Examples for secondary school students

Gutter
How much metal is needed for production 60 pieces of gutter pipes with the diameter 17 cm and length of 6 m? The plate bends add 6% of the material.
Slope
What is the slope of a line with an inclination 6.06 rad?
Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
Bonus
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
Cylinders
Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
n-gon
Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
Cinema
Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
Sea water
Mixing 62 kg of sea water with 84 kg rainwater is created water containing 3.1% salt. How many percent sea water contains salt?
Scrap
From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
Bath
In the bath is 30 liters of hot water. Then added 36 liters of cold water at temperature of 19 °C decreased temperature of water to 41 °C. What was the initial temperature of the hot water?
Sequence
In the arithmetic sequence is a₁=-1, d=4. Which member is equal to the number 203?
Center
In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
Toys
3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?
Hearts
5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row?
Spherical cap
From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
Events
Event P has probability of 0.84. What is the probability that the event P occurs in 3, 5, 7 try.
Pizza
A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza?
Sales
From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
Circle
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x₀, y₀] and radius of the circle r.

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