Component

Component: Logarithmic and exponential functions

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 1

Question 1

Written Paper Section I Question 1 - 2002 HSC

Evaluate an arithmetic expression. Solve linear, quadratic, and simultaneous equations. Differentiate a function and integrate a 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 2

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.

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 2

Question 2

Written Paper Section I Question 2 - 2002 HSC

Find the equation of a tangent to a curve. Differentiate and integrate functions. Use the sine rule to find the exact value of a ratio.

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 3

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.

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

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 5

Question 5

Written Paper Section I Question 5 - 2010 HSC

Show that the surface area of a cylinder has a minimum value for a particular value of its radius. Prove trigonometric identities and find the exact value of an integral. Find the ordinates at two x-values for areas under a curve enclosed by the x-axis, a given ordinate and the ordinates to be found, and the curve.

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 5

Question 5

Written Paper Section I Question 5 - 2001 HSC

State the domain and range of a given function. Solve numerical problems involving logarithms. Find the length of the radius of a given sector. Calculate the area of a given cross-section using the trapezoidal rule, and the approximate volume of water that flows past this section.

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 6

Question 6

Written Paper Section I Question 6 - 2001 HSC

Calculate a term and sum of the given arithmetic series. Find the decimal value of a pronumeral in an alternative expression of an exponential equation. Find the coordinates of two stationary points on a given curve. Determine the values of x for which the curve is concave up and give reasons for the answer. Find the possible values of a constant for which an equation related to the curve has three real solutions.

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.

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