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The document specifies time limits, mandatory responses, work-showing requirements, scoring constraints, and strict rules on conduct, prohibited materials, and use of calculators or electronic devices. It then presents multiple-choice items and open-ended problems covering algebraic manipulation, radicals, linear functions from graphs, logarithms, geometry angles, areas, and number theory identities, culminating in applications involving circles and a conical bottle water-volume geometry problem.",{"@graph":69,"@context":123},[70,84,106],{"@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/mathematics-entrance-examination-2023-exam-instructions-and-questions/143997/",{"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/mathematics-entrance-examination-2023-exam-instructions-and-questions/143997.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How long is the exam and are calculators allowed?","Question",{"text":113,"@type":114},"The exam lasts 1 hour and 10 minutes, and calculators are not allowed.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are the rules for showing working and where to write answers?",{"text":118,"@type":114},"Working and answers must be shown for all questions, and open-ended answers must be written in the spaces below each question; anything written on other pages is not marked.",{"name":120,"@type":111,"acceptedAnswer":121},"What are the main consequences for misconduct or unauthorized materials?",{"text":122,"@type":114},"Unauthorized exam-related materials or cheating lead to disqualification; failure to show pockets/containers and having any mobile phone or electronic device on you also results in disqualification without appeal.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},143997,1787697881,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Sample of Mathematics Entrance Examination 2023  \nDATE:  \nSESSION:  \n1. You have 1 hour and 10 minutes for the exam.  \n2. Answer all questions.  \n3. No calculators are allowed.  \n4. For Open-ended questions write your answers in the spaces below the questions. Answers with no evidence of calculations will not score any marks. Workings and answers written on anyother page will not be marked.  \nPlease note additional requirements:  \na) You are not allowed to leave during the first 30 minutes or the last 15 minutes of the examination.  \nb) You are not allowed to talk, to whisper, to turn around or to look at another candidate’s examination, all of which are offences, and you will be penalized. If you commit this offence, you will be given a single written warning; after which if you commit a further offence, you will be reported to an assessment board without a right of appeal or refund of the exam administration fee.  \nc) You cannot borrow another student’s stationery or materials.  \nd) If your pen runs out of ink, you may request a replacement from the invigilator. No other stationery or materials may be provided for you by the invigilator.  \ne) If you are found to have any unauthorized exam related materials during the examination this will constitute an offence and you will be disqualified from the exam.  \nf) If you are caught cheating in the examination, you will be disqualified from the exam.  \ng) Failure to show contents of your pockets or any other containers to the invigilators will be considered as an offence and you will be disqualified from the exam.  \nh) All mobile phones and other electronic devices must be switched off and left at a place indicated by the invigilators. If you are found to have a mobile phone or other electronic device (switched on or off) on you during the exam, this will be considered as unauthorized examination materials, and you will be disqualified from the exam without a right of appeal.  \nApplicant ID:  \nAll questions on this paper must be answered.  \nFor Multiple choice questions (1-17) select single answer choice.  \nFor Questions 18-20 write the answers in the space below each question.  \nWorking must be shown for all stages of the questions.  \n1. If 􀯫􀯫2 = 5, and 􀝔 ≠ −3, what is the value of 􀝔?  \n[2 marks]  \na) -8 b) -3 c) 0 d) 8  \n2. The park is full of people walking with their dogs.  \nIf Mary counts 45 heads and 140 legs, how many dogs are present in the park?  \n[2 marks]  \na) 25 b) 15 c) 20 d) 30  \n3. Solve the equation.  \n(125􀯫+1) × 25 = 625  \n[2 marks]  \n\n| a) −3 b)  1\u003Cbr>−\u003Cbr>3 | c)  1\u003Cbr>3 | d) 3 |\n| --- | --- | --- |\n\n4. Find the smallest number that can be exactly divided by all the numbers from 1 to 10.[2 marks]  \na) 4320 b) 3250 c) 5040 d) 2520  \n5. If 3√22√3 = 3√2 − 􀜽√3 then find the value of 􀜽 .  \n[2 marks]  \na) −1 b) 1 c) 2 d) -2  \n6. Find the value of x.  \n[2 marks]  \na) 5 b) 8 c) 10 d) ∅  \n7. Evaluate  \n16√3 × 5 × 17 × 257 + 1  \n[2 marks]  \na) 1 b) 2 c) 4 d) 8  \n8. Simplify  \n2􀝔 − 7  \n5  \n+  \n4􀝔 + 26  2􀝔 − 2  \n~~ ~~ −  \n15 3  \n[2 marks]  \na) 1 b) 2 c) −1 d) −2  \n9. Find the equation of the linear function represented by the graph below.  \n[2 marks]  \na) 􀝕 = 3􀝔 + 5 􀜾) 􀝕 = −3􀝔 + 5 􀜿) 􀝕 = 3􀝔 − 5 􀝀) 􀝕 = 2􀝔 + 5  \n10. Evaluate the value of 􀜽􀜾􀜿 , if  \n{􀜽􀜾 3􀜾1􀜿  31  \n[4 marks]  \na) 3 b) -3 c) 1 d) 0  \n11. Given 􀝔 = 􀯣􀯣􀯤􀯤 , 􀝕 = 􀯤􀯤􀯥􀯥 , 􀝖 = 􀯥􀯥􀯣􀯣, evaluate  \n(1 − 􀝔)(1 − 􀝕)(1 − 􀝖)  \n(1 + 􀝔)(1 + 􀝕)(1 + 􀝖)  \n[4 marks]  \na) 4 b) 2 c) 1 d) 0  \n12. Let 􀝊 be an integer than can be represented by 2􀯔 3􀯕 5􀯖 .  \nIf 􀜽, 􀜾 and 􀜿 are integers such that 0 \u003C 􀜽 \u003C 􀜾 \u003C 􀜿 , and 􀜽 + 􀜾 + 􀜿 = 7, what is a possible value for 􀝊?  \n[4 marks]  \na) 2700 b) 6750 c) 11250 d) 4500  \n13. Solve for x  \nlog 10 (􀝔 + 3) + log10 􀝔 = 1  \n[4 marks]  \na) 2 b) -5 and 2 c) 5 d) 5 and-2  \n14. For the function 􀝂(􀝔) = 􀜽􀝔2 + 24, 􀜽 is a constant and 􀝂(4) = 8. What is the value of 􀝂(−4)?  \n[4 marks]  \na) 0 b) 8 c) −8 d) -1  \n15. From the figure below find angle x.  \n[4 marks]  \na) 1000 b) 1200 c) 900 d) 1100  \n16. Solve for real x.  \n","cbCaia8NU9AJh6S8","https://ap.wps.com/l/cbCaia8NU9AJh6S8","pdf",339747,"English","# Exam Instructions\n## General rules and penalties\n## Question format\n# Mathematics Questions\n## 1-17 Multiple choice\n## 18-20 Open-ended and applied problems","[{\"question\":\"How long is the exam and are calculators allowed?\",\"answer\":\"The exam lasts 1 hour and 10 minutes, and calculators are not allowed.\"},{\"question\":\"What are the rules for showing working and where to write answers?\",\"answer\":\"Working and answers must be shown for all questions, and open-ended answers must be written in the spaces below each question; anything written on other pages is not marked.\"},{\"question\":\"What are the main consequences for misconduct or unauthorized materials?\",\"answer\":\"Unauthorized exam-related materials or cheating lead to disqualification; failure to show pockets/containers and having any mobile phone or electronic device on you also results in disqualification without appeal.\"}]","Mathematics Entrance Examination 2023 - Exam Instructions and Questions | PDF",13]