# Examples for secondary school students

1. Trapezoid 15 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
2. Salami How many ways can we choose 5 pcs of salami if we have 6 types of salami for 10 pieces and one type for 4 pieces?
3. Potatoes 6 The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, in the second hour he sold five-sixth of the remaining potatoes, and in the third hour he had sold the last 40kg of potatoes. How many kg of potatoes
4. Empty canister The canister is filled with oil weight 17 kg. If filled only half weight 9 kg. What weight does my empty canister have?
5. Trapezoid - central median The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
6. How far From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
7. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
8. Elements If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
9. Rectangular trapezoid The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
10. Seagull Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (w
11. Rectangle The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
12. 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.
13. Trapezium The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
14. Ratio iso triangle The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
15. Combinations How many elements can form six times more combinations fourth class than combination of the second class?
16. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
17. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
18. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
19. Cuboid and eq2 Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.
20. Body diagonal The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

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