# Component

## Component: Plane geometry

### Question 3

Written Paper Section I Question 3 - 2010 HSC

Find the midpoint, gradient and length of an interval and the equation of a line. Prove two given triangles are similar. Find the perpendicular distance of a point from a line. Sketch a curve. Obtain an approximation to a definite integral using the trapezoidal rule and compare the approximation to the exact value of the definite integral.

### Question 3

Written Paper Section I Question 3 - 2002 HSC

Calculate the value of an investment earning compound interest. Determine the value of a pronumeral using geometric reasoning. Find the midpoint of an interval, the coordinates of a particular point, the point of intersection of two lines, and the area of a specified triangle. Show a given equation is the equation of the perpendicular bisector of an interval.

### Question 4

Written Paper Section I Question 4 - 2001 HSC

Find the values of a constant for which a specified quadratic equation has no real roots. Prove expressions for the size of specified angles in a diagram. Sketch a trigonometric curve. Represent on a diagram the region bounded by the curve and a straight line. Find the exact value of the integral representing the region.

### Question 6

Written Paper Section I Question 6 - 2010 HSC

Show that a specified graph has no stationary points. Determine values for which the graph is concave down and for which it is concave up. Sketch the graph. Find an angle in radians, the length of an interval, and the area of a shaded region. Prove two specified triangles are congruent.

### Question 9

Written Paper Section I Question 9 - 2001 HSC

Verify the size of a specified angle and hence that two triangles within the given diagram are similar. Deduce an equation. Use the cosine rule to deduce the exact value of the cosine ratio of angles within the given diagram. Given an expression for the time rate of change of a quantity, find the initial rate. Find an expression for a volume. Verify and solve a given equation for a particular value of the volume.

### Question 10

Written Paper Section I Question 10 - 2010 HSC

Show two specified triangles are similar. Show relationships involving the side lengths of the similar triangles. Find an expression for the volume of a solid of revolution. Apply the expression found in solving a problem involving a hemispherical container.