CAIE A-Level Mathematics AS 1.3.5 Graph Intersections Questions

Practise solving coordinate geometry problems within the AS mathematics syllabus.

Exam points

solve coordinate geometry problems
apply algebraic coordinate methods
interpret geometric solutions

[Maximum number: 2]

Figure for Question CAIE A-Level Mathematics AS 1.3.5 Graph Intersections Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with equation $y=9\left(x^{-\frac{1}{2}}-4 x^{-\frac{3}{2}}\right)$ . The curve crosses the x-axis at the point A.

Find the x-coordinate of A.

$9\left(x^{-\frac{1}{2}}-4 x^{-\frac{3}{2}}\right)=0$ leading to $9 x^{-\frac{3}{2}}(x-4)=0$
OE. Set y to zero and attempt to solve.
x=4 only
From use of a correct method.

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CAIE A-Level Mathematics AS 1.3.5 Graph Intersections Questions question 1