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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.
What was the perimeter of the original piece of paper?
Answer…………………………….
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Question 7
Amir has a photo and a rectangular piece of card.
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The photo is 16 cm by 10 cm. The card is 30 cm by 15 cm.
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.
The piece of card he has left is mathematically similar to the photo.
Work out the value of x.
Answer…………………………….
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Question 8
In the figure below
M is the midpoint of OA
N is the midpoint of OC
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Answer:
I …………………
ii………………….
iii………………….
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END OF TEST
TOTAL FOR TEST 40 MARKS
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USE THIS PAGE FOR DRAFTS
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ENTRANCE TEST
LYCEUM OF WESTMINSTER INTERNATIONAL UNIVERSITY IN TASKENT
MATHEMATICS
July 2016
Test D1
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.
For Office Use Only
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
Solve the simultaneous equations
x + y = 4
x
2
+ y
2
= 40
Answer…………………………..
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Question 2
f(x)
≡ 2x
3
+ px
2
+ 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.
a) Find the value of p and the value of q.
b) Show that (x-
1
/
2
) is a factor of f(x)
Answer…………………………..
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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.
You must show all your working.
Answer: 1st………………..
2nd……………….
3rd……………….
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Question 4
a) Express (3 - √5)
2
in the form of m + n√5, where m and n are integers
b) Express
(3−√5)
2
1+√5
in the form p + q√5, where p and q are integers
Answer…………………………..
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Question 5
On the grid below
a) draw the circle with equation
𝑥
2
+
𝑦
2
= 34
b) draw the line with equation x + 2 y = 1
Estimate the points of intersection to one decimal place.
Estimated points of intersection………………………
……………………….
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Question 6
Trapezium AEFG has an area of 36cm
2
Work out the area of the shaded region.
Answer…………………………..
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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.
a) How many square tiles, each with side length 30 cm, must be bought for the walls?
Answer…………………………….
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…………………………….
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