Examples for secondary school students - page 127 of 237
Number of problems found: 4730
- Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4) - In the orchestra
In the school orchestra four musicians play – one the violin, one the clarinet, one the cello, and one the trumpet. During a performance not always all four play at once. Sometimes only one instrument plays, sometimes two, sometimes three, and sometimes a - Two number difference
The difference between the two numbers is -85. Their sum is 89. Determine these numbers. - Practice
How many ways can you place 20 pupils in a row when starting on practice? - Push-up work calculation
Zdenek, weighing 54 kg, made 15 push-ups on the crossbar. The height he reached was about 40 cm. What kind of work did he do? What would have been his performance if the whole exercise had taken him a minute and a half? - Two Typists Pages Written
The two typists wrote a total of 65 pages; although the first typed for an hour longer than the second, but typed 5 pages less; the second types 2 more pages per hour than the first. How many pages per hour does each typist write? - Gold rods
In one kingdom, two gold rods were inherited over generations. But King Emanuel had three sons who could not agree on anything. He therefore wanted to break one rod so as to make three rods out of two. The youngest son gets the shortest rod, the oldest so - Two cyclists 2
At the same time, two cyclists left towns A and B at constant speeds. The first one goes from town A to town B, and the second one from town B to town A. At one point during the trip, they met. After they met, the first cyclist arrived at town B in 36 min - Climb of the road
At what angle does the road rise if the climb is 8%? They rounded up for tens of minutes. - Card distribution ratio
The children have 568 cards distributed as follows: Jano and Mišo in the ratio of 3:7 and Mišo and Laco in the ratio of 3:5. How many cards does Mišo have? - Legs
Cancer has five pairs of legs, and the insect has six legs. Sixty animals have a total of 500 legs. How much more are cancers than insects? - Cube cut
The edge of the CC' guides the ABCDA'B'C'D'cube, a plane that divides the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine which ratio the edge AB divides by this plane. - Trapezoid side lengths
The circumference of the isosceles trapezoid is 34 cm. The difference in the length of the bases is 6 cm. The arm's length is one-third of the length of the longer base. Find the lengths of the trapezoidal sides. - Grade pupil comparison
There are 2 more pupils in the 7th grade than in the 8th grade. If the number of pupils in the 7th grade increased by 7 and the number of pupils in the 8th grade increased by a third of the original number, there would be the same number of pupils in both - Journey 5
A man has to make a journey of 84 km in 3 hours. He travels the first 30 km at 20 km/hr. At what rate must he travel the remaining distance to complete his journey on time? - Angle at the apex
In an isosceles triangle, the angle at the apex is 30° greater than the angle at the base. How big are the internal angles? - White Blue Balls Probability
There are eight white balls and several blue balls in the pocket. The probability of pulling out the white ball is 2/3. How many blue balls are in your bag? - Class Passing Rate Girls
There are 30 boys in the class, and 28 of them passed. All the girls passed. A total of 95% of the students passed the course. How many girls are in the class? - Movie Viewers Three Days
In three days, 3960 viewers saw the film. How many viewers watched the movie each day if we know: the second day saw 20% more viewers than the first day and the third 20% less than the first and second together. - Diluting Alcohol to Percentage
We want to prepare 200 g of 64% alcohol. We have enough 80% alcohol to dilute with water. How much 80% of alcohol and water will we need?
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