Mathematical Modelling with Linear and Quadratic Functions — Australian Curriculum (ACARA) Grade 9 Mathematics Worksheet (Set 2)

Australian Curriculum (ACARA)

Grade 9

Mathematics

40 questions

Using mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear or quadratic functions, interpreting solutions and evaluating the model (ACARA AC9M9A05), from a modelling angle.

Fill in the Blanks
Multiple Choice

Preview the questions

Showing 5 of 40 questions from this worksheet.

Mathematical Modelling with Linear and Quadratic Functions

This worksheet focuses on using mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear or quadratic functions, interpreting solutions and evaluating the model. Total: 40 marks.

Section A: Multiple Choice Questions

Choose the single best answer for each question.

A plumber charges a $50 call-out fee plus $80 per hour. Which function models the total cost, C, for h hours of work?

C = 50h + 80 C = 80h + 50 C = 130h C = 80h - 50

The path of a ball thrown in the air is modelled by the quadratic function h(t) = -5t^2 + 20t + 1, where h is the height in metres and t is the time in seconds. What does the '1' in the equation represent?

The maximum height of the ball The time it takes for the ball to hit the ground The initial height the ball was thrown from The speed of the ball

A company's profit, P, from selling x items is given by P(x) = -0.1x^2 + 100x - 5000. What shape is the graph of this profit function?

A straight line with a positive slope A parabola opening upwards A straight line with a negative slope A parabola opening downwards

The value of a car depreciates linearly over time. If its value V after t years is modelled by V(t) = 30000 - 2500t, what does the -2500 represent?

The initial value of the car The number of years until the car has no value The amount the car's value decreases each year The final value of the car

Which of the following scenarios is best modelled by a quadratic function?

The total cost of buying movie tickets at $15 each The distance travelled by a car moving at a constant speed The area of a rectangular garden with a fixed perimeter The amount of money in a bank account with a fixed weekly deposit

Section B: Fill in the Blanks

Complete the following statements.

35 more questions in the full worksheet

Create a free account to open all 40 questions, download the printable PDF with its answer key, assign it online, or remix it at a different difficulty.

Unlock the full worksheet Log in

No credit card required · Printable PDF · Auto-graded online assignments

Related worksheets

More Mathematics practice at Grade 9 level.

Grade 9 Mathematics

Variation of Parameters in Functions and Relations (Set 2)

Full mixed revision of variation of parameters in functions and relations (ACARA AC9M9A06).

24 questions Preview →

Grade 9 Mathematics

Variation of Parameters in Functions and Relations (Set 1)

Generalising emerging patterns from the variation of parameters on functions and relations (ACARA AC9M9A06), from a pattern-generalisation angle.

40 questions Preview →

Grade 9 Mathematics

Variation of Parameters in Functions

Experimenting with the effects of variation of parameters on graphs of related functions using digital tools, making connections between graphical and algebraic representations (ACARA AC9M9A06), from a parameter-exploration angle.

40 questions Preview →

Grade 9 Mathematics

Mathematical Modelling with Linear and Quadratic Functions (Set 1)

Full mixed revision of mathematical modelling with linear and quadratic functions (ACARA AC9M9A05).

24 questions Preview →

Grade 9 Mathematics

Graphing and Solving Quadratic Equations (Set 2)

Full mixed revision of graphing and solving quadratic equations (ACARA AC9M9A04).

24 questions Preview →

Grade 9 Mathematics

Solving Monic Quadratic Equations

Solving monic quadratic equations with integer roots algebraically (ACARA AC9M9A04), from an algebraic-solving angle.

40 questions Preview →