ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test A1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
Solve the simultaneous equations:
y - 2x = 1
w
w
w
.w
es
t
.u
z
y2 = 2x2 + x
Answer…………………………….…
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
Question 2
Write the number
a) 2.(816) in the simplest form of
𝑥
𝑦
where x and y are integers and y ≠ 0
b) Simplify the expression
3√2+2√3
3√2− 2√3
w
w
w
.w
es
t
Write your answer in its simplest form of a + b√𝑐
.u
z
Answer…………………………….
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
3
Question 3
For the geometric series
a + ar + ar2 + …….
the sum of the first two terms is 24 and the sum to infinity is 27.
1
w
w
w
.w
es
t
.u
z
Show that r = ± 3
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
4
Question 4
Given that f(x) = 2x3 + 3x2 - 5x - 6 and (x+1) is a factor, factorise fully the polynomial f(x).
w
w
w
.w
es
t
.u
z
State the set of values of x for which f(x) ≤ 0
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
5
Question 5
On the grid below
a) draw the circle with equation 𝑥 2 + 𝑦 2 = 25
b) draw the line with equation y = 2x + 1
w
w
w
.w
es
t
.u
z
Estimate the points of intersection to one decimal place.
Estimated points of intersection………………………
……………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
6
Question 6
In the diagram below AB is parallel to DE.
es
t
.u
z
a) Prove that triangle ABC is similar to triangle DEC.
.w
Answer…………………………….
b) Work out the value of x in the diagram below.
w
All values are in cms.
w
w
Give your answer to 2 decimal places.
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
7
Question 7
A water tank has a radius of 80cm and a length of 200cm.
It is half filled with water.
120 litres per day is used to water a garden.
For how many days can the garden be watered from the tank?
Use 3.14 for the value of 𝜋
Give your answer to the nearest whole day.
The volume of cylinder = 𝜋𝑟 2 𝑙
w
w
w
.w
es
t
.u
z
1cm3 = 1 millilitre
Answer…………………………….
Total for page 5 marks
Question 8
For more Westminster math exam sample and original tests join us www.west.uz
8
A bathroom floor is being tiled.
One size of square tile will cover the floor with 200 tiles.
Another square tile, with sides 2 cm less, will use 250 tiles to cover the same area.
w
w
w
.w
es
t
.u
z
Find the size of the larger tiles to the nearest cm.
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
9
w
w
w
.w
es
t
.u
z
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
10
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test B1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
A coach driver has to travel 560 km.
The driver usually drives at an average speed of r km/h.
He can arrive 45 minutes earlier if he increases his average speed by 6 km/h.
w
w
w
.w
es
t
.u
z
Find the value of r correct to the nearest whole number.
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
Question 2
An equilateral triangular field has sides of length, l.
a) Find an expression for the area of the field, leaving your answer in surd form.
Answer…………………………….
es
t
.u
z
b) Work out the area of the field when (in each case leave your answer in surd form)
(i)
l = 250√2 metres
Answer…………………………….
w
w
.w
l = 120(120√3 − 1) metres
w
(ii)
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
3
Question 3
The function f(x) is given by f(x) = 2x3 - x2 - 18x + 9
a) Show that (x – 3) is a factor of f(x)
w
w
w
.w
es
t
.u
z
b) Write f(x) in the form (x – 3)(ax2 + bx + c) and find the values of a, b, c
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
4
Question 4
w
w
w
.w
es
t
.u
z
The sum of the first ten terms of an arithmetic series is 60; the sum of the first twenty-two
terms is 220. Find the common difference and the first term of the series.
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
5
Question 5
On the grid below
a) draw the circle with equation 𝑥 2 + 𝑦 2 = 40
b) draw the line with equation y= x + 8
w
w
w
.w
es
t
.u
z
Estimate the points of intersection to one decimal place.
Estimated points of intersection………………………
……………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
6
Question 6
The figure below consists of a triangle, a rectangle and a parallelogram.
Answer…………………………….
w
w
.w
es
t
.u
z
a) Find the area of the figure below. All figures are in cms.
w
b) A similar figure has a total width of 32 cms.
What is the area of the larger figure?
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
7
Question 7
The size of each exterior angle of regular polygon is 24º.
a) Work out how many sides the polygon has.
