Examples for secondary school students - page 29 of 237
Number of problems found: 4730
- We randomly
We randomly select a three-digit number. What is the probability that the number 8 occurs at most once in its notation? - Body trajectory energy
A body of mass 4 g is shot perpendicularly from the ground and lands in 8 s. What is its kinetic energy at the beginning of its trajectory, what speed does it take off, and where does the distance from the ground stop? - Worker reward division
The reward of CZK 4,220 was divided among 3 workers in such a way that the second received CZK 400 more than the first, and the third received 30% more than the second. How much did each get? - Equation of a circle
Write the general equation of a circle with center S(2;5) and point B(5;6) lying on this circle. - Ball collision speed
Two inelastic/plastic balls move towards each other with equal velocities of 2 m/s. The weight of one ball is 3 kg, the other 1 kg. Determine the speed of the balls after the collision and the loss of kinetic energy. - Flywheel energy decrease
How much energy was supplied by the flywheel of the device if its number of revolutions decreased from 1200 to 720 revolutions per minute if it has a moment of inertia of 71.3 kg/m²? - Aquaristics
We consider 'words' (i.e., arbitrary strings of letters) obtained by rearranging the letters of the word 'AQUARISTICS'. All letters are treated as distinguishable from each other. The number of such words that also contain the string 'CAVA' (as consecutiv - Isosceles trapezoid
In an isosceles trapezoid, the basic lengths are 15 cm and 9 cm. The diagonals are 13 cm long. Calculate the perimeter and area of the trapezoid. - Geometric sequence terms
The two terms of the geometric sequence are a2=12 and a5=three halves. a) calculate the tenth term of the sequence. b) calculate the sum of the first 8 terms of the sequence. v) how many first terms of the sequence need to be added so that the sum is equa - Arithmetic geometric sequence Determine four numbers so that the first three form the successive three terms of an arithmetic sequence with difference d=-3 and the last three form the next terms of a geometric sequence with quotient q=one half.
- Arithmetic progression difference
Determine the difference d in AP if a1=3 and a1+a2=12 - Department age groups
The department has 90 members. There are 4 more older adults in the section than younger adults. There are 10 more older pupils than all adults. How many older and younger teenagers and how many older pupils are there in the section? - Athletics
160 students (from grammar schools and technical schools) participated in an athletics competition. The proportion of girls from grammar schools was 50%, and the proportion of girls from technical schools was 10%. Determine how many students were from gra - Arithmetic sequence indices In which arithmetic sequence is the sum of the first five terms with odd indices equal to 85 and the sum of the first five terms with even indices equal to 100?
- Arithmetic sequence middle An increasing arithmetic sequence has an odd number of terms. The middle term is 302. If we remove the 4 largest terms from the sequence, the middle term will be 296. Determine the difference in the sequence.
- Sequence sum formula Two arithmetic sequences have the same first term. The nth term of the first sequence is 15, and of the second sequence, 21. The sum of the first n terms of the first sequence is 63, and of the second sequence, 84. Write the sums of the first n terms of b
- Geometric series terms
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence. - Arithmetic sequence sum In which arithmetic sequence is S5=S6=60?
- Geometric sequence quotient Determine the quotient of the geometric sequence with the first term a1=36 so that s2 is less than or equal to 252.
- Ring bead combinations The ring consists of 4 beads. There are 5 different colors of beads in the package. How many possibilities are there to create one ring, and can the colors repeat?
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