Examples for secondary school students - page 58 of 212
Number of problems found: 4231
- AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38 - Metals
In the Hockey World Cup, play eight teams, and determine how many ways they can win gold, silver, and bronze medals. - Semicircle
To a semicircle with a diameter of 10 cm, inscribe a square. What is the length of the square sides? - Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and a 10 cm long arm. What is the length of the medians? - Triangle ABC
Triangle ABC has side lengths m-1, m-2, and m-3. What has to be m to be a triangle a) rectangular b) acute-angled? - Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille. - Three digits number
How many are three-digit integers such that they have no digit repeats? - Lottery
Fernando has two lottery tickets, each from the other lottery. In the first is 973 000 lottery tickets from them wins 687 000, the second has 1425 000 lottery tickets from them wins 1425 000 tickets. What is the probability that at least one Fernando's ti - Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and the hypotenuse 8.544. - Diameter
If the endpoints of the diameter of a circle are A(-9, 10) and B (-5, -4), what is the circle's radius? - Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS? - See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases. - Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid. - Tubes
Iron tubes in the warehouse are stored in layers so that each tube's top layer fits into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if the top layer has 9 tubes? How many tubes are in the bottom layer of tubes? - Roof
Tiles are stacked in rows on the trapezoidal-shaped roof. At the ridge are 15 tiles, and each subsequent row has one more tile than the previous row. How many tiles are covered the roof if the lowermost row has 37 tiles? - Without Euclid laws
Right triangle ABC with a right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws. - Maple
The maple peak is visible from a distance of 3 m from the trunk from a height of 1.8 m at an angle of 62°. Find the height of the maple. - Peak
Uphill leads 2 paths and one lift. a) How many options back and forth are there? b) How many options to get there and back by the not same path are there? c) How many options back and forth are there that we go at least once a lift? - Road
The average climb of the road is given by ratio 1:15. By what angle does road moderate climb? - Exp
If sqrt[7](20²-12²) = sqrt[n](256), then n is:
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