.u
z
Answer…………………………….
w
w
w
.w
es
t
b) What is the sum of the interior angles of this polygon?
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
8
Question 8
A circular swimming pool has a radius of 7 m and a depth of 1.4 m.
It is filled to the top with water.
The swimming pool develops a leak and loses 5 cubic meters of water every 2 hours.
After how long would the water in the swimming pool be at a depth of 0.9 m?
Use 3.14 for the value of 𝜋
Volume of cylinder = 𝜋𝑟²𝑑, where d represents the depth of the swimming pool.
w
w
w
.w
es
t
.u
z
Round your answer to the nearest hour.
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
9
w
w
w
.w
es
t
.u
z
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
10
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test C1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
Prove that (x-2) is a factor of 2x3 - 9x2 +7x + 6
w
w
w
.w
es
t
.u
z
Hence, or otherwise, solve the equation 2x3 - 9x2 +7x + 6 = 0
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
Question 2
The first three terms of a geometric series are 3(q+5), 3(q+3) and (q+7) respectively.
es
t
.u
z
a) Calculate the possible values of q
.w
Answer…………………………..
w
w
w
b) For each possible value of q find the common ratio, r, of the geometric series
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
3
Question 3
A road is 4535 m long.
Kirsty drove along the road in 204 seconds.
The average speed limit for the road is 80 km/h.
Estimate whether Kirsty's average speed was greater than 80 km/h?
w
w
w
.w
es
t
.u
z
You must show your working.
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
4
Question 4
The line 3x + 4y = 15 intersects the curve 2xy = 9 at A and B.
w
w
w
.w
es
t
.u
z
Find the coordinates of A and B
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
5
Question 5
On the grid below
a) draw the circle with equation 𝑥 2 + 𝑦 2 = 20
b) draw the line with equation y = x - 6
w
w
w
.w
es
t
.u
z
Estimate the points of intersection to one decimal place
Estimated points of intersection………………………
……………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
6
Question 6
A rectangular piece of paper can be cut in two ways to produce two identical rectangles
When the original sheet of paper is cut one way the total perimeter of the two rectangles is
100 cm.
When the original sheet of paper is cut the other way the total perimeter of the two
rectangles is 128 cm.
w
w
w
.w
es
t
.u
z
What was the perimeter of the original piece of paper?
Answer…………………………….
Total for page 5 marks
Question 7
Amir has a photo and a rectangular piece of card.
For more Westminster math exam sample and original tests join us www.west.uz
7
The photo is 16 cm by 10 cm. The card is 30 cm by 15 cm.
es
t
.u
z
Amir cuts the card along the dotted line shown in the diagram below.
Amir throws away the piece of card that is 15 cm by x cm.
.w
The piece of card he has left is mathematically similar to the photo.
w
w
w
Work out the value of x.
Answer…………………………….
Total for page 5 marks
Question 8
In the figure below
M is the midpoint of OA
N is the midpoint of OC
For more Westminster math exam sample and original tests join us www.west.uz
8
.u
z
es
t
.w
I …………………
ii………………….
iii………………….
Total for page 5 marks
w
w
w
Answer:
END OF TEST
TOTAL FOR TEST 40 MARKS
For more Westminster math exam sample and original tests join us www.west.uz
9
w
w
w
.w
es
t
.u
z
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
10
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test D1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
Solve the simultaneous equations
x+y=4
w
w
w
.w
es
t
.u
z
x2 + y2 = 40
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
Question 2
f(x) ≡ 2x3 + px2 + qx + 6
where p and q are constants.
When f(x) is divided by (x+1), the remainder is 12. When f(x) is divided by (x-1) the
remainder is -6.
w
.w
es
t
.u
z
a) Find the value of p and the value of q.
w
w
b) Show that (x-1/2) is a factor of f(x)
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
3
Question 3
Yusuf chooses three different integers between 1 and 50.
The first number is a prime number.
The second number is 4 times the first number.
The third number is 6 less than the second number.
The sum of the three numbers is greater than 57.
Find the three numbers.
w
w
w
.w
es
t
.u
z
You must show all your working.
Answer: 1st………………..
2nd……………….
