# Examples for secondary school students

- Faces diagonals

If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2 - Voltmeter range

We have a voltmeter which in the original set measures voltage to 10V. Calculate the size of the ballast resistor for this voltmeter, if we want to measure the voltage up to 50V. Voltmeter's internal resistance is 2 kiloohm/Volt. - Car down

Sarah buys a car costing $12,500. It depreciates in value by 8% in the first year, 10% the second year and 5% in the third year. Calculate the value of a car after the third year. - Wall and body diagonals

Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m - Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area). - Alien ship

The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - Angles of elevation

From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of - Space diagonal

The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube. - 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? - Glasses

There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls? - Distance between 2 points

Find the distance between the points (7, -9), (-1, -9) - The sum

The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2? - Divide 8

Divide 6840 by x y and z, in such a way that x has twice as much as y, who has half as much as z - Red and white

Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the opti - Reciprocal value

How do I calculate a number x that is 9 greater than its reciprocal (1/x)? - Two groups

The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done? - The Eiffel Tower

The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height. - The tractor

The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m? - Casey

Casey bought a 15.4 pound turkey and an 11.6 pound ham for thanksgiving and paid $38.51. Her friend Jane bought a 10.2 pound turkey and a 7.3 pound ham from the same store and paid $24.84. Find the cost per pound of turkey and the cost per pound of ham. - Age problems

A) Alex is 3 times as old as he was 2 years ago. How old is he now? b) Casey was twice as old as his sister 3 years ago. Now he is 5 years older than his sister. How old is Casey? c) Jessica is 4 years younger than Jennifer now. In 10 years, Jessica w

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