Examples for secondary school students - page 96 of 229
Number of problems found: 4578
- Decide 2
Decide whether points A[-2, -5], B[4, 3], and C[16, -1] lie on the same line - Non-conforming 19863
The probability that a quality product will meet all technical requirements is 0.95. What is the probability that all three randomly produced products will be: a) conforming, b) non-conforming - Substitution 19793
Calculate in arithmetic sequence a1, d, s7, if: a1 + a4 + a6 = 71 a5 - a3 - a2 = 2 Hint: Use the substitution method when solving the system. Pay due attention to the "minus" signs in the second equation of the system. - Sum of the seventeen numbers The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
- Forty-eight 19513
25% of children did not attend the course because they were ill. Forty-eight children passed the course. How many children were initially supposed to complete the course? - Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Calculate 19443
Calculate the height of the cylinder when r = 10 mm and S = 800 mm². Calculate the radius / r / of the cylinder when the height is 20 mm and S = 1000 mm².
- Quadrilateral 19413
Calculate the surface area of a regular quadrilateral pyramid given: a= 3.2 cm h= 19 cm Method: 1) calculation of the height of the side wall 2) area of the base 3) shell areas 4) the surface of a regular quadrilateral pyramid - Surface 19383 cone
The volume of a cone with a radius of 6 cm is 301.44 cm cubic. What is its surface? - Calculated 19363
Peter calculated the number of placement options with four teams, A, B, C, and D, in the first three places. He helped himself with a tree diagram. Complete the solution. - Intersection 19343
What is the sum of all coordinates of points at the intersection of the line p: x = -1-2t, y = 5-4t, z = -3 + 6t, where t is a real number, with the coordinate planes xy and yz? - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates [- 14; 0]? - Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Average speed
A car traveled from city A to city B at a speed of 40 km/h, then from B to C at 60 km/h, and finally from C to D at 50 km/h. Calculate the car's average speed over the entire route from A to D if the distance from A to B is 20% of the total distance and f
- Table and chairs
Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chairs between them if people randomly choose their place? - Tiles
The tile is square and has a side of 15 cm. What dimensions can a rectangle composed of 90 tiles have so that no tile remains? - Trapezoid: 18703
In the ABCD trapezoid: | AD | = | CD | = | BC | a | AB | = | AC |. Determine the size of the delta angle. - Speedometer 18693
The Macháček family went on a 3-day trip to Třeboň. They didn't want to get too tired but wanted to see a lot. Therefore, they drove at a walking pace, and at the end of the 3rd day, they measured 90 km on the speedometer. On the second day, they traveled - Pavel 3
Pavel has deposits in two accounts. One in a current account with an annual interest of 2% and the other in a savings account with an annual interest of 4%. Both deposits earned him CZK 1,000 per year. If Pavel transferred the deposit from one account to
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