3rd……………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
4
Question 4
(3−√5)2
1+√5
in the form p + q√5, where p and q are integers
w
w
w
.w
es
t
b) Express
.u
z
a) Express (3 - √5)2 in the form of m + n√5, where m and n are integers
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
5
Question 5
On the grid below
a) draw the circle with equation 𝑥 2 + 𝑦 2 = 34
b) draw the line with equation x + 2y = 1
w
w
w
.w
es
t
.u
z
Estimate the points of intersection to one decimal place.
Estimated points of intersection………………………
……………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
6
Trapezium AEFG has an area of 36cm2
w
w
w
.w
es
t
Work out the area of the shaded region.
.u
z
Question 6
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
7
Question 7
Naomi and Gary are redoing their bathroom. It is to have new tiles on the wall and laminate
flooring.
The widths of the tiled walls are 2.5 m and 3.5 m.
The height of both tiled walls is 2.8 m.
The floor is a rectangle measuring 2.5 m by 3.5 m, but the bath takes up a rectangle
measuring 1.7 m by 0.75 m.
es
t
.u
z
a) How many square tiles, each with side length 30 cm, must be bought for the walls?
.w
Answer…………………………….
w
w
w
b) What area of flooring is needed?
Answer…………………………….
c) Laminate flooring costs $7.98 per square metre. How much will it cost to cover the
bathroom floor?
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
8
Question 8
Find equation of a line which is parallel to the line with the equation 3x + y = 7 and which
w
w
w
.w
es
t
.u
z
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
9
w
w
w
.w
es
t
.u
z
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
10
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test E1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
Find the solutions to the simultaneous equations
x – 2y = 1
w
w
w
.w
es
t
.u
z
x2 + y2 = 13
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
Question 2
In an arithmetic progression, the 8th term is twice the 3rd term and the 20th term is 110.
Answer…………………………..
w
.w
es
t
.u
z
a) Find the common difference.
w
w
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
3
Question 3
The polynomial p(x) = x3 + ax2 – 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
w
w
w
.w
es
t
.u
z
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
4
Question 4
The point A has the coordinates (2, 5)
The point B has the coordinates (6, 7)
.u
z
a) Find the gradient of the line that passes through line AB
es
t
Answer…………………………..
w
w
w
.w
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
5
Question 5
What is the radius of a circle inscribed in a triangle with base of length 4 and height of
length 3?
w
w
w
.w
es
t
.u
z
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
6
Question 6
.u
z
In the diagram OBDE and OAFG are parallelograms.
es
t
B is the midpoint of OG. A is the midpoint of OE.
Express, in terms of a and b, the following vectors.
.w
Give your answers in their simplest form.
w
…………..
w
b)
w
a)
……………
c)
.…………..
d) Show
are parallel
……..……
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
7
Question 7
In the diagram below ∠W = ∠Y and VX is one fifth of VZ.
w
w
w
.w
es
t
.u
z
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
8
Question 8
On the grid below
a) Draw the line y – 3x = 4
b) Draw the curve y = 2x2 - 5
c) From observation of your line and curve estimate the points of intersection
Estimated points of intersection………………………
……………………….
Total for page 5 marks
.u
z
END OF TEST
w
w
w
.w
es
t
TOTAL FOR TEST 40 MARKS
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
9
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test F1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
−2
a) Find the value of 125 3
Answer…………………………..
.w
es
t
.u
z
b) Express (5 - √8)(√2 + 1) in the form, a + b√2, where a and b are integers
30
Answer…………………………..
w
w
w
c) Express √80 + √5 in the form c√5, where c is an integer
Answer…………………………..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
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.
.u
z
a) Find the number of grains to be placed on the thirteenth square of the
chessboard.
Answer…………………………..
es
t
b) He then said he would like as many grains of corn as the chessboard carried.
w
w
w
.w
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
3
Question 3
Given f(x) = 3x3 – 5x2 – 58x + 40
a) Find the remainder when f(x) is divided by (x – 3)
.u
z
Answer…………………………..
b) Show that (x – 5) is a factor of f(x).
w
w
w
.w
es
t
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
4
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.
w
w
w
.w
es
t
.u
z
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
5
Question 5
Given:
Circle O where
CD = 16
AB = 16
OB = 10
w
w
w
.w
es
t
.u
z
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
6
Question 6.
