# Examples for secondary school students

#### Number of problems found: 2232

- Parametric equation

Point A [6; -2]. Point B = [-3; 1] Write the parametric equation of the line BA so that t belongs to the closed interval 0; 3 - Annual growth

The population has grown from 25,000 to 33,600 in 10 years. Calculate what was the average annual population growth in%? - Seedbeds

The father wants to plant 2 seedbeds of carrot and 2 seedbeds of onion. Use a tree chart to find how many different options for placing the seedbeds he has. - Fraction to decimal infinite

Determine which digit is at 1000th place after the decimal point in the decimal expansion of the fraction 9/28. - Weighted harmonic average

Ten workers will do some work in 2 minutes, five workers in 10 minutes and three workers in 6 minutes. How many minutes per average worker per worker? - Harmonic mean

If x, y, z form a harmonic progression, then y is the harmonic mean of x and z. Find the harmonic mean of the numbers 6 and 5. - HP - harmonic progression 2

Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively. - HP - harmonic progression

Determine the 10th term of the harmonic progression 6,4,3,… - The pool

The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom? - The raw

The raw data presented here are the scores (out of 100 marks) of a market survey regarding the acceptability of new product launched by a company for random sample of 50 respondents: 40 45 41 45 45 30 30 8 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 35 - RC time constant

You introduced 1 Coulomb worth of electrons into the inner volume of a dielectric material with ϵr=6. Thirty minutes later, you found that only 36.79% of the electrons were in the internal volume. Determine the conductivity σ of the dielectric material. - Three groups

In the company, employees are divided into three groups. In the first group, which includes 12% of the company's total number of employees, the average salary is CZK 40,000, in the second group CZK 35,000, in the third group CZK 25,000. The average salary - MF graduate

78 school students graduate from mathematics or physics. There are three times more students who graduate from mathematics and do not graduate from physics than those who graduate from physics and do not graduate from mathematics. 69 students graduate fro - Proportional relationship

The ordered pairs (6,24) and (1, s) represent a proportional relationship. Find the value of s. - Andrew

Andrew had an offer for a job starting at 100000 per year and guaranteeing her to raise of 10000 a year for the next years. Find her salary for the 4th year. - Staircase

On a staircase 3.6 meters high, the number of steps would increase by 3 if the height of one step decreased by 4 cm. How high are the stairs? - Trapezoid 25

Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s. - Up and down motion

We throw the body from a height h = 5 m above the Earth vertically upwards v0 = 10 m/s. How long before we have to let the second body fall freely from the same height to hit the Earth at the same time? - Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - Sum 1-6

Find the sum of the geometric progression 3, 15, 75,… to six terms.

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