Examples for secondary school students - page 202 of 231
Number of problems found: 4612
- Geometric sequence 5
About members of the geometric sequence, we know: 3 a5:a3 = 27:25 7 a3 +5 a7 = 1 : 564 Calculate a1 (first member) and q (common ratio or q-coefficient) - Median
In the ABC triangle is given side a=10 cm and median to side a: ta= 13 cm, and angle gamma 90°. Calculate the length of the median to side b (tb). - Goat
The meadow is a circle with a radius r = 20 m. How long must a rope tie a goat to the pin on the meadow's perimeter to allow the goat to eat half of the meadow? - Right angled triangle
The hypotenuse of a right triangle is 17 cm long. When we decrease the length of the legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs. - Computer
The school purchased the computer 10000. The price of a computer always depreciates the same percentage as the previous year. After four years, the value of the computer is reduced to 1300. How much percent was the declining price of the computer each yea - Circles
In the circle with a radius, 7.5 cm is constructed of two parallel chords whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions, write both). - Nuts
How many must we have at least nuts if we can equally divide it among 10 children, 12 children, or 15 children and any nuts left? - Chambers
The decision-making committee consists of three people. For the commission's decision to be valid, at least two members must vote similarly. It is not possible not to vote in the commission. Everyone only votes yes or no. We assume that the first two memb - Class - boys and girls
In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl? - Triangle
Calculate the triangle sides if its area S = 630 and the second cathetus is shorter by 17. - Interesting property
Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle? - Cylinder diameter
The surface of the cylinder is 112 cm². The cylinder height is 5 cm. What is the diameter of this cylinder? - Mushrooms from the forest
Magda and Tereza go to pick mushrooms. Found 70 mushrooms. Magda found that between fungi, 5/9 bedel was found. Tereza discovered that she found 2/17 champignons among fungi. How many mushrooms were found, Magda? - Friends in cinema
5 friends went to the cinema. How many possible ways can they sit in a row if one of them wants to sit in the middle and the remaining place does not matter? - The camp
At the end of the camp, a 6 friends exchanged addresses. Any friend gave their remaining 5 friends their card. How many addresses did they exchange? - Three digits number
From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there? - Journey
The road from A to B measures 11.5 km. Firstly, up the hill, then level plane, and then downhill. Tourists go uphill at 3 km/h, on planes at 4 km/h, and downhill at 5 km/h. From point A to B, it went 2 hours, 54 minutes back, 3 hours, and 6 minutes. How l - Purchase
The mother bought five boxes of milk and 7 kg of potatoes and paid a total of CZK 147. The aunt bought seven boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How would CZK together have bee - Trapezoid - diagonal
A trapezoid has a length of diagonal AC crossed with diagonal BD in the ratio of 2:1. The triangle created by points A, the cross point of diagonals S, and point D has an area 164 cm². What is the area of the trapezoid? - ISO triangle
Calculate the area of an isosceles triangle KLM if its sides' length is in the ratio k:l:m = 4:4:3 and has a perimeter 352 mm.
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