ABCDEF and GHIJKL are regular hexagons with centre O.
w
in terms of a and b
………….
w
a) Write the vector
.w
es
t
.u
z
GHIJKL is an enlargement of ABCDEF, with scale factor 2.
w
b) Write the vector
c) Write the vector
in terms of a and b
……………
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
…….……..
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
7
Question 7
a) Is this triangle right-angled?
Explain your answer
es
t
.u
z
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
………………………………………………………………………………………………….
w
w
w
.w
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
8
Question 8
On the grid below
a) Draw the line y = x + 3
b) Draw the curve y = x2 + 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
w
w
w
.w
es
t
.u
z
TOTAL FOR TEST 40 MARKS
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
9
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test G1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
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?
.u
z
Give your answer to the nearest minute.
Answer…………………………….
es
t
b) Tame Valley is a company that makes yoghurt.
A machine fills trays of 25 pots with yoghurt.
.w
In one hour, the machine fills a total of 24000 pots.
w
w
w
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
2
Question 2
Show that
1+𝑥 2
2𝑥
(1−𝑥 2 )2 - (1−𝑥 2 )2
w
w
w
.w
es
t
.u
z
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
3
Question 3
Factorise completely f(x) = 2x3 - 3x2 - 5x - 6
w
w
w
.w
es
t
.u
z
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
4
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
w
w
w
.w
es
t
.u
z
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
5
Question 5
a) Find the perimeter of the sector.
Use 3.14 as the value of 𝜋
.u
z
Give your answer to 2 decimal places.
Answer…………………………….
w
w
w
.w
Give your answer in terms of 𝜋
es
t
b) Find the area of the sector.
Answer…………………………….
Total for page 5 marks
Question 6
For more Westminster math exam sample and original tests join us www.west.uz
6
in terms of a and b
es
t
.u
z
a) Write down the vector
.w
Answer…………………………….
w
b) DF : FG = 2 : 3
in terms of a and b
w
Work out the vector
w
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
7
.w
es
t
.u
z
a) Work out the length of PQ
Answer…………………………….
w
b) A cuboid has a volume of 64 𝑐𝑚2
w
Its size is increased by a scale factor of 2.
w
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
8
On the grid below
a) Draw the line y = 3x - 1
b) Draw the curve y = x2 - 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
w
w
w
.w
es
t
.u
z
TOTAL FOR TEST 40 MARKS
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
9
ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test H1
Time allowed: One hour 15 minutes
.u
z
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.
es
t
NO BOOKS, NOTES, CALCULATORS OR ANY SORT OF ASSISTING MATERIAL ARE
ALLOWED.
.w
For Office Use Only
w
w
w
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
1
Question 1
The roots of the equation
2x2 + 6x +3 = 0
are α and β.
w
w
w
.w
es
t
.u
z
Show that α2 + β2 = 6
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
2
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?
.w
es
t
b) What fraction of the company are men under 25?
.u
z
Answer …………….
Answer ……………
w
w
w
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
3
Question 3
The line AB has equation 3x + 5y = 11
a) Find the gradient of the line AB.
Answer…………………………….
Answer…………………………….
w
w
.w
es
t
.u
z
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.
w
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
4
Question 4
a) Work out the value of
√50+√18
√8
Answer…………………………….
2√7 − 1
w
w
w
.w
es
t
2√7 + 5
.u
z
(a) Express the following in the form, m + n√7 where, m and n are integers
Answer…………………………….
Total for page 5 marks
For more Westminster math exam sample and original tests join us www.west.uz
5
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.
w
w
w
.w
es
t
.u
z
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
6
es
t
.u
z
Question 6
The letter ‘T’ on this square grid has an area of 200cm2
.w
Calculate the perimeter of the ‘T’.
w
w
w
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
7
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?
w
w
w
.w
es
t
.u
z
Use 1 cm3 = 1 ml
Answer…………………………….
Total for page 5 marks
Question 8
For more Westminster math exam sample and original tests join us www.west.uz
8
On the grid below
a) Draw the line y = 4x + 1
b) Draw the curve y = 6 – x2
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
w
w
w
.w
es
t
.u
z
TOTAL FOR TEST 40 MARKS
USE THIS PAGE FOR DRAFTS
For more Westminster math exam sample and original tests join us www.west.uz
9