I/GCSE Mathematics Question Analysis Topic: Mathematics - Short Questions
Exam Questions:
1) Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right triangle.
2) Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half hours.
Answers:
For I/GCSE Mathematics, you should know:
1) First, let's name the points A, B and C respectively.
Next, let's calculate the distance between each point.
AB = √{[8 - (-2)]2 + (3 - 3)2} = √[(10)2 + (0)2] = √(100)
AC = √{[6 - (-2)]2 + (7 - 3)2} = √[(8)2 + (4)2] = √(64 + 16) = √(80)
BC √{(6-8) + [7 - (2)]}2 = √[(-2)2 + (4)2] = √(4 + 16) = √(20)
Now, should ABC be a right-angled triangle, the square of one side must be equal to the sum of the squares of the other two sides i.e., Pythagoras' theorem.
AB2 = [√(100)]2 = 100
and AC2 + BC2 = [√(80)]2 + [√(20)]2 = 100
Therefore, AB2 = AC2 + BC2 > satisifes the Pythagoras' theorem > a right-angled triangle
2) First, let's calculate the volume of water flowing through the pipe in one second, i.e.:
πr2h = π x (1)2 x 0.4 x 100 cm3
And in thirty seconds:
π x (1)2 x 0.4 x 100 x 30 x 60
The volume of the cylindrical tank would be:
π x (40)2 x h = πr2h
> π x (40)2 x h = π x (1)2 x 0.4 x 100 x 30 x 60
> h = [π x (1)2 x 0.4 x 100 x 30 x 60] / (π x 402)
> (0.4 x 100 x 30 x 60) / (40 x 40) = 45 cm.
Work hard for your I/GCSE Mathematics examination!
End of analysis. Great!