Mathematics 7356: Algebra and Functions Topical Past Paper Questions

A curve has equation $$ y=x-a\sqrt{x}+b $$ where $a$ and $b$ are constants. The curve intersects the line y = 2 at points with coordinates $ (1, 2) $ and $ (9, 2) $, as shown in the diagram below. (a) Show that $a$ has the value 4 and find the value of $b$ (b) On the diagram, the…

A craft artist is producing items and selling them in a local market. The selling price, £P, of an item is inversely proportional to the number of items produced, n When n = 10, P = 24 Show that $ P = \frac{240}{n} $ [1 mark] (b) The production cost, £C, of an item is inversely p…

The expression $$ \frac{3-\sqrt{n}}{2+\sqrt{n}} $$ can be written in the form $ a + b\sqrt{n} $, where a and b and n are rational but $ \sqrt{n} $ is irrational. Find expressions for $a$ and $b$ in terms of $n$. [4 marks] [4 11111111]