[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-167359-en":3,"doc-seo-167359-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},167359,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",4,"Exam","MathPro - Scholarship Mock Test - 1","Scholarship-level open-ended mock test for MathPro students, designed to assess deeper mathematical problem solving across geometry, counting, functions, algebra, logarithms, trigonometry, 3D geometry, proof, and applied problems. The paper contains 10 questions totaling 100 marks with a 1 hour 30 minutes time limit. Calculator use is forbidden and candidates must show clear working for every question; final answers are entered on the separate answer sheet.","MathPro | Scholarship  \nMathPro  \nMock Test \\#1  \nWIUT scholarship-level practice  \nTest type: Open-ended mock test  \nQuestions: 10 questions  \nMaximum score: 100 marks  \nTime allowed: 1 hour 30 minutes  \nCalculator: Not allowed  \nPrepared for MathPro students  \nby Lazizbek Matyoqubov  \nMathPro | Scholarship Mock Test \\#1 Page 1 of 7  \nBefore you start  \n1. Answer all 10 questions.  \n2. Show your reasoning clearly. A final answer without clear working may receive no marks.  \n3. Each question is worth 10 marks. Total: 100 marks.  \n4. Do not use a calculator, phone, smartwatch, notes, Google, or any electronic aid.  \n5. Write exact answers where possible. Use decimals only when the question asks for them.  \n6. Manage your time. If one question is taking too long, move on and return later.  \nScholarship-level focus  \nThis paper is designed to test deeper problem solving, algebraic accuracy, proof skills, geometry reasoning, and clean no-calculator execution.  \nThis paper is designed for MathPro students. Do not use a calculator.  \nNo calculator. Show workings for every question.  \nMathPro | Scholarship Mock Test \\#1 Page 2 of 7  \nAnswer Sheet  \nFinal answers only  \nWrite the final result for each question in the boxes below. Full working must still be shown on the question pages or on extra paper.  \nScore  \nQ1 /10  \nQ6 /10  \nQ2 /10  \nQ7 /10  \nQ3 /10  \nQ8 /10  \nQ4 /10  \nQ9 /10  \nQ5 /10  \nQ10 /10  \nTotal score:  \n/100  \nNo calculator. Show workings for every question.  \nMathPro | Scholarship Mock Test \\#1 Page 3 of 7  \nPART A Geometry, Counting & Functions | 30 marks  \n1. 10 marks  \nIn the rectangle below, two equal circles are tangent to each other and to the sides of the rectangle. The red region is the part of the rectangle below the diagonal but outside the circles.  \nFind the total area of the red region.  \n20  \n2. 10 marks  \nA device has a 5-digit password. Each digit can be any number from 0 to 9, but digits cannot be repeated. After every block of 5 unsuccessful attempts, the hacker must wait 15 seconds before making the next attempt. The hacker can test 100 passwords per second while not waiting.  \na) How many different possible passwords are there?  \nb) If the hacker tries every possible password, how long will it take in total? Give your answer in seconds, and then approximately in hours and minutes.  \nNo calculator. Show workings for every question.  \nMathPro | Scholarship Mock Test \\#1 Page 4 of 7  \n3. 10 marks  \nA company’s monthly income 􀪨 (􀫐), in thousands of dollars, is modeled by  \n􀪨 (􀫐) = −2􀫐2 + 20􀫐 + 100,  \nwhere 􀫐 is the amount of money spent on advertising, in thousands of dollars.  \na) Find the maximum possible monthly income.  \nb) Determine how much the company should spend on advertising to achieve this maximum income.  \nNo calculator. Show workings for every question.  \nMathPro | Scholarship Mock Test \\#1 Page 5 of 7  \nPART B Algebra, Logarithms & Trigonometry | 30 marks  \n4. 10 marks  \nSolve the equation:  \n1 1 1  \n~~ ~~ − ~~ ~~ = ~~ ~~  \n􀫐3 + 2 􀫐3 + 3 12 .  \n5. 10 marks  \nLet 􀪺 > 0 , 􀪺 ≠ 1 . If  \nlog􀪺 27 = 􀪻,  \nfind  \nlog √3 √6 􀪺  \nin terms of 􀪻 .  \n6. 10 marks  \nSolve the trigonometric equation for 0 ≤ 􀫐 \u003C 2􀵝 :  \nsin 3􀫐 + sin 5􀫐 = sin 4􀫐 .  \nNo calculator. Show workings for every question.  \nMathPro | Scholarship Mock Test \\#1 Page 6 of 7  \nPART C 3D Geometry, Proof & Applied Problems | 40 marks  \n7. 10 marks  \nIn a cube, the centre of the lower base is connected to the centres of the four side faces. The four side-face centres are connected in order, forming the base of a pyramid. The height of the cube is 6 units.  \nFind the volume of the created pyramid.  \n8. 10 marks  \nSeven equal touching disks are arranged inside the smaller of two concentric circles, as shown in Fig. 1. The annulus is the region between the two concentric circles. The area of the annulus is equal to the sum of the areas of all seven disks.  \nProve that the width of the annulus is equal to the radius of one small disk.  \nFig. 1  \n","cbCaifK2t1z6oSnW","https://ap.wps.com/l/cbCaifK2t1z6oSnW","pdf",44486,1,8,"English","en",105,"# Before you start\n## Scholarship-level focus\n# Part A Geometry, Counting & Functions\n## Geometry and area\n## Password counting\n## Quadratic income model\n# Part B Algebra, Logarithms & Trigonometry\n## Equation solving\n## Logarithms\n## Trigonometric equation\n# Part C 3D Geometry, Proof & Applied Problems\n## Pyramid volume from cube\n## Annulus and disk proof\n## Alloy ratio mixing\n## Speaker cost word problem","[{\"question\":\"How many questions and marks does the MathPro scholarship mock test include?\",\"answer\":\"The mock test contains 10 open-ended questions, each worth 10 marks, for a total of 100 marks.\"},{\"question\":\"Are calculators or electronic aids allowed during the test?\",\"answer\":\"No. Candidates must not use a calculator, phone, smartwatch, notes, or any electronic aid, and must show workings for every question.\"},{\"question\":\"What topics are covered across the test parts?\",\"answer\":\"Part A covers geometry, counting, and functions; Part B covers algebra, logarithms, and trigonometry; Part C covers 3D geometry, proof, and applied problems.\"}]","MathPro - Scholarship Mock Test - 1 | PDF",1788212083,20,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"mathpro-scholarship-mock-test-1","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/mathpro-scholarship-mock-test-1/167359/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-31",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"How many questions and marks does the MathPro scholarship mock test include?","Question",{"text":74,"@type":75},"The mock test contains 10 open-ended questions, each worth 10 marks, for a total of 100 marks.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Are calculators or electronic aids allowed during the test?",{"text":79,"@type":75},"No. Candidates must not use a calculator, phone, smartwatch, notes, or any electronic aid, and must show workings for every question.",{"name":81,"@type":72,"acceptedAnswer":82},"What topics are covered across the test parts?",{"text":83,"@type":75},"Part A covers geometry, counting, and functions; 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