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WS01 - Mathematics assignment

Mathematics, Year 10

By the end of Year 10, students recognise the effect of approximations of real  numbers in repeated calculations. They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying  linear,  quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically. Students make and test conjectures involving functions and relations using digital tools. They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions. Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts.  

 

They solve measurement problems involving surface area and volume of composite objects. Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles. They identify the impact of measurement errors on the accuracy of results. Students use mathematical modelling to solve practical problems involving  proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings. They use deductive reasoning, theorems and algorithms to solve  spatial problems. Students interpret networks used to represent practical situations and describe connectedness 

 

They plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association. They analyse inferences  and conclusions in the media, noting potential sources of bias. Students compare the distribution of continuous numerical  data  using various displays, and discuss distributions in terms of centre, spread, shape and outliers. They apply conditional probability  to solve problems involving compound events. Students design and conduct simulations involving conditional probability, using digital tools. 

Algebra

AC9M10A01

expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property

Algebra

AC9M10A04

use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings

Statistics

AC9M10ST03

construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity

Annotations

 

1. Describes the planning and approach taken to complete the first task. 

 

2. Uses a variety of approaches and interrogates their solutions to rigorously verify that their solutions were reasonable. 

 

3. Chooses appropriate methods and approximations for the situation, choosing to hold some variables constant. 

 

4. Identifies the variables that changed during the trials.

5. Collects and records measurement data in a table and uses the tabulated data to determine total and mean flight times. 

 

6. Represents the data in a comparative graph.

7. Interprets data and draws reasonable conclusions. 

 

8. Creates a column graph to represent the mean flight times using digital tools. 

 

9. Constructs a scatter graph to represent the data. 

10. Recognises the appropriate function to model the relationship and constructs a curve of best fit for the data, using appropriate digital tools. 

 

11.  Finds the equation of the quadratic function, using appropriate digital tools. 

 

12. Uses the equation of the function to find the coordinates of the turning point and relates this to the context of the problem. 

 

13. Interprets the solution to the problem in terms of the situation.

14. Investigates systematically the relationship between two variables.

15. Continues to investigate systematically the relationship between two variables. 

 

16. Uses tables to represent the relationship between the minimum and maximum number of tangents and the number of regions. 

 

17. Describes the investigation that took place as part of the modelling process.

18. Recognises the generalised pattern as being a different representation of triangular numbers. 

 

19. Uses appropriate graphing software to plot the coordinates and determines the function from the table of values. 

 

20. Finds a quadratic equation to describe the relationship between the tangents and regions.

21. Applies the quadratic formula to determine the roots of the equation. 

 

22. Recognises the negative solution is not proprietorial for the context. 

 

23. Substitutes the answer back into the equation to check if it is correct. 

 

24. Validates the solution by referring to the table of values.