# Examples for secondary school students

- Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - The cruise ship

The cruise ship has a speed of 12 km / h at a calm surface. When we sail 45 km along the river and 45 km back, it took us exactly 8 hours. Which (constant) speed of flow of the river? - Digit sum

The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number? - Equation of circle 2

Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x. - Repay, interest, loan

Ramchacha takes a loan amount of 240000 from a bank for constructing a house at the rate of simple interest of 12% per annum. After 1 yr. of taking the loan he rents the house at the rate of 5200 per month. Determine the number of years he would take to r - Complex number coordinates

Which coordinates show the location of -2+3i - Endless lego set

The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The - Two workers

Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself? - Test

The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers - Clouds

Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us? - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Fence and scale

The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made? - Tangent

What distance is the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Desks

A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob, - Wagons and cranes

Several of the same cranes unloaded 96 wagons. If there were 2 more cranes there would be less 8 wagons for each crane. How many cranes were here? - Red balls

In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%? - Cylinder horizontally

The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder? - Free fall

How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss? - Mother and daughter

The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now? - Big number

hat is the remainder when dividing number 10 to 47 - 111 by number 9?

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