Examples for secondary school students - page 19 of 237
Number of problems found: 4730
- 4B - truncated pyramid
Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10 cm and 4 cm and the slant height of the lateral face is 5 cm. - Me and my father
My father and I are currently 55 years old together. When we are 65 years old together, my father will be four times older than me. How old am I? - RRL Basics
What is the length of the smaller base and the height of an isosceles trapezoid if a = 9 dm, the leg is 6 dm, and angle ACB = 90°? - Three dice 2
What is the probability that exactly two of the three dice show the same odd number when three dice are rolled? - In class 24
There are a total of 16 students in the class, a quarter of whom are girls. A team of five is selected at random. Determine the probability that the team will have: a) at least 4 girls, b) at most 1 girl, c) no girls. - In a regular 5
In a regular triangular prism ABCV, the angle between the lateral face and the base plane is α = 45°. Determine the angle between the lateral edge and the base plane. - Christmas 4
There are only 3 packages left under the tree — two for Julia and one for Susan. Julia takes two at once. What is the probability that both packages belong to her? - 5D decimal
How many five-digit numbers contain exactly 2 fours and exactly 3 sevens in their decimal notation? - Between terminals
A resistor is connected to a 220 V source. A current of 220 mA flows through the resistor. Determine the current that flows through the resistor when it is connected to a 24 V voltage source. - The tower
From a window 8 m above the horizontal plane, the top of a tower can be seen at an elevation angle of 53°20′, and its base at a depression angle of 14°15′. How high is the tower? - HAMMER 4
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word CAL. - On a mass
Forces F₁ and F₂, each with a magnitude of 40 N, act on a mass point M. Their resultant has a magnitude of 60 N. Determine the angle between forces F₁ and F₂. - Area 51
The area of a triangle is 54.39, angle alpha is 32°, and angle gamma is 144°. - Gardener 5
A gardener bought 17 apple trees and 11 pear trees and paid a total of €111.65. How much did 1 pear tree cost, given that its price was 35 cents higher than the price of 1 apple tree? How much would the gardener pay for 28 apple trees and 15 pear trees? - Determine the surface area
Find the surface area of a cone of height 30 cm whose slant side makes an angle of 60° with the base plane. - Quadrilateral - irregular
Find the length of side d = |AD| in quadrilateral ABCD: a = 35 m, b = 120 m, c = 85 m, angle ABC = 105°, angle BCD = 72°. - Unit circle
In the Cartesian coordinate system, a unit circle is given on which points A and B lie. Point O is the origin with coordinates (0, 0), and point B has coordinates (1, 0). The size of angle BOA is 151°. Determine the x-coordinate of point A. - Prizes - competition
For the prizes for the three best competitors a sum of money in crowns was prepared. The first competitor got half of this sum. The second competitor got 300 crowns. The third competitor got the rest of the prepared amount, which was three times less crow - X-ray intensity
The intensity of X-ray radiation is halved when passing through a 13.5 mm thick lead layer. Determine the thickness of the lead plate that will reduce the radiation intensity to one tenth of its original value, given that the intensity decreases exponenti - Equation - integers
Solve the equation for the unknown x from the set of natural numbers: 1 + 6 + 11 + 16 + … + x = 970
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