Examples for secondary school students - page 29 of 232
Number of problems found: 4622
- 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. - 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? - Loan yield percentage
You lent €400. The borrower paid you €440 back in 5 months. What was the yield on this loan? - Circumscribed circle
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - Perpendicular forces
Distribute the force of magnitude F = 100 N into two perpendicular components with magnitudes F1 and F2 so that the angle between forces F1 and F is 43°52'. - Triangle angle area
Calculate the size of the largest angle in triangle ABC if a = 7 cm, b = 8 cm, and c = 13 cm. Calculate the area of the triangle, the height per side a. - Trapezoid interior angles
The area for shooting training has the shape of a trapezoid, the parallel sides of which are 36m, 21m long, and the remaining sides are 14m, 16m long. Determine the size of the interior angles with a longer base. - Triangle point coordinates
In triangle ABC, determine the coordinates of point B if you know that points A and B lie on the line 3x-y-5=0, points A and C lie on line 2x+3y+4=0, point C lies on the x-coordinate axis, and the angle at vertex C is right. - Volleyball tournament teams
The school volleyball tournament was played on a one-on-one basis. One match lasted 15 minutes, and 3 hours and 45 minutes were played. Calculate how many teams participated. - Column water force
A concrete column with a density of 3500 kg/m3, a height of 6 m, and a square base of a=25 cm lies at the bottom of the dam at a depth of 10 m. At the upper end, it is lifted by a rope by a crane. 1) with how much force does the pole stretch th - Line coefficient determination
In the equation of the line p: ax-2y+1=0, determine the coefficient a so that the line p: a) it formed an angle of 120° with the positive direction of the x-axis, b) passed through point A[3,-2], c) was parallel to the x-axis, d) had a direction of k = 4. - Arithmetic sequence terms
Write the first 5 terms of the arithmetic sequence if the first term is a1=7 and the difference d= - 3 - Product good probability
There are 49 products in the box, of which only 6 are good. We will randomly draw 6 products from them. What is the probability that at least four of the products drawn are good? - Seed plant probability The probability that a plant will grow from a seed is 75%. What is the probability that 5 plants will grow if we assemble 6 seeds?
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