# Examples for secondary school students - page 62

1. Basket of fruit In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which
2. Average speed 4 Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip?
3. Flying The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
4. Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
5. Two workers Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself?
6. Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
7. Sequence 11 What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ?
8. Angle of diagonal Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
9. Tractors Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately?
10. ABCD square In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
11. Dice We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
12. Performance Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together?
13. Equilateral triangle A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
14. Cube, cuboid, and sphere Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
15. Fruit tea Tea contains 7% of fruit components and 12% of sugar in this component. How many percents of sugar is represented in the whole tea?
16. 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 trapezium area in cm square and calculate how many differs perimeters of the.
17. The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
18. Largest angle of the triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
19. Endless lego set The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They
20. Triangles Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?

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