# Examples for secondary school students - page 59

1. Conical area
A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
2. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
3. Unknown number
I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number?
4. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
5. Two lands
The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
6. Competition
15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students?
7. Q of GP
Calculate quotient of geometric progression if a1=5 a a1+a2=12.
8. Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
9. Sum of members
What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
10. The gardener
The gardener bought trees for 960 CZK. If every tree was cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
11. Trapezium ABCD
In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
12. Harmonic and arithmetic means
The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calculat
13. Coefficient
Determine the coefficient of this sequence: 7.2; 2.4; 0.8
14. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
15. Difference AP 4
Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
16. Combinations
If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
17. Points in plane
The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points?
18. Elements
If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
19. Seagull
Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (wi
20. Word MATEMATIKA
How many words can be created from the word MATEMATIKA by changing the order of the letters, regardless of whether or not the words are meaningful?

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