Examples for secondary school students - page 73 of 237

Number of problems found: 4730

Three-digit numbers
How many three-digit numbers are not closer to 600 on the number axis than 400?
Free fall
The elevator car weighing 720 kg, is torn off at the height of 125 m and begins to fall in a free fall. How much kinetic energy did the elevator car have when it hit the ground floor of the building when the free fall of the car lasted 5 s?
Biology test
Peter Šťastný did not manage to study for the biology test due to urgent matters. In the test, for every correctly solved task there were 10 points, for a wrongly solved task 5 points were subtracted, one could also not answer, for which there were 0 poin
Perpendicular leg
Calculate the area of a right triangle whose longer perpendicular is six dm shorter than the hypotenuse and three dm longer than the shorter perpendicular.
Giraffe 2
The lifespan of a guinea pig is six years less than that of a giraffe. The lifespan of a tiger is four times that of a guinea pig. If the total lifespan of the three animals is 30 years, calculate the lifespan of the giraffe.
Free fall 5
Jeremy accidentally dropped his toy stuffed animal from the balcony of his apartment on the fourth floor. The toy hit the ground at a velocity of 16.0 meters per second. At impact, it took 2.0 seconds for the toy's velocity to reach 0 meters per second. I
Permutations with repetitions
How many ways can the digits 1, 2, 2, 3, 3, 3, 4 be permuted into four-digit, three-digit, and two-digit numbers without repetition? Example: 4 digits: 1223, 2213, 3122, 2313, 4321, etc. 3 digits: 122, 212, 213, 432, etc. 2 digits: 12, 21, 31, 23 Note: I
Saving in January
On the 1st of January, a student puts $10 in a box. On the 2nd, she puts $20 in the box, and so on, putting the same number of 10-dollars notes as the day of the month. How much money will be in the box if she keeps doing this for a) the first ten days of
Arithmetic progression 2
The 3rd term of an Arithmetic progression is ten more than the first term, while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic progression if the 7th term is seven times the first term.
The town
The town population is 56000. It is decreasing by 2% every year. What will be the population of the town after 13 years?
Tests
To obtain a grade A, Patrick must score an average of at least 70 on five tests. If his average mark for the four tests is 68, what is the lowest mark he can get on his fifth test and still obtain a grade A
Maturity value
IKEA Furniture can purchase furniture with a three-year simple interest loan at 8% interest per year. What is the maturity value of a 3500 loan?
The sides
The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle.
Binary words
How many 10-bit words can be created with precisely four units (e.g., 1111000000)?
Exchange € 100
Find out how many ways you can exchange € 100 if you have an unlimited number of 50, 20, 10, and 5 euro banknotes. Use a method other than listing all options systematically.
Find quadrant
Point Y is located at (4, -2) on a graph. Point Z is located five units to the left of Point Y. In which quadrant is Point Z located?
Four bicycles
In the department store, they sell bicycles for families with children. Women's bicycles are 10% more expensive than men's, and children's bikes are a third cheaper than women's. The family paid a total of CZK 31,030 for two children's, one man's, and one
The body
A body slides down an inclined plane at an angle of α = π/4 = 45° to the horizontal, with friction causing a deceleration of a = 2.4 m/s². At what angle β must the plane be inclined so that, after a small push, the body slides at a constant speed?
Fabric purchase
The tailor's salon bought 130 meters of fabric for € 1,037. The meter of the first fabric costs € 8.90, and the meter of the second fabric costs € 7.40. Thus, they bought 130 meters of fabric for € 1,037.
Sleep vs. watch TV time
Using a data set relating to the number of episodes I watch on TV in a day (x) versus the number of hours of sleep I get that night (y), I construct the linear model y=−0.6x+11 Which of the following general observations can you make from this model? a) I

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