# Examples for secondary school students - page 73

1. A car
A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
2. Three workshops
There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
3. Alice
Alice spent 5/11 of her money on a back pack. She has \$42 dollars left. How much was her back pack?
4. Collision
The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s2, the second body has an initial speed of 6 m/s and an acceleration of 2 m/s2. Find
5. 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?
6. Right isosceles triangle
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
7. 600 pencils
600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
8. Complex number coordinates
Which coordinates show the location of -2+3i
9. Minute average
In a factory, four workers are assigned to complete an order received for dispatching 1400 boxes of a particular commodity. Worker A takes 4 mins per box, Worker B takes 6 minutes per box, C takes 10 mins per box, D takes 15 mins per box. Find the average.
10. Investment
1000\$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
11. Car crash
On the road, with a maximum permitted speed of 60 km/h, there was a car crash. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, as
12. Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit
13. Potatoes
For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
14. Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
15. GP members
The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
16. Annual pension
Calculate the amount of money generating an annual pension of EUR 1000, payable at the end of the year and for a period of 10 years, shall be inserted into the bank to account with an annual interest rate of 2%
17. Intercept with axis
F(x)=log(x+4)-2, what is the x intercept
18. A jackpot
How many times must I play this jackpot to win? A jackpot of seven games having (1 X 2), i. E. , home win or away win.
19. Two equations
Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
20. STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.

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