# Component

#### Student Responses (15)

Band 5/6 response 1 Band 5/6 response 2 Band 5/6 response 3 Band 4/5 response 1 Band 4/5 response 2 Band 4/5 response 3 Band 3/4 response 1 Band 3/4 response 2 Band 3/4 response 3 Band 2/3 response 1 Band 2/3 response 2 Band 2/3 response 3 Band 1/2 response 1 Band 1/2 response 2 Band 1/2 response 3### Question 4

Written Paper Section I Question 4 - 2010 HSC

Find a term and a sum of an arithmetic series. Find the area between two curves. Calculate probabilities. Prove a relationship expressed in function notation.

#### Student Responses (15)

Band 5/6 response 1 Band 5/6 response 2 Band 5/6 response 3 Band 4/5 response 1 Band 4/5 response 2 Band 4/5 response 3 Band 3/4 response 1 Band 3/4 response 2 Band 3/4 response 3 Band 2/3 response 1 Band 2/3 response 2 Band 2/3 response 3 Band 1/2 response 1 Band 1/2 response 2 Band 1/2 response 3### Question 7

Written Paper Section I Question 7 - 2002 HSC

Explain why a given geometric series has a limiting sum and find the limiting sum. Given a formula for a quantity in terms of time, find the initial amount of the quantity, when a quarter is left, and the rate of change when a quarter is left. Explain a given probability and find other probabilities, including in relation to complementary events.

#### Student Responses (15)

Band 5/6 response 1 Band 5/6 response 2 Band 5/6 response 3 Band 4/5 response 1 Band 4/5 response 2 Band 4/5 response 3 Band 3/4 response 1 Band 3/4 response 2 Band 3/4 response 3 Band 2/3 response 1 Band 2/3 response 2 Band 2/3 response 3 Band 1/2 response 1 Band 1/2 response 2 Band 1/2 response 3### Question 7

Written Paper Section I Question 7 - 2001 HSC

Find the volume of a solid of revolution. Find probabilities in relation to multi-stage events. Calculate the initial displacement of a particle moving in a straight line. Show that a given equation represents an equivalent statement of the equation for the displacement of the particle, and hence find expressions for the velocity and acceleration of the particle. Determine the limiting velocity of the particle.

#### Student Responses (11)

Band 5/6 response 1 Band 5/6 response 3 Band 5/6 response 2 Band 4/5 response 1 Band 4/5 response 2 Band 3/4 response 1 Band 3/4 response 2 Band 2/3 response 1 Band 2/3 response 2 Band 1/2 response 1 Band 1/2 response 2### 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.

#### Student Responses (15)

Band 5/6 response 1 Band 5/6 response 2 Band 5/6 response 3 Band 4/5 response 1 Band 4/5 response 2 Band 4/5 response 3 Band 3/4 response 1 Band 3/4 response 2 Band 3/4 response 3 Band 2/3 response 1 Band 2/3 response 2 Band 2/3 response 3 Band 1/2 response 1 Band 1/2 response 2 Band 1/2 response 3### Question 8

Written Paper Section I Question 8 - 2001 HSC

Calculate values of constants in equation modelling exponential population growth. Find the probability of a single-stage event and of a multi-stage event. Determine the maximum and minimum values of the rate of change of a quantity. Sketch the graph of the quantity as a function of time and identify any points on the graph where the concavity changes.