Examples for secondary school students - page 70

  1. Distance problem 2
    geodetka_1 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  2. Coordinates of midpoint
    linear_eq_4 If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
  3. Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  4. Paratrooper
    padak After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land fr
  5. Curve and line
    parabol 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?
  6. The pool
    inlet_1 The pool contains 220 m3 of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B?
  7. 75th percentile (quartille Q3)
    statistics Find 75th percentile for 30,42,42,46,46,46,50,50,54
  8. The length
    rectangle_14 The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
  9. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  10. Precious metals
    gold_3 In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3 4
  11. Radioactive material
    radium A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
  12. Alice
    usd_10 Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack?
  13. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  14. Account operations
    penize_49 My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?
  15. Std-deviation
    standard-dev Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
  16. Minute average
    workers_40 In a factory, four workers are assigned to complete an order received for dispatching 1400 boxes of a particular commodity. Worker A takes 4 mins per box, Worker B takes 6 minutes per box, C takes 10 mins per box, D takes 15 mins per box. Find the average.
  17. A car
    car_31 A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
  18. Right isosceles triangle
    euclid_theorem_1 Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
  19. Investment
    penize_49 1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
  20. Non linear eqs
    q2_non_linear Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7

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