# Component

## Component: Series and applications

### 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.

### Question 3

Written Paper Section I Question 3 - 2002 HSC

Calculate the value of an investment earning compound interest. Determine the value of a pronumeral using geometric reasoning. Find the midpoint of an interval, the coordinates of a particular point, the point of intersection of two lines, and the area of a specified triangle. Show a given equation is the equation of the perpendicular bisector of an interval.

### 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.

### 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 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.

### 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.

### Question 9

Written Paper Section I Question 9 - 2010 HSC

Apply geometric series to financial situations. Determine the values for which a given function is increasing and at its maximum. Find a further value of the function. Draw a graph of the function.

### 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.

### 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.