Exam-Style Questions.

The following table shows corresponding values for two variables \(x\) and \(y\).

(a) If \(y\) is inversely proportional to the square of \(x\) find an equation for \(y\) in terms of \(x\).

(b) Find the positive value for \(x\) when \(y = 20\).

Worked Solution

(a) Sketch a graph on the axes below left that shows that \(y\) is directly proportional to \(x\).

(b) Sketch the graph of \(y = -x^3\) on the axes above right.

(c) It is possible to draw many rectangles that have area \(48 cm^2\).

Draw a graph to show the relationship between length and width for rectangles with area \(48 cm^2\) and sides less than \(50cm\).

Worked Solution

At a constant temperature, the volume of a gas \(V\) is inversely proportional to its pressure \(p\). By what percentage will the pressure of a gas change if its volume increases by 15% ?

Worked Solution

Which of the following statements are correct if \(xy = c\) and \(c\) is a constant.

• (a) \(y\) is directly proportional to \(x\)
• (b) \(y\) is directly proportional to \(\frac{1}{x}\)
• (c) \(y\) is inversely proportional to \(\frac{1}{x}\)
• (d) \(x\) is directly proportional to \(y\)

Worked Solution

If \(a\) is inversely proportional to \(b\) and \(b\) is directly proportional to \(c^2\) find a formula for \(a\) in terms of \(c\) given that \( a=20 \) and \(c = 4 \) when \(b = 8 \).

Worked Solution