# 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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