# Examples for secondary school students

#### Number of problems found: 2028

• Goat Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
• Sum of the seventeen numbers The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
• Space diagonal The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
• The angle of view Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
• Ball game Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
• Cosine Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
• Divisors The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
• The projectile The projectile was fired horizontally from a height of h = 25 meters above the ground at a speed of v0 = 250 m/s. Find the range and flight time of the projectile.
• Nuts Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts.
• 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?
• Map Forest has an area of ​​36 ha. How much area is occupied by forest on the map at scale 1:500?
• Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
• A triangle A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
• Midpoint of segment Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B?
• Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
• Three faces of a cuboid The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
• Sum of money On a certain sum of money, invested at the rate of 10% compounded annually, the difference between the interests of the first year and the third year is 315 . Find the sum.
• Fall sum or same Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.
• Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
• Angle of the body diagonals Using vector dot product calculate the angle of the body diagonals of the cube.

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