# Examples for secondary school students - page 69

1. The tourist
The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone?
2. A candle
A candle shop sells scented candles for \$16 each and unscented candles for \$10 each. The shop sells 28 candles today and makes \$400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How m
3. Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
4. 2 pipes
2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone?
5. Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
6. Water lilies
Water lilies are growing on the pond and their number is doubled every day. The whole layer is covered in 12 days. How many days will it cover 8 layers?
7. Microorganisms
The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
8. Age
In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
9. Bottles
The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
10. The sum 2
The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer.
11. 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.
12. A man 2
A man divides \$10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
13. Right triangular prism
We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of.
14. Circle annulus
There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
15. Test scores
Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?
16. Free fall
The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
17. Standard deviation
Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
18. Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
19. Symmetry by plane
Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0
20. Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x

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