# Examples for 9th grade - page 18

- 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) - Triangle SSS

Calculate perimeter and area of a triangle ABC, if a=58, b=83 and c=31. - Cuboid

Find the cuboid that has the same surface area as the volume. - Three friends

The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid? - Book

Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book? - School

School attend 792 children, boys and girls ratio is 4:5. How many more girls go to school (than boys)? - Rotary cylinder

The rotating cylinder has a surface area 69.08 cm^{2.}The area of the shell is 62.8 cm^{2.}What is the diameter of the cylinder? - The city

At the end of 2010 the city had 529000 residents. The population increased by 1.1% each year. What is the population at the end of 2013? - Chess

How many different ways can initiate a game of chess (first pass)? - Hockey players

After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other? - Price reduction

Price of camera is 800 USD on sale its price reduced to 423 USD. Calculate the percentage reduction in the price of the camera. - Balance

The rod are 1.7 m long hanging weights 2 kg and 12 kg on ends. Where are centre of rod (distance from weight 2 kg) to be in balance? - Confectionery

The village markets have 8 kinds of sweets, one weighs 15 grams. How many different ways a customer can buy 0.915 kg sweets. - Children

Less than 20 children is played various games on the yard. They can create a pairs, triso and quartets. How many children were in the yard when Annie came to them? - Rhombus diagonal

Area of rhombus is 417. One diagonal measures 45, find length of other diagonal. - Mushrooms

Fresh mushrooms contain 96% water, dried 12%. How many kg of fresh mushrooms is needed to collect to get 7 kg dried? - IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm. - Donuts

In the dining room at one table sit Thomas, Filip and Martin. Together they eat 36 donuts. How many donuts eaten everyone, when Filip ate twice as much as Thomas and Martin even half over Filip? - Tributaries

The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries? - Triangular prism

Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.

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