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**Question 1.**

Three resistors are connected as shown in the Figure. The resistances are R2 = 2 ohm, R3 = 3 ohm and R1 = r ohm, where r is not specied (can vary). Derive the total resistance of this system as an expression containing the symbol r.

**Question 2.**

The altitude to the hypotenuse of a right triangle divides the triangle into two smaller triangles. What do you conclude about the original triangle and the two new triangles? Explain.

**Question 3.**

The radius of a cylinder is three times longer than the radius of a cone, and the height of the cylinder is half as long as the height of the cone. What is the ratio of the volume of the cylinder to that of the cone?

**Question 4.**

By hand, without using a calculator, roughly sketch the linear functions represented by the following equations. High accuracy is not required. On your graphs, indicate only values of x-intercepts and y-intercepts (if they exist).

**1.**x = –?y– ? 4 ,

**2.**y = 2

**Question 5.**

By hand, without using a calculator, roughly sketch the functions

High accuracy is not required. On your graphs, indicate the values of x- intercepts and y-intercepts (if they exist) and any other special values which, in your opinion, deserve being shown.

**Question 6.**

An architect designs a rectangular window such that the width of the window is 40 cm less than the height. If the perimeter of the window is 500 cm, what are the width and height?

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