Examples for secondary school students - page 22 of 237
Number of problems found: 4730
- Calculate 5
Calculate the area and perimeter of a trapezoid with side a = 10, angle α = 40°, angle β = 50°, and side c = 3. - Quadratic without formula
A quadratic equation is given: x²-x-2=0 Without solving this equation, construct a quadratic equation whose roots are the square of the roots of the given equation. - Construction - Euclid
Using Euclid's theorems, construct a triangle ABC with height on side c and size v = √8 cm. Choose the length of the hypotenuse c correctly. Write the construction procedure. - Dimensions - rectangle
One side of the rectangle is 12 cm longer than the other. If we reduce each dimension by a third, the area of the rectangle will be reduced by 60 cm². Determine the dimensions of the rectangle. - Atmospheric pressure
How and by how much hPa will the atmospheric pressure change when we take the cable car from Skalnate Pleso to Lomnický štít? The altitudes of the cable car stations are 1754 m above sea level and 2634 m above sea level. - Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people. - Probability - coin
When tossing a coin 4 times in a row, what is the probability that a sign will come up 3 times? - Heptagon perimeter
Calculate a regular heptagon's perimeter if its shortest diagonal length is u=14.5 cm. - The Celebration
Five boys and five girls were nominated for a celebration at a local school. How many ways can the prom king, prom queen, and two other students be chosen from those nominated? (The king must be a boy, and the queen must be a girl) - Harvest Weights Distribution
Martin brought twice as much harvest as Thomas and Philip, 15 kg more than Martin. They got a total of 65 kg of harvest. How much did each person bring? - Intersection + tangents
Given a circle with a radius r = 4 cm and a point A for which |AS| applies = 10 cm. Calculate the distance of point A from the intersection of the points of contact of the tangents drawn from point A to the circle. - Transformation of voltage
A current of 0.5 A flows through the transformer's primary coil connected to a voltage of 120 V. Calculate the voltage and current in the secondary coil if the transformation ratio is equal to the number 5. - Bulb lifespan
The probability that the bulb will burn for more than 800 hours is 0.2. There are 3 light bulbs in the hallway. What is the probability that after 800 hours, at least one will be lit? - Granulate for pH Adjustment
Bathing water should have a pH value in the range of 6.8 - 7.2. How much granulate should we add to increase the pH value from 6.2 to 7 if a dose of 100 g/10 m³ increases the pH by approx. 0.1? P.S. It's not 800 grams. - Soap bubble
A conductive soap bubble with a radius of r=2 cm and charged to a potential of φ= 10000 V will burst into a drop of water with a radius of r1= 0.05 cm. What is the potential φ1 of the drop? - Additional Force on Body
A body with a mass of 5 kg moves in a vertical downward direction with an acceleration of a= 12 m/s². What force acts on it in addition to its weight? - Heat for Phase Change
How much heat is needed to turn 1 kg of ice at a temperature of -10℃ into steam at a temperature of 100℃? - Calculate
A bicycle wheel rotates with a frequency of f = 25 Hz. By braking, its rotation is slowed uniformly and the wheel stops after a time of t₀ = 30 s from the start of braking. Calculate the angular deceleration ε and the number of revolutions the wheel makes - Coordinates of line points
I have a point A=[2,1] and a line y+x-5=0. How do I determine the coordinates of point A', which is the image of point A according to the given straight line? - Numbers 6D
Find out how many natural six-digit numbers exist whose digit sum is four.
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