# Examples for secondary school students - page 41

1. 3 days
Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day.
2. Volume of three cuboids
Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.
It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
4. Speedometer
The speedometer of a car reads 66 km/h. It's accurate to within 4.1% What is the maximum possible error?
5. Four sides of trapezoid
Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
6. Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
7. Triangle IRT
In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
8. Medicine
We test medicine on 6 patients. For all drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work?
9. ABS
What is the value of ? ?
10. Cube 9
What was the original edge length of the cube if after cutting 39 small cubes with an edge length 2 dm left 200 dm3?
11. Support colum
Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
12. SD - mean
Mean is 10 and standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range 6.5 to 13.5?
13. Sequence
Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
Quadratic equation ? has roots x1 = 80 and x2 = 78. Calculate the coefficients b and c.
15. Triangle
The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
16. Alcohol mixing
How much 55% alcohol we must pour into 1500 g 80% alcohol to form a 60% alcohol? How much 60% alcohol created?
17. Salary in enterprise
The average salary in the company is 27 000 CZK, 30% of workers have the lowest average income of 19 thousand CZK. There were an increase in the salary in this group by 2%. How much % increased the average salary across the company?
18. Rhombus and diagonals
The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
19. The fence
I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord i
20. Compound interest
Compound interest: Clara deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Both money and interest remain deposited in the bank. How many CZK will be in the bank after 3 years?

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