Component

Component: Real 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 - 2010 HSC

Use basic arithmetic and algebra. Determine the equation of a circle. Find the derivative of a function. Find the limiting sum of a geometric series. Determine the domain of 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 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 4

Question 4

Written Paper Section I Question 4 - 2002 HSC

Solve and graph an absolute value inequation. Solve a simple trigonometric equation for a specified range. Calculate the length of a side and the area of a given triangle. Show that a given pair of coordinates represents the point of intersection of two curves. Find the size of the shaded area bounded by the two curves.

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 - 2002 HSC

Sketch a function representing a semi-circle and state the range of the function. Given the gradient function of a curve, determine the equation of the curve. Sketch the curve, labelling turning points and the y-intercept. Determine for what values of the independent variable x the curve is concave up. Calculate the volume of a container formed by rotating part of a given curve.

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