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The paper contains 28 multiple-choice and short-answer style problems covering core algebra, equations and inequalities, functions, logarithms, geometry, and word problems. It emphasizes selecting the correct option without showing working and completes the assessment within one hour and ten minutes under strict restrictions such as no calculators or electronic devices.",{"@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-first-mock-no-1/142967/",{"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-first-mock-no-1/142967.png","ImageObject",300,407,{"name":92,"@type":93},"Logic","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-05","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the key rules for answering this mock mathematics paper?","Question",{"text":113,"@type":114},"Read each question carefully and provide only the final answer without showing all your work. Calculators, phones, or any devices are not allowed, and the time allowed is one hour and ten minutes.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which math topics are covered in the questions?",{"text":118,"@type":114},"The questions cover minimum values and expressions, simultaneous equations, angle problems, quadratic and polynomial equations, logarithms, simplifying algebraic expressions, functions, inequalities, area of figures, factorization, and geometry including distance and partition by ratios.",{"name":120,"@type":111,"acceptedAnswer":121},"Are there questions that require full working rather than only a final answer?",{"text":122,"@type":114},"Yes. Questions 26, 27, and 28 explicitly request the complete solution and provide space below for work.","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},142967,1787692049,{"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":39,"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":46},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","Westminster International University in Tashkent  \nFirst mock  \nMathematics Entrance Examination  \nCandidate Name:    \nGroup:    \nTeacher Name:    \nInstructions:  \n• Read each question carefully  \n• Provide the final answer only; do not show all your work  \n• Calculators, phones or any devices are not allowed  \nTime allowed: One hour and ten minutes  \n1. What is the minimum value of 􀝂 (􀝔) = 2􀝔2 + 4􀝔 − 4 ?  \nCircle correct answer:  \nA) −4 B) 0 C) −8 D) −6  \n2. Solve the simultaneous equations: { 32􀜽􀜽 − 46􀝇􀝇  1150  \nCircle correct answer:  \nA) (􀜽; 􀝇) = (5; 0) B) (􀜽; 􀝇) = (3; 1) C) (􀜽; 􀝇) = (2; 2) D) (􀜽; 􀝇) = (3; 0)  \n3. Find all solutions in degrees within the interval (0°; 180°) .  \n􀝏􀝅􀝊2􀝔 = 􀜿􀝋􀝏 (3􀝔 − 􀟨2)  \nCircle correct answer:  \nA) 􀰗5 ; 3􀰗5 ; 2􀰗5~~ ~~ B) 2􀰗5 ; 5􀰗5~~ ~~ C) 3􀰗5 ; 3􀰗5 ; 􀟨 D) 􀰗5 ; 3􀰗5  \n4. Solve the equation: 􀝔 2 − 15􀝔 + 50 = 0  \nCircle correct answer:  \nA) 􀝔1 = 5, 􀝔2 = 11 B) 􀝔1 = 4, 􀝔2 = 7 C) 􀝔1 = 5, 􀝔2 = −4 D) 􀝔1 = 10, 􀝔2 = 5  \n5. Solve the equation: log~~4 ~~(52􀯫+3) = 12  \nCircle correct answer:  \nA) 􀝔 = 14 B) 􀝔 = 3 C) 􀝔 = 15 D) 􀝔 = 1  \n6. Simplify the expression: 3􀯣632􀯤 ∙ 􀯣~~ ~~32􀯣􀯤2 : 􀯣~~ ~~2􀯣􀯤  \nCircle correct answer:  \nA) 3􀝌 B) 19 C) 􀝌 − 􀝍 D) 1  \n7. In the figure, the two horizontal lines are parallel, and the two transversal lines are also parallel. If the angles are as shown, find the value of 􀝔 + 􀝕 .  \nCircle correct answer:  \nA) 45° B) 90° C) 100° D) 50°  \n8. A pedestrian walks 7.8 km in 3 hours.  \nWhat distance (in km) will this person walk at the same speed in 4 hours?  \nCircle correct answer:  \nA) 10.6 B) 10.4 C) 10.8 D) 10.5  \n9. Find the equation of the function:  \nCircle correct answer:  \nA) 􀝕 = 2􀝔2 + 8􀝔 − 6  \nC) 􀝕 = −􀝔2 + 8􀝔 − 3  \nB) 􀝕 = −2􀝔2 + 4􀝔 − 5  \nD) 􀝕 = −􀝔2 + 6􀝔 − 5  \n10. Solve the inequality: 4 − 􀝔 2 > 6􀝔 . How many integer numbers satisfy the inequality?  \nCircle correct answer:  \nA) 3 B) 4 C) 6 D) 7  \n11. Given the linear function where 􀝂(3) = 7 and 􀝂(5) = 9, find 􀝂(􀝔) .  \nCircle correct answer:  \nA) 􀝂(􀝔) = 2􀝔 + 3 B) 􀝂(􀝔) = 􀝔 + 4 C) 􀝂(􀝔) = 3􀝔 D) 􀝂(􀝔) = 􀝔 + 3  \n12. Find the area of the shaded region if the side of square ABCD is 6√2 .  \nCircle correct answer:  \nA) 18 B) 36√2 C) 36 D) 36√3  \n13. Solve the equation: 4􀝔√2􀝔 − 1 = 10􀝔 − 5  \nCircle correct answer:  \nA) 􀝔1 = 12 , 􀝔2 = 58 , 􀝔3 = 52 B) 􀝔1 = 12 , 􀝔2 = 57 , 􀝔3 = 32  \nC) 􀝔1 = 13 , 􀝔2 = 78 , 􀝔3 = 52 D) 􀝔1 = 14 , 􀝔2 = 38 , 􀝔3 = 32  \n14. Find the real value of 􀝔 such that √􀯫􀯫−34 = 0  \nCircle correct answer:  \nA) 􀝔 = 1 B) 􀝔 = 2 C) 􀝔 = 3 D) 􀝔 = 4  \n15. A store sold 12 notebooks and 8 pens for 136,000 sums.  \nOn the next day, the store sold 7 notebooks and 10 pens for 122,000 sums.  \nFind the price of one notebook and one pen.  \nCircle correct answer:  \nA) Notebook – 8,000 sums; Pen – 5,000 sums B) Notebook – 6,000 sums; Pen – 8,000 sums  \nC) Notebook – 10,000 sums; Pen – 2,000 sums D) Notebook – 7,000 sums; Pen – 6,000 sums  \n 34􀳙   1  \n16. Solve for 􀝊: 272􀳙 = 9  \nCircle correct answer:  \nA) 􀝊1 = 2, 􀝊2 = 3 B) 􀝊1 = 1, 􀝊2 = 2 C) 􀝊1 = 0, 􀝊2 = 1 D) 􀝊1 = 3, 􀝊2 = 4  \n17. Simplify: 6􀯫􀯫1−1  \nCircle correct answer:  \nA) 7􀝔 + 2 B) 􀝔 + 2 C) 􀝔 + 4 D) 6􀝔 + 1  \n18. The vertex of parabola is at (4; 2) . The parabola opens downward and passed through the points (3; −1) and (5; −1) . Write the equation of the parabola.  \nCircle correct answer:  \nA) 􀝕 = −3(􀝔 − 4)2 + 2 B) 􀝕 = −2(􀝔 + 2)2 + 3 C) 􀝕 = −(􀝔 − 3)2 + 2 D) 􀝕 = − 32 (􀝔 + 2)2 − 3  \n19. Find the value of 􀝔  \nCircle correct answer:  \nA) 10 B) 12 C) 813 D) 313  \n20. Factorize 3􀝔2 + 13􀝔 − 10  \nCircle correct answer:  \nA) (􀝔 + 4)(3􀝔 − 2) B) (􀝔 + 5)(3􀝔 − 2) C) (􀝔 − 3)(2􀝔 − 1) D) (2􀝔 − 1)(􀝔 + 1)  \n21. Find the distance between the two points:  \nA(−2; 0) B (−4; 4)  \nCircle correct answer:  \nA) √5 B) 2√5 C) 3 D) 4  \n22. A uniform wire of length 80 meters is divided into three parts in the ratio 5: 7: 13 (by length) .  \nFind the length (in meters) of the part with the smallest mass.  \nCircle correct answer:  \nA) 16 B) 17 C) 16.6 D) 16.4  \n23. Solve the equation: 33􀯫+2 ∙ 3􀯫+2 = 27􀯫+4  \nCircle correct answer:  ","cbCaipI7RIbLDkXX","https://ap.wps.com/l/cbCaipI7RIbLDkXX","pdf",1025680,"English","# Instructions\n# Multiple-choice questions (1-25)\n## Algebra and equations\n## Functions, logarithms, inequalities\n## Geometry and applied word problems\n# Longer solution questions (26-28)","[{\"question\":\"What are the key rules for answering this mock mathematics paper?\",\"answer\":\"Read each question carefully and provide only the final answer without showing all your work. Calculators, phones, or any devices are not allowed, and the time allowed is one hour and ten minutes.\"},{\"question\":\"Which math topics are covered in the questions?\",\"answer\":\"The questions cover minimum values and expressions, simultaneous equations, angle problems, quadratic and polynomial equations, logarithms, simplifying algebraic expressions, functions, inequalities, area of figures, factorization, and geometry including distance and partition by ratios.\"},{\"question\":\"Are there questions that require full working rather than only a final answer?\",\"answer\":\"Yes. Questions 26, 27, and 28 explicitly request the complete solution and provide space below for work.\"}]","Mathematics Entrance Examination - First Mock - №1 | PDF"]