# Examples for secondary school students

1. Boys to girls
The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?
2. Flowers 2
Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there?
3. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
4. Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
5. Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
6. Account operations
My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?
7. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
8. Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
9. Associative law multiplication
In a warehouse, you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first)
10. Expressions 3
If k(x+6)= 4x2 + 20, what is k(10)=?
11. The pond
We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
12. Octane value
I loaded 10L 95 octane gasoline and 5L 100 octane gasoline. What is the resulting octane value of the gasoline in the tank?
13. Sum of two primes
Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
14. SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
15. Median and modus
Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
16. Electric input power
Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =?
17. Transformer
Solve the textbook problems - transformer: a) N1 = 40, N2 = 80, U2 = 80 V, U1 =? b) N1 = 400, U1 = 200 V, U2 = 50 V, N2 =?
18. Reciprocal equation 2
Solve this equation: x + 5/x - 6 = 4/11
19. A book
A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
20. Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.

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