Examples for 9th grade

Circle and hexagon
Calculate the radius of a circle whose circumference is 8.4 cm longer than the circumference of the inscribed regular hexagon.
Triangle midpoints
Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
Concentric circles
In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
Balls
The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is it content (surface area)?
Again saw
From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
Parking
120 vehicles parking on the morning. Pasenger car is charged 20 CZK, 50 CZK per bus. The guard collected for parking 2640 CZK in total. How many cars and how many buses stood in the parking?
Bevel
I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
Angles and sides of the triangle
Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
Train from Prague
First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
Digging companies
Company A would dig a pit for 12 days, company B for 15 days, company C for 20 days and the company D for 24 days. Work began together companies C and D, but after three days joined them other two companies. How long took to dig a pit?
Train from Brno
First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
Seamstress 2
Seamstress bought two kinds of textile in whole meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?
Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
Seamstress
Seamstress bought two kinds of textile together 25 meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?
Median
In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
Eva
When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet?
Cross-country competition
Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B?
RT and ratio
A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
Nuts
How many we must have at least nuts if we can equally divide it to 10 children, 12 children or 15 children and any nut left?

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