# Examples for secondary school students

1. Standard deviation Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
2. Express train International express train drove from Kosice to Teplice. In the first 279 km, the track was repaired, and therefore it was moving at a speed of 10km/h less than it was scheduled to drive. The rest of the 465 km trip has increased the speed by 8 km/h than
3. Non linear eqs Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
4. Symmetry by plane Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0
5. Water reservoir One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously?
6. Odd/even number Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time. Prove. ..
7. Std-deviation Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
8. How many 2 How many three lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed
9. Rectangular trapezoid The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
10. Degrees Fahrenheit ? The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I. A temperature increase of 1 degree Fahrenheit is equi
11. Midpoint 4 If the midpoint of a segment is (6,3) and the other end point is (8,-4) what are thw coordinate of the other end?
12. Coordinates of midpoint If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
13. A car A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
14. Free fall The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
15. Home cleaning Mr. Smith is cleaning up a big mess at home. In the closet, he finds a solution that is 5% bleach, and another stronger solution that is 20% bleach. For this particular job, he needs 600mL of 15% bleach. How much of each type (to the nearest mL) should he
16. Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
17. A man 2 A man divides \$10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
18. Precious metals In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3
19. Right 24 Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
20. Right isosceles triangle Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?

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