Entrance test lyceum of westminster international university in taskent mathematics
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2016-West.uz-Westminster lyceum - MATH-EXAM-SAMPLE-Tashkent
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Total for page 5 marks
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Question 8 Find equation of a line which is parallel to the line with the equation 3x + y = 7 and which passes through the origin.
Answer………………………….. Total for page 5 marks
END OF TEST TOTAL FOR TEST 40 MARKS For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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ENTRANCE TEST LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT MATHEMATICS July 2016 Test E1 Time allowed: One hour 15 minutes ANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. ANSWERS WITH NO EVIDENCE OF CALCULATIONS WILL NOT SCORE ANY MARKS. NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.
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Question 1 Find the solutions to the simultaneous equations x – 2y = 1 x 2
2 = 13
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 2 In an arithmetic progression, the 8th
term is twice the 3rd term and the 20th term is 110.
a)
Find the common difference.
Answer………………………….. b) Determine the sum of the first 100 terms
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 3 The polynomial p(x) = x 3
+ ax 2
– 4x + b, where a, and b are constants.
Given that x – 2 is a factor of p(x) and that a remainder of 6 is obtained when p(x) is divided by (x + 1), find the values of a and b
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 4 The point A has the coordinates (2, 5) The point B has the coordinates (6, 7)
a) Find the gradient of the line that passes through line AB
Answer…………………………..
b) Find the equation of the line that is parallel to line AB and goes through the point C(-1, 1).
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 5 What is the radius of a circle inscribed in a triangle with base of length 4 and height of length 3? Use the diagram to illustrate your method.
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 6
In the diagram OBDE and OAFG are parallelograms.
B is the midpoint of OG. A is the midpoint of OE. Express, in terms of a and b, the following vectors.
Give your answers in their simplest form. a)
…………..
b)
……………
c)
.…………..
d) Show are parallel ……..……
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Question 7
In the diagram below ∠W = ∠Y and VX is one fifth of VZ.
If the area of triangle VWX is 5, what is the area of triangle XYZ?
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 8 On the grid below a) Draw the line y – 3x = 4 b) Draw the curve y = 2x 2 - 5 c) From observation of your line and curve estimate the points of intersection
Estimated points of intersection……………………… ………………………. Total for page 5 marks END OF TEST TOTAL FOR TEST 40 MARKS USE THIS PAGE FOR DRAFTS For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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ENTRANCE TEST LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT MATHEMATICS July 2016 Test F1 Time allowed: One hour 15 minutes ANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. ANSWERS WITH NO EVIDENCE OF CALCULATIONS WILL NOT SCORE ANY MARKS. NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.
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PLEASE DO NOT TURN OVER THIS PAGE UNTIL TOLD TO DO SO
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Question 1 a) Find the value of 125
−2 3
Answer………………………….. b) Express (5 - √8)(√2 + 1) in the form, a + b√2, where a and b are integers
Answer…………………………..
c) Express √80 + 30 √5
Answer…………………………..
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Question 2 The man who invented the game of chess was asked to name his reward. He asked for 1 grain of corn to be placed on the first square of his chessboard, 2 on the second, 4 on the third and so on until all 64 squares are covered. a) Find the number of grains to be placed on the thirteenth square of the chessboard.
Answer…………………………..
b) He then said he would like as many grains of corn as the chessboard carried. How many grains of corn did he claim as his prize? Leave your answer in an exponential form.
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 3 Given f(x) = 3x 3 – 5x 2 – 58x + 40 a) Find the remainder when f(x) is divided by (x – 3)
Answer…………………………..
b) Show that (x – 5) is a factor of f(x). Hence or otherwise, find all the solutions of f(x) = 0
Answer………………………….. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 4 Lucy buys three crates, each containing 48 cartons of fruit juice, at a discount supermarket. Each crate costs $12. She sells 110 cartons at the school fair for 40 cents each. The rest of the cartons were sold at 30 cents each on a stall in the playground the next day.
Work out the percentage profit of loss Lucy makes for the school.
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 5 Given:
Circle O where CD = 16
AB = 16
OB = 10
Estimate the length of OF
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 6. ABCDEF and GHIJKL are regular hexagons with centre O.
GHIJKL is an enlargement of ABCDEF, with scale factor 2. a) Write the vector in terms of a and b
………….
b) Write the vector in terms of a and b ……………
c) Write the vector in terms of a and b
……………..
d) Write the vector in terms of a and b
................. e) Write the vector in terms of a and b
…….……..
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Question 7
a) Is this triangle right-angled? Explain your answer
………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………….
b) Below are two triangles, ABC and BCD.
Find x
Give your answer to the nearest 1 decimal place
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 8 On the grid below a) Draw the line y = x + 3 b) Draw the curve y = x 2 + 3x c) From observation of your line and curve estimate the points of intersection
Estimated points of intersection……………………… ………………………. Total for page 5 marks END OF TEST TOTAL FOR TEST 40 MARKS USE THIS PAGE FOR DRAFTS For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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ENTRANCE TEST LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT MATHEMATICS July 2016 Test G1 Time allowed: One hour 15 minutes ANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. ANSWERS WITH NO EVIDENCE OF CALCULATIONS WILL NOT SCORE ANY MARKS. NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.
The Script Secure Code*
The Script Secure Code* Application number:
Signature:
PLEASE DO NOT TURN OVER THIS PAGE UNTIL TOLD TO DO SO
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Question 1 a) There are 18200 gallons of fuel in a fuel tank.
