# Examples for secondary school students

1. 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?
2. 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.
3. Isosceles triangle 9 Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
4. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
5. Accelerated motion - mechanics The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration?
6. Reciprocal value How do I calculate a number x that is 9 greater than its reciprocal (1/x)?
7. 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.
8. 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?
9. 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?
10. 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 optio
11. Depth angles At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
12. 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.
13. 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
14. Two math problems 1) The sum of twice a number and -6 is nine more than the opposite of that number. Find the number. 2) A collection of 27 coins, all nickels, and dimes, is worth \$2.10. How many of each coin are there? The dime, in United States usage, is a ten-cent coin
15. 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.
16. An investment How long will it take for an investment to double at a simple interest rate of 5.10% p. A. ? Express the answer in years and months, rounded up to the next month.
17. 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
18. 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.
19. 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 wi
20. 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.

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