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SCIENTIFIC KNOWLEDGE TEST:

INSTRUCTIONS

This mathematical and logical part of the examination consists of ten problems.

In ALL these questions (as in the institute) international SI units are used. This

means that:

A) the comma ',' is used to separate THOUSANDS1,200,150 = One million two hundred thousand one hundred and fifty.

B) the full stop '.' is the decimal separator

2.5 = two point five (two and a half)

------------------------------------------------------------------------------ Use separate paper provided for your calculations and answers of the questions 1-5.

1. Solve the following pair of the equations

=+

=+

21)(3)(7

15)(2)(5

yxyx

yxyx

2. Simplify the expression ( ) ( ) 22 baba + and calculate its exact value, when300100=a and

300100=b

3. The sun was shining in the yard of engineer Jack Smith. Jack was reading in the shadow

cast by the pine tree planted by his grandfather Tom Smith. The length of the horizontal

part of the shadow was 6.0 m and the height of the vertical part of the shadow on the wall

was 3.6 m. The height angle of the rays of the sun was 42. Find the height of the pine tree.

4. You make a deposit of 2000 into your account. The interest rate is 5% and the interest

is added into the account first after one year and then annually. How long will it take your

savings to grow to 10000 ?

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5. In the picture below the numbers in the squares show the number of matches in the

square. There are 84 matches altogether. Each full column and row contains 27 matches.

Take away 4 matches and rearrange the matches in a similar way so that still each full

column and row contains 27 matches and in the middle there is an empty square.

6 15 615 15

6 15 6

-------------------------------------------------------------------------------Use separate paper provided for your calculations and answers of the questions 6-10.

6. The initial distance between two particles is 0.70 km. The particles head towards each

other at speeds of 2.5 m/s and 4.5 m/s, respectively.

a) When will they meet?b) Where will the meeting take place?

7. The ballistic pendulum is a block of 3.0 kg mass suspended from a thread 2.5 m long. A

bullet with a mass of 9.0 g hits the block and sticks in it, the result being a deflection of

the system by an angle of 18 o. Find the bullets speed.

8. A steel balk has a length of 50.485 m at the temperature of 5.0 oC. What would be the

length of the balk at the temperature of -22 oC, when the coefficient of linear expansion

( ) is 0.000012 / oC?

9. An electric radiator which is an ordinary constant resistor emits a heating power of

1.2 kW at a mains supply voltage of 230 V. What is the total heating power in each

respective instance when two such radiators are connected

a) in parallel, and

b) in series to the 230 V supply voltage?

10. Suppose you begin with 2.8 mg of a pure radioactive substance and 3.6 h

later determine that 0.35 mg remain. What is the half-life of the substance?