**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.

AB^{2} = [√(100)]^{2} = 100

and AC^{2} + BC^{2} = [√(80)]^{2} + [√(20)]^{2} = 100

Therefore, AB^{2} = AC^{2} + BC^{2} > 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.:

πr^{2}h = π x (1)^{2} x 0.4 x 100 cm^{3}

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 = πr^{2}h

> 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 40^{2})

> (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!