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Component: Applications of calculus to the physical world

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

Question 7

Written Paper Section I Question 7 - 2010 HSC

Determine the velocity and displacement of a particle and the time that it first comes to rest. Find the equation of a tangent to a parabola. Show a specified line is vertical and another specified line is a tangent to the parabola.

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

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

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

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

Question 8

Written Paper Section I Question 8 - 2002 HSC

Find the value of constants in an exponential decay equation. Calculate when one-eighth of a quantity undergoing exponential decay remains. Sketch the graph of a trigonometric function modelling the motion of a particle. Find when and where the particle is at rest and describe the motion.

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

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.

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 9

Question 9

Written Paper Section I Question 9 - 2002 HSC

Sketch a logarithmic function and use Simpson's rule to approximate a related integral. Apply geometric series to a financial situation. Find an equation for the speed of a car in terms of time. Determine the distance a jet is behind the car after a given time and the time for the jet to catch up with the car.

Student Responses (13)

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 1/2 response 1 Band 1/2 response 2

Question 9

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.

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 10

Question 10

Written Paper Section I Question 10 - 2001 HSC

Apply geometric series concepts to financial situations. Find two expressions to describe travel situations and use the expressions to solve a real-world problem.

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