# Examples for secondary school students

1. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
2. Right circular cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
3. Camel and water 84% of the camel's weight is water. After drinking, its weight increased to 832 kg and water accounted for 85% of its weight. How much did it weigh before drinking?
4. Two rectangles 2 A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
5. Median The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.
6. Geometric progressiob If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
7. The hiker The hiker will travel 40% of the route on the first day 1and/3 of the rest od second day. Last day 30 km. What was the length of the 3-day trip? How many kilometers did he walk each day?
8. Base of prism The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
9. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
11. Records Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
12. Seat How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
13. Drilling machine A manufacturing firm purchased a heavy duty drilling machine. They were given two payment options: Option 1: Make a payment of \$46,000 immediately to settle the invoice for the machine. Option 2: Make a payment of \$21,500 immediately and the balance of
14. Genetic disease One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited
15. Prices The price of the product was increased by 35%. How many percents of the new price we have to make it cheaper so that its price is equal to the original price?
16. GP - three members The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c
17. Set of coordinates Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation?
18. Three members GP The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
19. Probability of malaria A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patie
20. Six speeds A drilling machine is to have 6 speed ranging from 50 to 750 revolution per minute. If the speed forms a geometric progression, determine their values.

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