Examples for secondary school students - page 127 of 230
Number of problems found: 4597
- Symmetry by plane
Determine the coordinates of an image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0 - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7 - Water reservoir
One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously? - Competition 7328
Adam was practicing for a darts competition in class. Every day at home, he threw darts at a target in which the individual fields were worth 1,3 and 5 points. He threw 9 darts every day and always scored 27 points. He is in good form and never missed a t - Three-digit numbers
Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there? - Inequality 7320
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - Confectionery
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Determine 7314
The hiker went from A to B and back in 3 hours and 41 minutes. The road from A to B is first uphill, then flat, and finally downhill. A hiker walked up a hill at a speed of 4 km/h, on a flat surface at a speed of 5 km/h, and down a hill at a speed of 6 km - Kindergarten 7313
The children in the kindergarten drank 20% of the prepared tea in the morning. They drank another 10% of the left tea afternoon. After the whole day, there were still 9 liters of tea left. How many liters of tea was prepared in the kindergarten in the mor - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters - Grandparents
The grandfather set aside €1200 for savings. At the beginning of each month, he deposited €100 in the bank at an interest rate of 3%p. A. At the end of the year, he had €1,219.68 in the bank. Grandma immediately put the entire amount of €1,200 into the ba - Std-deviation
Calculate the standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90 - Simultaneously 7272
The distance from Žilina to Košice is 260 km. From both places, 2 cars started opposite each other simultaneously. A car from Žilina travels at a speed of 58 km/h. The speed of a car from Košice is 72 km/h. In how many hours will these two cars meet? - A car
A car weighing 1.05 tonnes, driving at the maximum allowed speed in the village (50 km/h), hits a solid concrete bulkhead. Calculate the height that would have to fall on the concrete surface to make the impact intensity the same as in the first case! - Middle finger
Jana counts on one hand one by one. She starts counting from her thumb through her index finger, middle finger, and ring finger and comes to her little finger and has the number 5. Then she immediately returns to her ring finger (6), to her middle finger - How many 2
How many three-lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed? - Degrees Fahrenheit
C= (5)/(9)(F−32) The equation above shows how temperature F, measured in degrees Fahrenheit, relates to temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I. A temperature increase of 1 degree Fahrenhei - Provides 7260 How much money does a brother have, and how much does a sister have if she pays: if a brother gives a sister CZK 24, they will have the same. If a sister provides a brother with CZK 27, will the brother have twice as much?
- Decomposed 7258
The number 135 can be decomposed into the product of two factors, so one will be three greater than 40% of the other. What are these factors?
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