West.uz-Westminster lyceum - MATH-EXAM-SAMPLE - Tashkent 2019 - Mathematics Entrance Examination Sample

Aug 25, 2026

Mathematics M1 entrance examination sample for West.uz-Westminster lyceum in Tashkent (July 2019). The test lasts 1 hour 15 minutes and contains 10 questions worth 5 marks each, for a total of 50 marks. Candidates must answer all questions in detail and show all working on the same page as the question; answers written on draft pages or separate sheets are not graded. Books, notes, calculators and any assisting materials are prohibited. The sample includes algebraic simplification, number divisibility patterns, parabola geometry with tangency and area, concentration mixture problems, number theory with primes and divisibility implications, rectangle area change under percentage reductions, circle tangent shaded-area computation, and simultaneous non-linear equation solving.

LanguageEnglish

CategoryExam

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Examination Information

Instructions and Allowed/Prohibited Materials

Question 1-10 Overview

Marking Requirements

ENTRANCE EXAMINATION MATHEMATICS M1 Date: July 2019 Time allowed: 1 hour 15 minutes 10 questions by 5 marks. Total: 50 marks ANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. THE ANSWERS PROVIDED IN THE DRAFT PAGE OR IN SEPARATE SHEETS WILL NOT BE CONSIDERED. NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED. KITOB, DAFTAR, KALKULYATOR YOKI BOSHQA YORDAMCHI MATERIALLARDAN FOYDALANISH TAQIQLANADI. ПОЛЬЗОВАНИЕ КНИГОЙ, ТЕТРАДЬЮ, КАЛЬКУЛЯТОРОМ ИЛИ ЛЮБЫМВСПОМОГАТЕЛЬНЫМ МАТЕРИАЛОМ ЗАПРЕЩАЕТСЯ . | Application number: | | | --- | --- | | Signature: | | PLEASE DO NOT TURN OVER THIS PAGE UNTIL TOLD TO DO SO Question 1. Simplify and find what values 􀜽 and 􀜾 can take. ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ 2 (􀜽􀜽􀜽~~ ~~~~ ~~􀜾 − √􀜽􀜾 ) (√􀜽􀜽~~ ~~~~ ~~􀜾~~ ~~ ) Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 2. Find the sum of all two-digit natural numbers are divisible by 2 but not by 3. Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 3. The parabola y = 4x2 – 12x + 5 crosses the x-axis at points A and B as shown on the right figure. Line segment CD in rectangle ABCD is tangent to the parabola at its vertex. What is the area of rectangle ABCD? Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 4. How many liters of an 80 % acid solution must be added to 15 liters of a 6 % acid solution to get a 20 % acid solution. Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 5. The numbers a, p, and q are different positive integers and p and q are prime. If ais divisible by p and q and if 􀜾 = 􀯣􀯔∙~~ ~~􀯤~~ ~~, then which of the following must be true? I. b is not divisible by both p and q II. If b is divisible by r, then a is divisible by r III. b is a positive integer Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 6. When the width and length of a rectangle are each reduced by 20%, the area of the new rectangle is 12 units less than the area of the original rectangle. What is the area of the original rectangle? Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 7. The point O is a center of the circle. D is a tangent point. Find the shaded area if 􀜣􀜤 = 4, 􀜣􀜥 = 2. Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 8. Solve the simultaneous non-linear equations: { (􀢞􀢞􀢟􀢟(􀢞􀫛􀫞 − 􀢟􀫛 ) = 􀫝􀫞 Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks Question 9. Three billionaires have a total of 30 billion dollars between them. If billionaire A has 300 million more than billionaire B and billionaire B has 600 million more than billionaire C, how much more money do billionaires B and C combined have than billionaire A alone? Answer without the correct and detailed solutions will not be marked. Provide the detailed solution below. Write your answer here: ……………………………. Total for page 5 marks

FAQs

How long is the Mathematics M1 entrance exam and what is the total number of marks?

The exam lasts 1 hour 15 minutes and consists of 10 questions, each worth 5 marks, for a total of 50 marks.

What are the key rules for writing answers?

Answers must be given in detail with all working shown on the same page as each question. Draft pages or separate sheets are not accepted for grading.

Are calculators, books, or notes allowed during the exam?

No. Books, notes, calculators, and any assisting materials are prohibited.

Aug 25, 2026

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