# Examples for secondary school students - page 33

- Traffic collision

When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village. - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Midpoint of segment

Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B? - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - Garden

The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m^{2}. Calculate the dimensions of the garden. - Vector

Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5]. - Sequence 3

Write the first 5 members of an arithmetic sequence: a_{4}=-35, a_{11}=-105. - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Triangle ABC

In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC. - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC. - Hearts

4 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 4 hearts in a row? - Friends

Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - The dice

What is the probability of events that if we throw a dice is rolled less than 6? - Chord - TS v2

The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS? - Car

At what horizontal distance reaches the car weight m = 1534 kg speed v = 85 km/h when the car engine develops a tensile force F = 1691 N. (Neglect resistance of the environment.) - Three digits number

From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there? - RT and circles

Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23. - Sum of series

Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+.... - Car value

The car loses value 15% every year. Determine a time (in years) when the price will be halved. - Miraculous tree

Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?

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