# Examples for secondary school students

#### Number of problems found: 2186

• Triangle TBC TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
• Pumps The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? Two wattmeters are connected to measuring power in a 3 phase balanced load. Determine the total power and power factor if the two wattmeters read 1000 watts each (1) both positive and (2) second reading is negative.
• Finite arithmetic sequence How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?
• Columns of two and three When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class? A license plate has 3 letters followed by 4 numbers. Repeats are not allowed for the letters, but they are for the numbers. If they are issued at random, what is the probability that the 3 letters are in alphabetical order and the 3 numbers are consecutiv
• Vector sum The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
• Pharmacy The pharmacy adds to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How much percent alcohol the pharmacy got?
• Chord BC A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
• At the At the presentation of the travelers came three times as many men than women. When eight men left with their partners, there were five times more men than women at the presentation. How many were men and women originally?
• Stones 3 Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
• 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.
• Circle inscribed Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
• Photos Three friends Mirka, Lucka, and Hanka, collect photos. If Mirka had 3 more photos than she has, she would have as many as Hanka. If Lucka had 5 photos less than she has, she would be like Hanka. How many photographs does each have if they have 431 togethe
• Rhombus OWES OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area?
• Cone If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
• Cube construction A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
• Three-day trip The cyclist on three-day trip travel 30% of the total route on the first day, 3/5 of the rest on the second day and 35 km on the third day. How many kilometers did travel cyclists each day and how many?
• 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.
• Alfa beta gama The triangle's an interior angle beta is 10 degrees greater than the angle alpha and gamma angle is three times larger than the beta. Determine the size of the interior angles.

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