# Examples for 9th grade - page 83

1. Trapezium
The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
2. Savings 2
Jozef and Michael saved 46 euros together. Michael saved 22 euros more than Jozef. How much did save each of them?
3. Slope
Find the slope of the line: x=t and y=1+t.
4. Circle chord
Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.
5. Storm
So far, a storm has traveled 35 miles in 1/2 hour in direction straight to observer. If it is currently 5:00 p. m. and the storm is 105 miles away from you, at what time will the storm reach you? Explain how you solved the problem.
6. Bakery and flour
The bakery tray for flour was filled to 3/4 volume. After removing 875 kg of flour, it was filled to only 2/5 of the volume. How many tons of flour is in the full tray?
7. The rope
A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners?
8. Classroom
There are eighty more girls in the class than boys. Boys are 40 percent and girls are 60 percent. How many are boys and how many girls?
9. Mother and daughter
The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
10. Folded square
ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
11. Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
12. Magic number
The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
13. Big number
hat is the remainder when dividing number 10 to 47 - 111 by number 9?
14. Iron collecting
Class 7A collected 3.2 tonnes of iron more than class 7B. Together they collected 6.4 tonnes of iron to the secondary raw material collection. How much did each class collect?
15. Surface of cubes
Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
16. Area of iso-trap
Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
17. Diagonals
A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
18. Diagonal
he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
19. Points on line segment
Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
20. Remainder
A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?

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