The fuel is pumped from the fuel tank into a plane at a rate of 1500 litres per minute. 1 gallon = 4.5 litres
How many minutes will it take to empty the fuel tank completely? Give your answer to the nearest minute.
Answer…………………………….
b) Tame Valley is a company that makes yoghurt. A machine fills trays of 25 pots with yoghurt.
In one hour, the machine fills a total of 24000 pots. Work out how many seconds the machine takes to fill each tray of 25 pots. Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 2 Show that ( 1+𝑥 2 1−𝑥
2 ) 2 - ( 2𝑥 1−𝑥 2 ) 2
has the same numerical value for all x (x ≠ ±1) and determine this value.
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 3 Factorise completely f(x) = 2x 3 - 3x 2 - 5x - 6 Hence, or otherwise, solve the equation f(x) = 0
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 4 (k – 6), k and (k + 18) are successive terms of a geometric series. Which of the following is/are true about k? (1) k is an even number (2) k is an odd number (3) k is a prime number No marks will be awarded without working out.
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 5
a) Find the perimeter of the sector. Use 3.14 as the value of 𝜋
Answer…………………………….
b) Find the area of the sector. Give your answer in terms of 𝜋
Answer……………………………. Total for page 5 marks Question 6
www.west.uz 7
a)
Write down the vector in terms of a and b Answer…………………………….
DF : FG = 2 : 3 Work out the vector in terms of a and b Give your answer in its simplest form.
Answer……………………………. Total for page 5 marks Question 7
A cuboid has length 3 cm, width 4 cm and height 12 cm For more Westminster math exam sample and original tests join us www.west.uz www.west.uz 8
a) Work out the length of PQ
Answer…………………………….
b) A cuboid has a volume of 64 𝑐𝑚 2
Its size is increased by a scale factor of 2.
Calculate the new volume of the cuboid.
Answer……………………………. Total for page 5 marks Question 8 For more Westminster math exam sample and original tests join us www.west.uz www.west.uz 9
On the grid below a) Draw the line y = 3x - 1 b) Draw the curve y = x 2 - 5
c) From observation of your line and curve estimate the points of intersection
Estimated points of intersection……………………… ………………………. Total for page 5 marks END OF TEST TOTAL FOR TEST 40 MARKS USE THIS PAGE FOR DRAFTS For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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ENTRANCE TEST LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT MATHEMATICS July 2016 Test H1 Time allowed: One hour 15 minutes ANSWER ALL QUESTIONS IN DETAIL, SHOWING ALL YOUR WORK ON THE SAME PAGE AS THE QUESTION. ANSWERS WITH NO EVIDENCE OF CALCULATIONS WILL NOT SCORE ANY MARKS. NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE ALLOWED.
The Script Secure Code*
The Script Secure Code* Application number:
Signature:
PLEASE DO NOT TURN OVER THIS PAGE UNTIL TOLD TO DO SO
For more Westminster math exam sample and original tests join us www.west.uz www.west.uz 2
Question 1 The roots of the equation 2x 2 + 6x +3 = 0 are α and β.
Show that α 2 + β
2 = 6 Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 2 In a company of 100 people the ratio of men to women is 3:2
40% of the men are under the age of 25 10% of the women are under the age of 25 All answers must be given as fractions in their simplest form
a) What fraction of the company are men?
Answer …………….
b) What fraction of the company are men under 25?
Answer …………… c) What fraction of all the people in the company are over the age of 25?
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 3 The line AB has equation 3x + 5y = 11 a) Find the gradient of the line AB.
Answer…………………………….
b) The point A, has coordinates (2, 1). Find an equation of the line which passes through the point A and which is perpendicular to AB.
Answer……………………………. c) The line AB intersects the line with equation 2x + 3y = 8 at the point C. Find the coordinates of C.
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 4 a) Work out the value of √50+√18
√8
Answer…………………………….
(a) Express the following in the form, m + n√7 where, m and n are integers
2√7 − 1
2√7 + 5
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 5 A plumber charges a callout fee of $p plus $t for each 15 minutes he is working on a job. A job lasting 45 minutes costs $56.20. A job lasting 1.5 hours costs $98.50. What is the callout charge and the total cost of a job lasting 1.25 hours?
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 6
The letter ‘T’ on this square grid has an area of 200cm 2
Calculate the perimeter of the ‘T’. Give the correct units for the answer.
Answer……………………………. Total for page 5 marks For more Westminster math exam sample and original tests join us www.west.uz www.west.uz
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Question 7 A rectangular swimming pool has the dimensions:
Length 20 m Width 4 m
Depth 1.5 m It is filled to the top with water. The water evaporates by 250 litres per day.
After how many days does the level of the water in the pool fall below 50% of its capacity? Use 1 cm
3
= 1 ml
Answer……………………………. Total for page 5 marks Question 8 For more Westminster math exam sample and original tests join us www.west.uz www.west.uz 9
On the grid below a) Draw the line y = 4x + 1 b) Draw the curve y = 6 – x 2
Estimated points of intersection……………………… ………………………. Total for page 5 marks END OF TEST TOTAL FOR TEST 40 MARKS USE THIS PAGE FOR DRAFTS For more Westminster math exam sample and original tests join us www.west.uz www.west.uz Document Outline
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