Examples for secondary school students - page 32 of 237
Number of problems found: 4730
- Bank withdrawal fee
The grandparents had €2,500 in the bank valued at 2% p.a. After the quarter, and they took the money with the evaluation. How much money was it? The bank honored the fee for early withdrawal in the amount of 0.05% of the deposited amount. - Operation asterisk pairs
The * (asterisk) operation assigning one number to two pairs of numbers is introduced as follows: (a, b)*(c, d) = ac+bd We know that: (x,2)*(-1, v) = -1 and (2,-1)*(u, v)=5 and (u, v)*(1,1)=-2 What is (1,2)*(x, y) equal to if y=3? - Favourite singers
A poll carried out among 200 students of one school found out which of the singers V. Neckář, K. Gott, W. Matuška is the most popular. It brought the following results: Gott is popular with 78 students, Matuška with 75 students, and Neckář with 101. It wa - Coefficient of friction
A car moves along a horizontal road at a speed of 15 m/s. After turning off the engine, the car traveled a distance of 225 m. What was the coefficient of friction for this motion? - Circle and chord
The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc? - Three-digit - sum
A three-digit number has a digit sum of 16. If we change the digits in the hundreds and tens places in this number, the number is reduced by 360. If we swap the ten's and one's digits in the original number, the number increases by 54. Find this three-dig - Bread weight rejection
The weight of a loaf of bread should be 900 g. Loaves whose weight differs by more than 30 g from this value must be rejected. Determine the probability that a loaf is rejected if its weight has a normal distribution N(900,40). - Airport 4
The airport in Košice collected the following data on aircraft delays within one week: (Solve the following tasks without classification into intervals. Round the results to 2 decimal places) Aircraft delay in min.: 541; 545; 575; 520; 572; 544; 524; 567; - Tie price calculation
CZK 895 was paid for three ties. A blue tie was 18% more expensive than a gray one, and a brown one was CZK 100 more expensive than a gray one. Calculate the prices of individual ties. - Collection of medicinal plants
A pensioners' club organised a collection of medicinal plants. Two pensioners could not participate in the collection for health reasons, the others decided to collect dead-nettle, elder, and coltsfoot. All three herbs were collected by 7 pensioners, dead - Pyramid edge calculation
The foundations of a regular truncated quadrilateral pyramid are squares. The lengths of the sides differ by 6 dm. Body height is 7 dm. The body volume is 1813 dm³. Calculate the lengths of the edges of both bases. - Pavla Irena age
Paula is 2x older than Irene. Four years ago, Paula was 6 times as old than Irene was then. In how many years will the ages of Paula and Irene be in the ratio of 4:3? Thanks - Triangle angle bisector
In the triangle, ABC, the angles alpha and beta axes subtend the angle phi = R + gamma/2. R is a right angle of 90°. Verify. - Motorcyclist gully fall
An undisciplined motorcyclist drove at an unreasonable speed on a mountain road, lost control in a bend, and left the roadway at 90 km/h. He was falling into a gully 36 m deep. Draw a cross-sectional picture of the whole situation. How far did the motorcy - Agricultural
Last year, the Agro agricultural company sowed wheat on a total area of 29 ha and rye on a total area of 18 ha. From all these fields, it harvested a combined total of 137.4 tonnes of grain. The sum of the average yields per hectare of wheat and rye was 5 - Meeting handshake count
After the meeting, all participants shook hands with each other - a total of 105 times. How many people were there at the meeting? - Hot cocoa
Santa and Baby Jesus met together for hot cocoa with cinnamon in the Šenov Drevjanka. Santa finished his cocoa 18 minutes earlier and as he was in a hurry he immediately left for the North Pole. At the moment when Baby Jesus also finished his cocoa, he no - Karel grade average
Charles has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one. - Probability - test
The test contains 11 questions; each question has 4 options (only one correct). Find the probability that fewer than 2 questions will be answered correctly, given that the probability of correctly answering any question is 1/4. (Write the result as a whol - Elevation of the tower
We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39°25''. If we come towards its foot 50 m closer to place B, we can see the top of the tower from it at an elevation angle of 56°42''. How tall is the towe
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