Examples for secondary school students - page 68

  1. Find two
    eq222_7 Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
  2. Same area
    euclid_4 There is a given triangle. Construct a square of the same area.
  3. Barrel with water
    sudy_5 The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
  4. Rectangle - area, perimeter
    rectnagles_2 The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
  5. The swimmer
    river_3 The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
  6. Bridge cards
    cards2 How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
  7. Mixing water
    teplomer_17 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?
  8. SSA and geometry
    ssu_veta The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
  9. Integer
    abs1 Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
  10. Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  11. Pavement
    chodnik2 Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
  12. Points collinear
    collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
  13. Associative law multiplication
    sale_4 In a warehouse, you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first)
  14. Cancel fractions
    zlomky_15 Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
  15. Inverted nine
    In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
  16. Digits
    seq_5 Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
  17. Driver
    cargo_truck_4 The driver of the car at a speed of 100 km/h faced the obstacle and began to brake with a slowing of 5 m/s². What is the path to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
  18. Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  19. Resistance
    Rezistor_2 A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
  20. Three sides
    triangle_vysky_2 Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .

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