Examples for secondary school students - page 147 of 231

Number of problems found: 4612

Cube changes
How much percent will the surface and volume of the cube decrease if the diagonal decreases by 10%? b) if the diagonal increases by 10%?
Wheat Barley Caliber Harvest Tons
They harvested 390 tons. Wheat is 18% more than barley and 126 tons less caliber than wheat and barley combined. How many tons of barley, wheat, and caliber were there?
Task calculation
Jana had to calculate 70 tasks, and if she had solved two more daily tasks than she had planned, she would have finished four days earlier. How many days did she have to calculate the tasks?
Metal cube
The steel cube has a length of its edge of 5 cm. It is made from steel with a density of 7800 kg/m³. What is the weight of this steel cube?
Course dimensions
The rectangular course is 12 m longer than its width. Suppose its length increases by 10 m and its area increases by 600 square meters. What are its dimensions?
Cyclist speed
Two cyclists rode towards each other simultaneously from opposite ends of the 28km long route. Each covered the entire route at a constant speed, the fastest being at the finish line 35 minutes earlier. On the route, the cyclists passed each other after 1
Loan Interest Rate Equalization
Karel took out a loan of EUR 600 from Ivan 20.2 at a 20% annual rate. From January 10.5, a loan of 1100 Euros at a 14% rate. From Milan 15.9, a loan of 900 Euros at an 11% rate. All three return 30.12. Determine the annual interest rate for all three loan
Pocket money
Honza receives pocket money and wants to buy something good with it. If he purchased four cakes, he would have CZK 5 left. If he wanted to buy five cakes, he would be 6 CZK short. If he had bought two pies and three doughnuts, he would have spent all his
Conical area
A right-angled triangle has sides a=12 and b=19 at the right angle. The hypotenuse is c. If the triangle rotates on the c side as an axis, find the volume and surface area of the conical area created by this rotation.
Dice probability
Jana rolls two dice at the same time. What is the probability that she will score a total of four points?
Mowing Lawn with Mowers
The football club owns five identical mowers. If they used two of them, they would mow the playground lawn in 10 hours. How long would it take to mow the lawn if they used all five mowers?
Fence and scale
The garden with 80 m of fencing is drawn on a plan as a square with a side length of 4 cm. At what scale is this plan made?
Identity Matrix Zeros
How many zeros does the unit matrix E contain, which has three units in the main diagonal?
Geometric Sequence Quotient Sum
Calculate the quotient of the geometric sequence if the sum of the first two terms equals 1.1 and a6 = 10000. A quotient is a natural number.
Sequence Third Term Value
Find the value of the third member of the sequence if the sequence is given by: 3^n + 93.
Matrix Square Determinant
The determinant of matrix J has the value 0. What will be the value of the determinant of matrix C, which we get as the square of matrix J?
Theatre performances
A total of 15,744 CZK was collected as admission for three theatre performances. The revenue from the second performance was 20% higher than the revenue from the first performance and the revenue from the third performance was 10% lower than the revenue f
Geometric Progression Term Value
Calculate a3 GP if you know that q = 4 and a1 + a2 + a3 = 89.25 and a4 = 272.
Matrix Sarruss Rule Rows
How many rows does a square matrix A have if we use Sarruss's rule to calculate its determinant?
Matrix Rows Columns Count
The rectangular matrix M contains 21 elements and has three columns. How many rows does matrix M have more than square matrix F, which contains four elements?

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