# Problems for secondary school students

- The Hotel

The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r - Final exam

There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage? - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm^{2}and side is 13 cm long. - Kuba,

- Two trains

Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak - Substitution method

Solve goniometric equation: sin^{4}θ - 1/cos^{2}θ=cos^{2}θ - 2 - Families 2

There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys. - Tractors

Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor? - Water current speed.

Two cities along the river are 100 km apart. The powerboat downstream runs for 4 hours, upstream for 10 hours. Determines the river's current speed. - Diagonals of a rhombus 2

One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm^{2}, find the side of the rhombus. - The pool

The pool contains 220 m^{3}of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B? - Diagonals of the rhombus

How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm^{2}? - Solve 3

Solve quadratic equation: (6n+1) (4n-1) = 3n^{2} - Express train

International express train drove from Kosice to Teplice. In the first 279 km, the track was repaired, and therefore it was moving at a speed of 10km/h less than it was scheduled to drive. The rest of the 465 km trip has increased the speed by 8 km/h than. - Mixing water

The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix? - Effective and mean voltage

A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source, R2 is connected to a voltmeter which measures the mean voltage and has an internal resistance R3 = 200300 Ω, the measured value is - Three unknowns

Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0 - Pooja

Pooja and Deepa age is 4:5, 4 years back it was 8:11. What is the age of Pooja now? - Standard deviation

Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10 - Symmetry by plane

Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0

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