Examples for secondary school students - page 39

  1. Arc-sector
    vzorec arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
  2. Unknown number
    unknown Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
  3. Rectangle pool
    basen_5 Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
  4. Theorem prove
    thales_1 We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  5. Rhombus
    rhombus-diagonals_3 One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
  6. Tray
    vanicka Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
  7. Inscribed circle
    Su55k02_m10 Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
  8. Hexagon rotation
    hexagnos A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
  9. The city
    m_f In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
  10. Tubes
    pipes_1 Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?
  11. Annual income
    income The annual incomes (in thousands of $) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
  12. Square ABCD
    squares_5 Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
  13. James
    nine James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
  14. Equation
    cubic How many real roots has equation ? ?
  15. Four sides of trapezoid
    lichobeznik-stredni_pricka_3 In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
  16. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  17. Diamond diagonals
    kosostvorec_9 Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  18. Two triangles SSA
    ssa Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
  19. Cleaners
    clean Milan would clean up the room for 2.5 hours, Eric would take 10 hours. How long they swept the room together?
  20. Prism
    prism Base of perpendicular triangular prism is a right triangle with cathetuses 4.5 cm and 6 cm. What is the surface of the prism, if its volume of 54 cubic centimeters.

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