Examples for secondary school students

1. Equation with abs
Solve this equation with absolute value member: ?
2. Money
Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael.
3. Prism bases
Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
4. Exponential equation
Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625
5. The rectangle
Determine the area of the rectangle where the length and width are in the ratio 5:2 and its length is 7.5 cm longer than its width. Determine also its length and its width.
6. Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
7. Unknown amount of money
Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis.
8. Vegan shop
To the shops brought together 23.2 kg of goods, fruits, vegetables and nuts. fruit was 4.7 kg more than vegetables, nuts was 1.5 kg less than the fruit. Determine the amount of fruits, vegetables and nuts.
9. Dividing money
Imrich, Daniel and Dezider shared an unknown amount in the ratio 1:2:4, where Dezider received 750 euros more than Imrich and Daniel got half as much as Dezider. Determine an unknown amount of money and determine the amounth that got Imrich, Daniel and D
10. Quotient
Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
11. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
13. Threesome
Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael.
14. Determine AP
Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
15. Coins
Denis and Zdeno together have 97 coins. If Denis had 4 coins less than he has now, the number of the coins would be in the ratio 14: 17. Determine the number of coins owned by Denis and Zdeno.
16. Nuts
Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts.
17. Cleaners
Milan would clean up the room for 2.5 hours, Eric would take 10 hours. How long they swept the room together?
18. Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
19. Fifth member
Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
20. Blueberries
Miko and Anton have a total of 1,580 blueberries. Miko and Anton have them in the ratio 2: 3. Determine how much each of them has.

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