# Examples for secondary school students

1. Three reds What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
2. Regular n-gon In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
3. Inner angles The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
4. Sequence 11 What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ?
5. Arithmetic progression In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ?
6. Photocopier A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
7. Water channel The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo
8. Tricolors From the colors - red, blue, green, black and white, create all possible tricolors.
9. Cuboid edges in ratio Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
10. Vector 7 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
11. Krkonose CZ Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater
12. Cuboid - volume and areas The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
13. Cuboid walls Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
14. Cuboid height What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
15. Average speed 4 Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip?
16. Hollow sphere The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
17. Roof 7 The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
18. Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
19. VCP equation Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
20. BTC bubble One of the world's experts in bubbles -- Prof. Robert Shiller, a Yale economist -- said Bitcoin "was an amazing example of a bubble" back in 2014. If you exchange fiat US dollar \$100 to BTC in 2010, now in 2017 have value of 72.9 millions dollars. Find

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