Examples for secondary school students - page 45

  1. Sines
    sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
  2. Right angled triangle
    fun-triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
  3. Three dice
    3_cubes When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
  4. Cubes - diff
    cube_2 Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
  5. Log
    exp_log Calculate value of expression log |3 +7i +5i2| .
  6. Book
    books_1 Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
  7. Debt
    usd_4 Joe and Caryl have a debt of $100,500. Joe makes $90,000 per year, and Caryl makes $35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries?
  8. Quadrilateral 2
    quadrilateral Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
  9. The city
    city_1 At the end of 2010 the city had 155000 residents. The population increased by 2.1% each year. What is the population at the end of 2013?
  10. Bearing
    compass A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
  11. Water reservoir
    water_tower The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
  12. Diamond
    diagonals-rhombus Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
  13. Class - boys and girls
    kresba In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
  14. Car and cyclist
    cyclist_6 Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car?
  15. Scalar dot product
    dot_product Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
  16. Enterprise
    podniky_socik The value of annual production enterprise is 7.1 million USD. The average annual growth rate is 1.5%. What will be value of production at the end of the fifth year?
  17. Medians and sides
    3angle Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
  18. Wavelength
    wave_length Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
  19. Bank
    money_3 Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
  20. Interesting property
    rectangles Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?

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