Westminster International University in Tashkent - Entrance Exam Set - Mathematics 2005-2007

Aug 25, 2026

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Mathematics entrance exam paper set covering algebra, simultaneous equations, quadratic equations, arithmetic progressions, trigonometry, and geometry. Includes instruction on time management and working methods, with requirements to present rough calculations and no calculator use. Questions require solving for unknowns, finding maximum values from sinusoidal functions, drawing graphs of linear equations, and interpreting trapezium angle relationships, alongside number and digit-rearrangement word problems.

LanguageEnglish

CategoryExam

FormatPDF

Pages25

Reading Time1 h 3 min

AccessFree to download

Instructions

M11

M12

M13

M14

# Westminster International University in TashkentA set of entrance exams onMathematics 2005-2007 Time allowed:One hour ten minutes Answer all questions. It is advised that you work quickly and that you leave behind questionsthat are taking you too long to answer. You should only bring in writing material (pens,pencils,erasers,rulers).No calculators are allowed. All your rough calculations have to be presented.Answers with noevidence of calculations will not score any marks. Use the blank pages of the exam paper to do your rough work. Nothing should be removed from the exam room. M11 ## Question 1 Answer x= ## Question 2 The curve with equation y=3+k sinx,where kis a constant,passes through the point withcoordinates a)Find the value of k and b)find the largest value of y. Answer:a)k= ;b)max y= ## Question 3 Anna,Bakhrom,Caterina and Dildora have 27,000 Uzbek cym between them;Anna hasthree times as much as Caterina,and Bakhrom five times as much as Dildora;also,Annaand Bakhrom together have 5,000 cym less than eight times what Caterina has.Find howmuch each has. ## Question 4 a)Solve the simultaneous equations x+y=7 and x²+y²=49; b)Draw the graph ofx+y=7. Answer:a)x= and y= or x= and y= ## Question 5 The sum of five numbers in arithmetic progression is 40 and the sum of their squares is410;find the five numbers. Answer:The 5 numbers are , , , , ## Question 6 An equilateral triangle has sides of length 6 meters.On each side of the triangle a square isdrawn external to the triangle.Find the area of the complete figure. √3=1.73 M12 ## Question 1 Solve Answer x=, ## Question 2 Findall angles 0 x p for which a)cos3x=05 and b) Answer a)x= or or ;b)x= ## Question 3 A number consists of three digits,the right-hand one being zero.If the left-hand and themiddle digits are interchanged the number becomes smaller by 180;if the left-hand digit ishalved and the middle and right-hand digits are interchanged the number becomes smallerby 454.Find the number. Entrance exam set ## Question 4 c)Solve the simultaneous equations3x+6y=456x-3y=45 d)Draw the graph of the two lines above,clearly showing the point of intersection. Answer:a)x= and y= ## Question 5 The last term of an arithmetic progression is ten times the first,and the last but one term isequal to the sum of the 4 and the 5ᵗ.Find the number of terms. Answer:Number of terms= ## Question 6 ABCD is a trapezium with AB parallel to CD and BC=AD.The diagonals AC and BDmeet at P.If angle ACD=40°,find angle ABD and angle APD. M13 Question 1Solve x²+x-12=0. Answer x= or Question 2 Ealuate Answer E= ## Question 3 A dealer bought a horse,expecting to sell it at a 10%profit,but he was forced to sell it for5000 cym less than he expected.When he calculated what had happened,he found he hadlost 15%on what the horse cost him.What did he pay for the horse? Question 4 e)Solve the simultaneous equations x+2y=13 and 3x+y=14; f)Draw the graph of 3x+y=14. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

FAQs

What tools are allowed for the exam and are calculators permitted?

Bring only writing materials such as pens, pencils, erasers, and rulers. No calculators are allowed.

How are rough calculations expected to be handled?

All rough calculations must be presented, and answers without evidence of calculations will not receive marks.

Which types of math topics appear in the questions?

The paper includes algebra (including simultaneous and quadratic equations), trigonometry, arithmetic progression problems, and geometry tasks such as triangles, trapeziums, and angle calculations.

Aug 25, 2026

Upload by Logic