# Component

## Component: The quadratic polynomial and the parabola

### Question 1

Written Paper Section I Question 1 - 2001 HSC

Solve basic arithmetic and algebra problems. Find a primitive of a function.

### Question 2

Written Paper Section I Question 2 - 2010 HSC

Differentiate and integrate functions. Solve an inequality. Determine the gradient of a tangent to a curve.

### 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 5

Written Paper Section I Question 5 - 2002 HSC

Find the number of terms and the sum of an arithmetic series. Calculate a sector angle to the nearest degree. Find the vertex and focus of a parabola.

### Question 8

Written Paper Section I Question 8 - 2010 HSC

Calculate a population that is growing exponentially. Determine the probability that two coins tossed together will both show tails. Find values that determine the equation of a sine graph. Draw a graph on the same set of axes as the given graph. Find the values of a coefficient in the equation of a function for which the function is an increasing function.

### 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.