Examples for secondary school students - page 18 of 237
Number of problems found: 4730
- AP - sum15
Calculate the sum of the first 15 terms of the arithmetic sequence if a₁ = 5 and d = −3. - Rent increase
Calculate how much rent should be increased each year to keep pace with annual inflation of 7%. The rent in the first year is €550. Calculate the correct rent for each of the first 5 years so that the real value of the rent remains constant. - On the windowsill
On the windowsill, 6 different flowers in flower pots are to be arranged next to each other. Four are flowering (one of them is a primrose), the rest are decorative with leaves (one of them is a fern). Determine: a) how many different arrangements can be - Dielectric change
An air capacitor with flat parallel plates has a capacitance of C₀ = 10 pF and a plate separation of d = 1 cm. A dielectric sheet of thickness Δ = 1 mm is inserted midway between the plates. What will be the capacitance of the device? (Edge effects may be - Conductor - induction
A conductor consisting of two circular loops with radii R = 5 cm is placed in a magnetic field with induction B = 0.6 T perpendicular to the field direction. What is the electromagnetic voltage induced in this conductor when the magnetic field disappears - Effective rate
Calculate the effective health-insurance contribution rate of a beginning self-employed person, if he applies a flat-rate expense of 60%, after deduction of expenses the tax base is divided by the Bulgarian constant 1.486 and then contributions are paid - - How many 147
What is the minimum number of consecutive natural numbers from 1 to n that must be added so that their sum exceeds 1,000,000? - Spherical sector
Calculate the volume and surface area of a spherical sector if the spherical cap that forms part of the sector has a base radius r₁ = 6 cm and a height h = 2 cm. - Calculate the cylinder
Calculate the volume of a cylinder, given: S = 144π cm² height = 6 cm - View angle
From a tower 20 m high and 20 m away from a river, the width of the river appears to span an angle of 15°. How wide is the river at this location? - After-school club
30 children in a school club need to split into two teams. They put 15 white and 15 black marbles into a basket and draw lots. The teams will be made up of children who draw marbles of the same colour. Patricia drew first and pulled out a white marble. Af - Tunnel - quadrilateral
How long will tunnel AB be, given distances AD = 35 m, DC = 120 m, CB = 85 m, angle ADC = 105°, and angle BCD = 71°, where ABCD is a quadrilateral? - Sale of a bill of exchange
A businessman bought a bill of exchange 6 months before its maturity. After deducting interest at an annual rate of 10%, he paid €19,000 for it. How much interest was deducted from the face value of the bill? - 9 rectangles
A large rectangle is divided into 9 small rectangles. How many rectangles are there in total (of all sizes)? - Rotational motion of a cylinder
Calculate the kinetic energy of a cylindrical body with radius r = 0.08 m and mass m = 1.5 kg at time t = 5 s, given that the body rotates about an axis through the centre of the cylinder with a constant angular acceleration ε = 5 rad/s², starting from re - Footballers 2
Footballers have jerseys numbered 7, 8, 9, 10, and 11. The coach wants to send them to attack: a) so that no two even-numbered jerseys are adjacent, b) so that no two odd-numbered jerseys are adjacent. How many options does he have in each case? - Multiple-choice
A multiple-choice test consists of 4 questions. Each question has three different answers, with only one being correct. A student answers each question randomly. Determine the expected number of correct answers the student gets. - Physics - board, lever
A wooden board weighing 0.5 kg is placed on a table. How far can it protrude over the edge of the table without falling if a weight of 0.2 kg is placed at its overhanging end? - GP - free
For a geometric sequence, the following relationship between the first and third terms holds: a₁ − a₃ = −1.5 a₃ − a₁ = 1.5 Calculate the common ratio q and the first term a₁. - Equality of Moments A lever with a mass of 3 kg and a length of 2 m has weights of 5 kg and 8 kg attached at its two ends. Find the point where the lever must be supported so that it is in balance.
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