# Examples for 8th grade - page 44

1. Slope RR
A line has a rise of 2 and a run of 11. What is the slope?
2. Divisors
The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
3. Tetrahedral prism - rhomboid base
Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
4. Mixing
If we mix 5 kg of goods of one kind and 3 kg second one, resulting mixture cost 16.50 EUR/kg. If these quantities are mixed in reverse - first three kilograms and 5 kilograms second cost of mixture is 18.50 EUR/kg. What is the price of one kg of goods of.
5. Cuboid - simple
Calculate the surface area and volume of a cuboid if a = 8 cm, b = 14 cm and c = 6 cm.
6. Tippler
Bottle with cork cost 8.8 Eur. The bottle is 0.8 euros more expensive than cork. How much is a bottle and the cork?
7. Cutting circles
From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?
8. Midpoint of segment
Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B?
9. Tree
How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
10. Two wine
In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine?
11. Lie/do not lie
The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer.
12. Decomposition
Make decomposition using prime numbers of number 155. Result write as prime factors (all, even multiple)
13. Semicircle
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
14. Rhombus
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
16. Right triangle
Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.