# Examples for 9th grade

#### Number of problems found: 2612

- One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area. - Triangle in a square

In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Coins

On coins found was stated that from the year 87 BC. It is right? - Two numbers

The sum of the two numbers is 1. Find both numbers if you know that half of the first is equal to one seventh of the second number. - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Three figures - numbers

The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures. - Train 2

The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel? - Roof of the church

The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof? - Pedestrian and the cyclist

Pedestrian and cyclist went against each from the two cities that are distant 40 km. Pedestrian started 30 minutes before the cyclist and walk an average speed of 5 km/h. What speed went cyclist when met after 120 minutes from the start of the pedestrian? - Cylinder

The 1.8m cylinder contains 2000 liters of water. What area (in dm^{2}) of this container is the water? - Two lands

The common area of the two neighboring lands is 964 m^{2}. The second land is 77 m^{2}smaller than twice the size of the first land. Find the areas of each land. - Sweets

We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture? - ICE train

German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journey - Stock

Enterprise sold 7/12 of their products to foreign markets and 2/5 of the remainder sold at home. How many % of the products is still in stock? - Wall height

Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm. - Drilling machine

A manufacturing firm purchased a heavy duty drilling machine. They were given two payment options: Option 1: Make a payment of $46,000 immediately to settle the invoice for the machine. Option 2: Make a payment of $21,500 immediately and the balance of $2 - Angle of deviation

The surface of the rotating cone is 30 cm^{2}(with circle base), its surface area is 20 cm^{2}. Calculate the deviation of the side of this cone from the plane of the base. - Grass

Peter and Stano lawn grass for 3 hours 12 minutes. How long would it take to Peter if Stano lawn grass himself for 384 minutes. - Sweets

3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations - Three-digit numbers

How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?

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