Examples for secondary school students - page 23 of 231
Number of problems found: 4612
- Acceleration Before Break
A body of mass 500 kg is lifted with a uniformly accelerated rectilinear motion using a rope. Determine the acceleration at which the rope breaks if it sustains a load of 15,000 N. - Motion with Decreasing Acceleration
The acceleration of a mass point during its rectilinear movement decreases uniformly from the initial value a0 = 10 m/s2 at time t0 = 0 to a zero value for a period of 20 s. What is the speed of the mass point at time t1 = 20 s, and what is the path of th - Mark statistics frequency
Marks with equal weight 2,1,3,2,2,3,1,3,1,1,2,4,2,2,3,1,1,2,1,3 specify: 1) arithmetic mean 2) absolute and relative frequency 3) mode and median 4) create a chart - Probability - coloured balls
The cube has 6 blue, 8 red, and 10 green balls. The player randomly draws 3 balls. Determine the probability that he draws balls of the same color. - Student deposit years
A student deposited €500 in a savings bank at 2.5% interest. In what time (in years) will he earn as much interest as he invested? - Airplane mechanical energy
An airplane weighing 100 tons flies at an altitude of 11 km at a speed of 850 km/h. What is its kinetic, potential, and total mechanical energy? - CFO Director The financial director has determined the following profitability scenarios for the profitability of the new branch of the company: Profit of 5 million CZK with probability 0.1. Profit of 3 million CZK with probability 0.3. Profit of 1 million CZK with pr
- Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - Administrative
There are 21 employees working in a warehouse - manual and clerical workers. When adjusting the wages, they reduced the daily wage of each clerical worker by €3 and increased the daily wage of each manual worker by €2, so the total daily wage increased by - Point plane distance
Calculate the distance of point A[ 4; 2; -3 ] from the plane : 2x - 2y + z + 5 = 0 - Triangle area angle
The area of a right triangle ABC is 346 cm2, and the angle at vertex A is 64°. Calculate the lengths of the overhangs a and b. - Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC. - PIN probability number
The mobile PIN has 4 characters. What is the probability that the PIN contains the number 7 and ends with the number 5? - Sound Doppler observer
A sound source emits a tone with an absolute pitch of 500 Hz and moves towards the observer at a speed of 5 m/s. Sound travels at a speed of 340 m/s. How fast is an observer moving who hears a tone with an absolute pitch of 522 Hz? - From experience
From the experience of an insurance company employee, it turned out that the insurance benefit under household insurance is more than 25,000 CZK with a probability of 0.3. What is the probability that among the next ten insurance claims there will be: a) - Function inverse square
The inverse function to the function f(x) = √(x-3) for x ≥ 3 is the function: - Cube small diagonal
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals. - Point collinear coordinates
Given are points A [1;a2;a3], B [3;-4;-1], C [-3;-1;8]. Points A, B, and C lie in a straight line. Calculate the coordinates a2, a3 - Function graph intersection Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common.
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