Examples for secondary school students - page 28 of 231
Number of problems found: 4612
- Geometric sequence sum
Determine s5 of the geometric sequence if: a1 + a2 = 10 and a4 - a2 = 120 - Trainee triangular wedge
Trainees stand on the marks in rows exactly 1.5 m apart. They form an expanding triangular wedge (in each subsequent row, there is one more exerciser), while the distance between the front exerciser and the back row is 30 m. Determine the number of traine - Deposit double years
The bank offers interest on the deposit of 4 percent per annum. In how many years will the deposit double? - 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 4g is shot perpendicularly from the ground and lands in 8s. 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? Thank you - 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 3kg, the other 1kg. 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 distinguishable from each other here. The number of such words that also contain the expression “CAVA” (as consecutive l - 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 (gymnasiums and technical schools) participated in the athletics race. The proportion of girls from the gymnasium was 50%, the proportion of girls from the technical schools was 10%. Determine how many students were from the gymnasiums and ho - 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.
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