# Grade - examples - page 111

1. Vector - basic operations There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w.
2. Triangles Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
3. The cube - simple Calculate the surface of the cube measuring 15 centimeters.
4. After 16 years After 16 years will Dana be five times older as she was four years ago. After how many years will Dana celebrate her 16th birthday?
5. Borrowed book Jane must as soon as possible return a borrowed book. She figured that when she read 15 pages a day return book in time. Then she read 18 pages a day and then return the book one day before. How many pages should have a book?
6. Painters 4 One painter will do the job for 12 days. After a 4 1/3 day he comes second to help him and complete work together for 8 days. How long would work the second painter himself?
7. Broken tree The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
8. Cube 5 The surface of the cube is 15.36 dm2. How will change the surface area of this cube if the length of the edges is reduced by 2 cm?
9. Tiles How many tiles of 20 cm and 30 cm can build a square if we have a maximum 100 tiles?
10. Interst on savings The bank offers 1.6% interest. How many euros have to insert at the beginning if we received € 15 on the interest?
11. School School attend 792 children, boys and girls ratio is 4:5. How many more girls go to school (than boys)?
12. Roman numerals 2+ Add up the number writtens in Roman numerals. Write the results as a roman numbers.
13. Coal storage The coal storage distribute received coal shipment within three days. The first day distribute third of the shipments, the second day of two-fifths of the rest and the third day 300 tons of coal. How many tons of coal distributed first and second day?
14. Roman numerals 2- Subtract up the number written in Roman numerals. Write the results as Roman numbers.
15. Saving Paul save 155Kč in 46 2 Kc and 5Kc coins. How much saved 2Kc and 5Kc coins?
16. Car Car goes some distance in 3 hours and 20 minutes. If it increase speed by 10 km/h, i goes this distance in 2.5 hours. Calculate the distance.
17. Mushrooms For five days, we have collected 410 mushrooms. Interestingly every day we have collected 10 mushrooms more than the preceding day. How many mushrooms we have collected during 4th day?
18. Isosceles - isosceles It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB.
19. Right angled triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
20. Loan If you take a bank loan \$ 10000 and we want to repay after the year, we have to pay the total amount \$ 10320/ What is the annual interest rate on this loan?

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