0 are 􀝔 = −􀜾~~ ~~±~~ ~~√(􀜾2􀜽2~~ ~~−~~ ~~4􀜽􀜿)  \n􀜽  \nsin 􀜣  \n=  \n􀜾 􀜿  \n~~ ~~ = ~~ ~~  \nsin 􀜤 sin 􀜥  \n􀜽 2 = 􀜾 2 + 􀜿 2 − 2􀜾􀜿 cos 􀜣 or cos 􀜣 = 􀜾~~ ~~2~~ ~~+􀜿2􀜾2􀜿~~ ~~−~~ ~~􀜽~~ ~~2  \n􀜣 = 12 􀜽􀜾 sin 􀜥  \n􀜸 = 43 􀟨􀝎3  \n􀜸 = 13 􀟨􀝎2 ℎ  \n􀜸 = 13􀜣ℎ  \n􀝏 = √∑~~ ~~(􀝔􀝊~~ ~~−~~ ~~􀝔1)2  \n􀝏 = √∑~~ ~~􀝔~~ ~~2􀝊−−(∑1􀝔~~􀝊~~)2  \n,  \nwhere 􀝊 is the sample size.  \nAttempt ALL questions  \nTotal marks – 40  \n1. Evaluate 2 4 ÷ 1 2  \n9 3.  \nGive your answer in its simplest form. 2  \n2. Expand and simplify (􀝔 − 3)(2􀝔2 − 3􀝔 + 1) . 3  \n3. A function is defined as 􀝂(􀝔) = 􀝔 2 − 􀝔 + 3.  \nGiven that 􀝂(􀝌) = 5 , find the value(s) of 􀝌 . 3  \n4. Express √18 + 4√2 − √50 3  \n5. The ages of 10 customers in a coffee shop are listed below.  \n13 16 16 17 21 29 36 45 49 51  \nCalculate the median and interquartile range of the ages. 3  \n6. Write the following in order, starting with the smallest.  \nsin 60° sin 180° sin 330°  \nJustify your answer. 2  \nV  \n7. In triangle STV  \n• ST = 8 centimetres  \n• SV = 6 centimetres  \n• angle VST = 30°  \nGiven that 􀝏􀝅􀝊30° = 12 , show that sin 􀜵􀜸􀜶 = 23.  \nS  \nT  \n3  \n1  \n8. (a) Expand and simplify 􀝔 (􀝔2 − 􀝔 −1) 2  \n(b) Hence, evaluate when 􀝔 = 9. 2  \n9. Given 􀢇 = ( 1) and 􀢈 = ( 2)  \nCalculate |2􀢇 − 􀢈| . 3  \n10. In a cycling race, riders start at separate times.  \nThe scatter graph shows the relationship between the time spent cycling, T minutes, and the distance remaining to the finish, D kilometres.  \nA line of best fit has been drawn.  \nPoint A represents a cyclist who has been cycling for 2 minutes and is 30 km from the finish.  \nPoint B represents a cyclist who has been cycling for 8 minutes and is 12 km from the finish.  \n􀜶  \n(a) Find the equation of the line of best fit in terms of D and T. 3  \n(b) Use your equation to estimate how far a cyclist is from the finish after 5 minutes. 1  \n11. A parabola has equation 􀝕 = 􀝔 2 + 4􀝔 + 3.  \n(a) Write the equation in the form 􀝕 = (􀝔 + 􀜽)2 + 􀜾 . 2  \n(b) Sketch the curve 􀝕 = 􀝔 2 + 4􀝔 + 3 , showing the coordinates of the turning point and the point of intersection with the 􀝕 −axis. 2  \n12. The diagram shows the circle with centre O.  \n• QR is a tangent at point M.  \n• MN is a diameter.  \n• Angle MPQ is 113° .  \nCalculate the  \nsize of shaded angle MQP.  \n3  \n􀜱  \n􀜯  \n􀜳  \n􀜰  \n􀜴  \n13. The diagram shows the straight lines 4􀝔 − 6􀝕 = 17 and 3􀝔 + 􀝕 = 10.  \n􀝕  \n4􀝔 − 6􀝕 = 17  \n􀝔  \n􀜲  \n3􀝔 + 􀝕 = 10  \nEstablish the coordinates of the point of intersection, P. 3  \n[ END OF QUESTION PAPER ]","cbCaijswg95EOmEd","https://ap.wps.com/l/cbCaijswg95EOmEd","pdf",290989,"English","# Practice Exam Instructions\n## Allowed materials and marking guidance\n# Question Paper\n## Algebra and functions\n## Surds and indices\n## Statistics\n## Trigonometry\n## Geometry and bearings\n## Coordinate geometry and graphs","[{\"question\":\"Is a calculator allowed for this exam paper?\",\"answer\":\"No calculator is allowed. Answers must be completed without a calculator.\"},{\"question\":\"What do students need to include to earn full marks?\",\"answer\":\"Students must show their working, state units where appropriate, and attempt all questions.\"},{\"question\":\"What kinds of topics are covered in Paper 1?\",\"answer\":\"The paper covers algebraic manipulation and functions, surds and radicals, statistics (median and interquartile range), trigonometry, and geometry/graph questions including a scatter graph and a parabola.\"}]","N5 Essential Skills National 5 Mathematics Practice Exam 2026 - Paper 1 - (Non-calculator) | PDF",1790754579]