# Examples for secondary school students

#### Number of problems found: 2059

• 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.
• Cut and cone Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
• Circle chord What is the length x of the chord circle of diameter 115 m, if the distance from the center circle is 11 m?
• Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
• Lee is Lee is 8 years more than twice Park's age, 4 years ago, Lee was three times as old. How old was Lee 4 years ago?
• Geometric progression 4 8,4√2,4,2√2
• Horizon The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
• Roof Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
• Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
• Triangle midpoints Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
• Nuts How many we must have at least nuts if we can equally divide it to 10 children, 12 children or 15 children and any nut left?
• The body The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
• Center of line segment Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .

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