Examples for 8th grade

Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm³. What is its surface in dm²?
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?
Parallelogram perimeter
The ABC triangle with sides a = 5cm, b = 3cm, c = 40mm has the center of the sides of the K,L,M. How many cm have the KBLM parallelogram perimeter?
Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
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 ?
Chord
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
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?
Functions f,g
Find g(1) if g(x) = 3x - x² Find f(5) if f(x) = x + 1/2
The ladder
The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
Boys and girls
There are 48 children in the sports club, boys are 10 more than girls. How many girls go to the club?
Walkers
Walker, which makes 120 steps per minute, make distance from point A to point B for 55 minutes. The length of his step is 75cm. For how long does this distance go boy who will do 110 steps 60 cm long in a minute?
Highway repair
The highway repair was planned for 15 days. However, it was reduced by 30%. How many days did the repair of the highway last?
Container
The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
Calf
The weight of the calf meat obtained is 65% of the total weight of live calves. What was the weight of a calf from which 285 kg of meat was obtained?
MO8-Z8-I-5 2017
Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm², the rectangle MBCK area is 63
Alcohol mixture
Three liters of 96 percent alcohol we set up a certain amount of distilled water to form a 54-percent alcohol. How many liters of distilled water were used?
One million
Write the million number (1000000) by using only 9 numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions.
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.
Interior designer
To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?

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