# Integers - 9th grade (14y) - examples

1. Simplify Simplify expression - which expression is equivalent to: 3(m + 2) − 4(2m − 9)
2. Collection of stamps Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
3. Monkey Monkey fell in 23 meters deep well. Every day it climbs 3 meters, at night it dropped back by 2 m. On what day it gets out from the well?
4. Diofant 2 Is equation ? solvable on the set of integers Z?
5. Diofant equation In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
6. Dice How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
7. Sequence In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
8. Sugar - cuboid Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i
9. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
10. Rectangle The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
11. Line Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
12. Monty Hall Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
13. Ladislav in Amsterdam Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books?
14. Package The package has no more than 67 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left remain. On the one blouse consumes 3.8 m of cloth and on one dress 1.7 m. Determine the amount of the cloth in the package.
15. Gauss Help little C.F. Gauss sum all the integers from 1 to 400.
16. Legs In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people? It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points. Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker? In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are i \$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?