Examples for secondary school students - page 60

  1. Minimum of sum
    derive_1 Find a positive number that the sum of the number and its inverted value was minimal.
  2. Variation equation
    fun2_4 Solve combinatorics equation: V(2, x+8)=72
  3. Imaginary numbers
    Complex_conjugate_picture.svg Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
  4. Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356
  5. Third member
    seq_6 Determine the third member of the AP if a4=93, d=7.5.
  6. Parabola 3
    parabola_2 Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
  7. Folded square
    square_folded ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
  8. Mother and daughter
    family_20 The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
  9. Wagons and cranes
    wagon_1 Several of the same cranes unloaded 96 wagons. If there were 2 more cranes there would be less 8 wagons for each crane. How many cranes were here?
  10. Solve equation
    hrusky_2 solve equation: ?
  11. Hexagon cut pyramid
    truncated_hexa_pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
  12. Big number
    modulo_1 hat is the remainder when dividing number 10 to 47 - 111 by number 9?
  13. ABCD
    trig_1 AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
  14. Combinations
    trezor_1 How many elements can form six times more combinations fourth class than combination of the second class?
  15. Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ?
  16. Free fall
    volny pad How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
  17. Diagonals
    rhombus_3 A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
  18. Cuboids
    3dvectors Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
  19. Trapezium internal angles
    lichob_2_2 A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
  20. Circle - AG
    circle2 Find the coordinates of circle and its diameter if its equation is: ?

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