Examples for secondary school students - page 236 of 237
Number of problems found: 4733
- Road
Between cities A and B there is a route 9 km long with an average gradient of 9‰ klesanie. Calculate the height difference between cities A and B. - Angles in triangle
In a triangle, the ratio of angles β to γ is 6:8. Angle α is 40° greater than β. What are the sizes of the angles of the triangle? - Jewel
A rhombus-shaped jewel has an area of 23 mm² and a side length of 5.9 mm. Calculate the size of the acute angle of the rhombus. - Triangle SAS
Calculate the area and perimeter of a triangle if two sides are 46 m and 33 m long and the angle between them is 170°. - Circle chord
What is the length of a chord of a circle with diameter 115 m if the chord's distance from the centre is 11 m? - Rectangle
The area of a rectangle is 893. Its length is 28 more than its width. What are the dimensions of the rectangle? - Cube - angles
Calculate the angle alpha (α) between the face diagonal and the base of a cube. Calculate the angle beta (β) between the space diagonal and the base of the cube. - Playing cards
In how many possible ways can 6 playing cards be shuffled? - Triangle SAA
A triangle has one side of length 23 m and two interior angles of 60°. Calculate its perimeter and area. - Square and circles
A square with side 68 km has a circumscribed circle and an inscribed circle. Determine the radii of both circles. - Trapezoid
Calculate the area of trapezoid ABCD with sides |AB|= 78 cm, |BC|=51 cm, |CD|=15 cm, |AD|=30 cm.. - Quadratic equation
Solve a quadratic equation: 2x²+28x-550=0 - Ships
At 0:00, the ship set sail at 22 km/h. At 9:00 followed by 43 km/h sailboat. When does the sailboat catch up with the ship? How many minutes will catch uptake? - School trip
The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number) - Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)? - Sandpile
Sand was piled into an approximately conical shape. Workers wanted to determine the volume (amount of sand) and measured the circumference of the base and the total length of both slant sides of the cone. What is the volume of the sand cone if the circumf - Triangle SSS
Calculate the perimeter and area of triangle ABC if a = 45, b = 30, and c = 50. - Slope of track
Calculate the average gradient (in per mille and in degrees) of the railway tracks between Prievidza (309 m above sea level) and Horná štubňa (624 m above sea level), given that the track is 37 km long. - Party
At a party, everyone clinked glasses with everyone else. They clinked 45 times in total. How many people were at the party? - N-gon
How many diagonals does a convex 30-gon have?
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