# Examples for 8th grade - page 15

- Slope

What is the slope of a line with an inclination 52°? - KLMN

In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN. - Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 40% (JUNIOR RAILPLUS EURO - Wood in the forest

The amount of wood in the forest was estimated at 24000 m^{3.}How much wood will be in forest after 3 years if the annual growth of wood is 3% each year and logging 360 m^{3}each year? - 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°? - Train

A passenger train traveled for 4 hours 136 km. 2.7 hours after its departure started fast train and caught it on 324 km. How many km/h is different its average speeds? - Lead cube

Calculate the edge of the cube made from lead, which weighs 11 kg. The density of lead is 11341 kg/m^{3.} - Cylinder - h

Cylinder volume is 129 cm^{3.}Base radius is 3 cm. Calculate the height of the cylinder. - Barrel 3

Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel? - Stock market

Simon one day decided to invest € 88000 to the stock market. After six months he invested July 5 stock markets fell by 56%. Fortunately for Simon from July 5 5 to October 5 his shares have risen by 39%. Simon is then: ? - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Rhombus

Internal angles of rhombus is in ratio 3:6. How many times is the shorter diagonal longer than side of rhombus? - Parallelogram

Calculate area of the parallelogram ABCD as shown if |AB| = 45 cm, |BC| = 23 cm and angle BAD = 30° - Wire D

Wire length 5 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Tea blend

Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k - Pentagon

Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Arm

Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 16 cm and a height v=10 cm. - Division

Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 1:6:3. How many candies should each get if in bag were 210? - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 6 so that it is divided into three parts in the ratio 3:2:5. Calculate the circumference of the triangle ABC. - Prism

The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?

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