Lyceum Exam Maths 2015 - Test A1 - Entrance Test

Aug 25, 2026

Entrance Test for the Lyceum of Westminster International University in Tashkent, Mathematics (July 2015), Test A1. The paper requires detailed working without books, notes, calculators, or other assisting materials. Topics include simplifying expressions, expanding and rewriting (3-√5)^2, factoring a cubic polynomial into linear factors, solving series problems for a given value, finding remainders via division by x-2, solving simultaneous equations using labeled axes, computing volumes from cube slices of thickness x, and working with a number chart and right-angled triangles to answer several sub-questions.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Question 1

Simplify the following

Question 2

Express (3-√5)^2 in the form m+n√5

Express (3-√5)^2 in the form p+q√5

Question 3

Factor the polynomial p(x)

Question 4

Determine the term whose value is 22 in the series

Find the remainder when p(x) is divided by x-2

Question 5

Points of intersection of two equations

Question 6

Volume of cube slices in terms of x

Question 7

Question 8

Number chart and two right-angled triangles

ENTRANCE TEST LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENTMATHEMATICS July 2015 Test A1 Time allowed:One hour 15 minutes ANSWER ALL QUESTIONS IN DETAIL,SHOWING ALL YOUR WORK ON THE SAME PAGE AS THEQUESTION. NO BOOKS,NOTES,CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED. KITOB,DAFTAR,KALKULYATOR YOKI BOSHQAYORDAMCHI MATERIALLARDANFOYDALANISH TAQIQLANADI. nOnb30BAHME KHMroǔ,TETPAAbIO,KANbKyn8TOPOM MnM NIO5bIM BCnOMOrATENbHbIMMATEPWANOM3ANPE山IAETCA. Question 1 Simplify the following S严宗出品SL①50F器OT字只U山?L号a岩望望 t.me/ma Co6cTBOHHOCTb MeAyHapoAHoro BecTMMHCTepcKoro YHMBepcMTeTa B TauKeHTe Cnnonb30BaHMR B HeKOMMepyecKMx uengx Question 2 (a)Express(3-√5)²in the form of m+n√5,where m and n are integers(2 marks) mnooeuoen noxioECnAT1H0xeNer2ecnayouet cune hia0emwi…Ps uonb30BaHMA日HeKOMMepheCKX uengX (b)Express(3-√5)²in the form p+q√5,where p and qare integers1+√5 (3 marks) coocTeHoCTb MeAyHapoAHoro BeCTMHCTepckoro YHueepchTera B TaukeHTe Question 3 The polynomial,p(x)is given byp(x)=x³+7x²+7x-15(a)Express p(x)as the product of three linear factors(3 marks) Question 4 2%,4,5Y₂,7,…………Determine the number of the term whose value is 22 in the series club (b)Find the remainder when p(x)is divided by x-2 sternuZ (2 marks) 0gcTBeHHO5TMeKowwepvec eunae2 Total for page 5 marks (08aHis BHenocoe Co6cTBCHHOCTb MeAyHapoAHoro BeCTMMHCTepckoro YHMBepcMTeTa B TauKeHTe Question 5 Find the co-ordinates of the points of intersection of these equations: x²+y²=13 2x+y=7 (You must label your axes) | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | me/ma Points of intersection………………… ··· ··· ··· Total for page 5 marks 3rw ieaMeHe0Hue dredn ox0距ECnATHOcaerecneryomen caie hitp/yceum wiut uzlyceumndexphpleadmisionlenryrequiemenig Ang nonb3OBaHM9 B HeKOMMepyecKMx uengx # Question 6 A cube has edges of 10cm each.Three slices,each of thickness xcm are cut off the cube. 10cm x cm Slice A is cut off the side.Slice B is cut off the top.Slice Cis cut off the front.What is the volume of each slice in terms of x? Slice A…… …………cm³Slice B…… … … ………cm³Slice C………… ……………cm³ Total for page 5 marks 9TW ak3ameHauoHHbe npnmepbI MOKHO 5ECIIATHO ckalaTb no cneayoueǔ ccbInke: htp:/yceum.wiut.uzlyceumlindex.phplen/admissionentry-requirements Co6cTBeHHOCTb MeknyHapoAHoro BeCTMMHCTepckoro YHuBepcMTeTa B TaukeHTe Ang nonb3OBaHMR B HeKOMMepyecKMX uengX Co6CTBeHHOCTb MekAyHapoAHoro BecTMMHCTepckoro YHMBepcMTeTa B TawkeHTe 3w ereaveHaoHue drpu Mox0 BEcATHOokavar2ocneayouen cunmce.htp/yceum wut uzlyceumindexphplenadmistonlentryrequirements 3rw ieaMeHe0Hu

FAQs

What are the allowed materials for this Lyceum Maths entrance test?

No books, notes, calculators, or any assisting materials are allowed. All answers must be shown in detail on the same page as the questions.

How do you handle Question 2 about (3-√5)^2?

Rewrite (3-√5)^2 into the requested surd forms: first as m+n√5 with m and n integers, then as p+q√5 with p and q integers.

What does Question 5 require?

Find the coordinates of the intersection points of the equations x^2+y^2=13 and 2x+y=7, and label your axes.

Aug 25, 2026

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