# Examples for secondary school students

1. A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
2. Two equations Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
3. Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
4. Water lilies Water lilies are growing on the pond and their number is doubled every day. The whole layer is covered in 12 days. How many days will it cover 8 layers?
5. Roof cover Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m2 of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
6. The room The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
7. Largest angle of the triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
8. A bridge A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
9. Average age The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company?
10. Father 7 Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages?
11. A candle A candle shop sells scented candles for \$16 each and unscented candles for \$10 each. The shop sells 28 candles today and makes \$400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How
12. Dice We throw five times the dice. What is the probability that six fits exactly twice?
13. The bulbs The bulbs are connected serially two bulbs and one resistor. Each bulb has a resistivity of 100 ohms and resistor of 60 ohms The voltage source in the circuit is 24 volts. Do you know what voltage to measure on individual appliances?
14. Sixty Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?
15. Flying The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
16. Find the 2 Find the term independent of x in the expansion of (4x3+1/2x)8
17. Exponential warm Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degr
18. Three points 2 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
19. Curve and line The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C? A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?