# Examples for secondary school students

#### Number of problems found: 2059

• Rectangle The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
• Birth Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?
• Two parallel chords The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
• Boys and money 270 USD boys divided so that Peter got three times more than Paul and Ivan has 120 USD more than than Paul. How much each received?
• Circular motion Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
• Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
• Inscribed circle A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
• Computer The computer was purchased 10000,-. Each year, the price of a computer depreciates always the same percentage of the previous year. After four years, the value of the computer is reduced to 1300,- How many percent was depreciated price of the computer eac
• Scalar dot product Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
• The funnel The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel.
• Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
• Blueberries Miko and Anton have a total of 1,580 blueberries. Miko and Anton have them in the ratio 2: 3. Determine how much each of them has.
• Pillar Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
• Workman - shift The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components?
• Nice prism Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
• Simple interest 4 Find the simple interest if 5243 USD at 4.3% for 261 days. Assume a 361-day year.
• Construct Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
• Annual pension Calculate the amount of money generating an annual pension of EUR 1000, payable at the end of the year and for a period of 10 years, shall be inserted into the bank to account with an annual interest rate of 2%
• Rhombus OWES OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area?
• 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...