Examples for secondary school students - page 70
- Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
- Coordinates of midpoint
If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
- Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
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
- Curve and line
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?
- The pool
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?
- 75th percentile (quartille Q3)
Find 75th percentile for 30,42,42,46,46,46,50,50,54
- The length
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.
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.
- Precious metals
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
- Radioactive material
A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack?
- Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
- Account operations
My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?
Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
- Minute average
In a factory, four workers are assigned to complete an order received for dispatching 1400 boxes of a particular commodity. Worker A takes 4 mins per box, Worker B takes 6 minutes per box, C takes 10 mins per box, D takes 15 mins per box. Find the average.
- A car
A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
- Right isosceles triangle
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
- Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7