# Examples for 9th grade - page 2

- Cross section

The cross section ABCD of a swimming pool is a trapezium. Its width AB=14 metres, depth at the shallow end is 1.5 metres and at the deep end is 8 metre. Find the area of the cross section. - Cube wall

Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume. - Cube surface area

The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased. - Lines

How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line? - Three-digit

How many three-digit natural numbers do not have the number 7? - Digits

How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated. - Book read

If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have? - Ratio of two unknown numbers

Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given? - Mason with assistant

Mason had to complete the work in 10 days. Two and a half days later his assistant arrived. Together they completed the work in next three and a half days. How many days would he need an assistant for the same work? - Direct route

From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t - Cars speeds

Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes? - 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. - Testing

Students of high school have 10 points for each good solved task. The wrong answer is deducted by 5 points. After solving 20 tasks, student Michael had 80 points. How many tasks did he solve correctly and how many wrong? - Garden

Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden? - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Pool

If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately? - Bonus

Gross wage was 826 USD including 31% bonus. How many USD were bonuses? - Troops

Route is long 203 km and the first day first regiment went at an average speed 20 km/h and journey back 19 km/h. The second day went second regiment same route at an average speed 18 km/h there and back. Which regiment will take route longer? - Right Δ

Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. - Logic

A man drinks a barrel of water for 31 days, woman for 58 days, for how many days they drink barrel together?

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