WIUT 23-24 REAL-EXAM PROBLEMS - Mathematics Entrance Examination Rules and Sample Questions

Aug 25, 2026

Uploaded by Quinn

Mathematics entrance examination for Westminster International University in Tashkent, specifying a 1 hour 10 minutes time limit and strict assessment rules. The exam requires completing all questions, presenting full working on the same page, and prohibits calculators, pre-prepared notes, dictionaries, and consulting other candidates’ papers. Additional instructions restrict leaving the room, forbid whiteout/correction fluid, require using blue or black non-erasable pen, and regulate device usage. The problem set includes factorization, rational equations, geometry for perimeter and area, functions with domain and range, geometric progression sums and proofs, exponent rules, equation solving, algebraic expressions, linear slope from graphs, triangle area comparison, trapezium geometry, investment and proportional returns, Venn diagram counting, and volume/surface area of a rectangular prism.

LanguageEnglish

CategoryExam

FormatPDF

Pages63

Reading Time2 h 39 min

AccessFree to download

Instructions and Exam Rules

Question Set

Algebra and Equations

Functions and Graphs

Sequences and Proofs

Geometry and Measurement

Westminster International University in Tashkent Mathematics Entrance Examination DATE: i. Time allowed: One hour ten minutes ii. Answer all questions. iii. No calculators are allowed. iv. All your working must be presented on the same page as the question. Answers with no evidence of calculations will not score any marks. v. Write your answers in the spaces below the questions. vi. Nothing should be removed from the exam room. Please note the additional requirements: vii. You are not allowed to leave the exam room during the examination. viii. You are not allowed to talk, to whisper, to turn around, use any pre-prepared notes, calculators, dictionaries or to look at another candidate’s examination papers, all of which are considered violation of exam rules and may incur a penalty. You will be given no warning; should you do any of these things you will be reported to the Assessment Board for penalty application. ix. You may use non-erasable blue or black pen to write your answers including graphs. Any answers written in pencil will not be marked. x. You may not use whiteout/correction fluid. If you make a mistake, simply draw a line through the mistake with pen and continue. xi. You may not borrow another student’s stationery or materials even with the consent of the invigilator. xii. If your pen runs out of ink you may request a replacement from the invigilator. If any are available a replacement will be provided for you. No other stationary or materials may be provided for you by the invigilator. xiii. All mobile phones and other electronic devices must be switched off and left at a place indicated by the invigilators. | Candidate name: | | | --- | --- | All questions on this paper must be answered. Write the answers in the space below each question. Show ALL working for each question. 1. Factorize: 15􀜽􀜾 − 6􀜾 + 10􀜽 − 4 2 marks 2. Solve the rational equation: 2 1 8 ~~ ~~ − ~~ ~~ = ~~ ~~ 􀝔 + 3 2􀝔 + 1 2􀝔2 + 7􀝔 + 3 3 marks 3. There is given a figure. a) What is the perimeter of this figure? 3 marks b) Work out the area of the unshaded region. 2 marks Total for page: 10 marks 4. There is given a function 􀝕 = √􀝔 − 1 a) Draw the graph of the function on the grid below b) Find the domain of function 3 marks 2 marks c) What is the range of the function? 2 marks Total for page: 7 marks 5. Knowing that the following numbers form a geometric progression 2 6 18 54 … a) Work out the sum of the first 6 terms of these series 3 marks b) Prove that 1458 is a term of this progression 3 marks 6. Perform the indicated operations. Write each answer using only positive exponents. Assume all variables represent positive real numbers 1 3 9􀯠2 􀯡2 1 􀯠 −7􀯡 (􀯠3 􀯡)2 2 marks Total for page: 8 marks 7. Work out the value of a and b from the given equation: 16 = 1 + 1 13 􀯔 2 +1􀳍 a= b= 5 marks 8. If 􀜽 + 1􀯕 = 4 and 􀜾 + 1􀯔 = 3, then what is the value of 􀯔􀯔􀯕􀯕=? -------------- 3 marks 9. For the function 􀝂(􀝔) = −3􀝔 + 4 find and simplify 􀝂 (􀝔 + 􀜿) − 􀝂(􀝔) 􀜿 --------------- 3 marks Total for page: 11 marks 10. According to the graph below, find out the slope of a linear function 3 marks 11. Which of the triangles has a bigger area? Explain your answer. 4 marks Total for page: 7 marks 12. There is given a trapezium with sides 5cm, 4cm, 3cm. a) Find out the value of x 3 marks b) Work out the area of the trapezium. 4 marks 13. Jack’s dad invested some money and for every $12 he invested he got a total of $15 back. If Jack’s dad invested $300, how much in total did he get back? 3 marks Total for page: 10 marks 14. The Venn diagram shows a class of music students and instruments they learn. (S-saxophone, F-flute) . S F 7 5 10 a)What is the total number of students in the class? 3 marks b) How many students learnt neither saxophone nor flute? 3 marks c) How many students learnt only saxophone or the f

FAQs

What tools are allowed for this mathematics entrance examination?

Calculators are not allowed, and the use of dictionaries, pre-prepared notes, and consultation of other candidates’ papers is prohibited. Answers must be written in the spaces provided using a non-erasable blue or black pen; pencil is not marked.

What are the key requirements for presenting answers?

All questions must be answered, and full working must be shown on the same page as each question. Answers with no evidence of calculations do not score marks, and nothing should be removed from the exam room.

What types of questions are included in the paper?

The paper includes factorization, solving rational equations, geometry problems (perimeter, area, trapezium and triangle comparisons, and volume/surface area), function graphing with domain and range, geometric progression sums and proof tasks, exponent operations, and algebraic and counting problems such as Venn diagrams.

Aug 25, 2026

Uploaded by Quinn