Entrance examination mathematics


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the detailed solution below.
























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: …………………………….

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Question 2.
Find the sum of all two-digit natural numbers are divisible by 2 but not by 3.
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Page 4 of 12
Question 3.


The parabola y = 4x
2
– 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?

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Page 5 of 12
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.

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Page 6 of 12
Question 5.


The numbers a, pi and q are different positive integers and p and q are prime. If a
is divisible by p and q and if
𝑏 =
𝑎
𝑝∙𝑞
, then which of the following must be true Ii bi 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

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Page 7 of 12

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?

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Page 8 of 12
Question 7.

The point O is a center of the circle. Dis a tangent point. Find the shaded area if
𝐴𝐵 = 4, 𝐴𝐶 = 2.


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Page 9 of 12
Question 8.

Solve the simultaneous nonlinear equations
{
(𝒙 − 𝒚)(𝒙
𝟐
− 𝒚
𝟐
) = 𝟒𝟓
𝒙 + 𝒚 = 𝟓


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Page 10 of 12
Question 9.

Three billionaires have a total of 30 billion dollars between them. If billionaire A has
300 million more than billionaire Band billionaire B has 600 million more than billionaire Chow much more money do billionaires Band C combined have than billionaire A alone

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Page 11 of 12
Question 10
.

Given OQ parallel toWR;
WV=VU=TU=WT=OW=QR and PQ=TS;
WOQR a rectangular and
PQTS a parallelogram.
i)
find the values of x and y
ii)
find the figure's total perimeter

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Page 12 of 12
END OF THE TEST
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