Examples for secondary school students
Number of problems found: 2028
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.
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
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.
Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts.
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?
Forest has an area of 36 ha. How much area is occupied by forest on the map at scale 1:500?
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?
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.
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.