# Examples for secondary school students - page 59

1. 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?
2. The gardener The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
3. Q of GP Calculate quotient of geometric progression if a1=5 a a1+a2=12.
4. 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.
5. Sum of members What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
6. 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
7. Right triangle eq2 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
8. 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
9. Coefficient Determine the coefficient of this sequence: 7.2; 2.4; 0.8
10. 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?
11. Difference AP 4 Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
12. 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?
13. 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?
14. Elements If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
15. 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
16. Minimum of sum Find a positive number that the sum of the number and its inverted value was minimal.
17. Imaginary numbers Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
18. Variation equation Solve combinatorics equation: V(2, x+8)=72
19. Series and sequences Find a fraction equivalent to the recurring decimal? 0.435643564356
20. Third member Determine the third member of the AP if a4=93, d=7.5.

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