# Grade - examples - page 22

1. Report card
Ivor hit 4× grade 5 at the beginning of the school year. How many times must now catch grade 1 to get grade 2 on the report card?
2. Plan of the village
Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality.
3. Water
Into a full cylindrical tank high 3.6 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.9 m, 0.7 m. How many liters of water will come out?
4. Motion
From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
5. Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
6. Dice
How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
7. Sale
If the product twice price cut by 25%, what percentage was price cut in total?
8. Peroxide
How much distilled water (in liters) must pharmacists pour into 300 ml of 23.6% solution of hydrogen peroxide to get 2.7% solution to gargle?
9. Square grid
Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
10. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
11. Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
12. Football league
In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
13. 2x cone
Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
14. The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
15. Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
16. Unknown x
If we add to unknown number 21, then divide by 6 and then subtract 51, we get back an unknown number. What is this unknown number?
17. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
18. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
19. Trapezoid
Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
20. Inheritance
After death father (♱ 62) remained mother (his wife) and its 3 children. Inheritance by law is that in first mother will automatically get half of the property and other one half inherite by heirs witch are mother and her 3 children by same share. Cal

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.