ORANGE HIGH SCHOOL MATHEMATICS

Name: Class Teacher:.. ORANGE HIGH SCHOOL MATHEMATICS YEAR 9 2015 - Assignment 2 TIME ALLOWED - 2 weeks Due: Monday 3 rd August 2015 INSTRUCTIONS Read all questions carefully and answer each question in the space provided. All working out should be shown in every question. Correct grammar, punctuation and spelling should be ensured for questions requiring full sentence answers. Calculators may be used. The mark for each question is indicated. Trigonometry: /38 Linear Functions: /27 Evaluation: /15 TOTAL: /80

YEAR 9 TRIGONOMETRY SECTION 1 Engage Explore Explain Elaborate Evaluate What is Trigonometry? Investigate the relationship between sides and angles in right-angled triangles. Students are to research the origins of Trigonometry and investigate the occupations in which this area of mathematics is useful. Students explain how Trigonometry is used to perform calculations and make judgements in different situations. Students explain what they understand and question about the applications of Trigonometry. Students conduct further investigation of applications of Trigonometry including Australian standards for access ramps and calculating the heights of objects of an inaccessible height. Students reflect on their learning in the Evaluation Section. Reflect using the learning grid and self assessment. What have I learned? What did I do well? What did not go so well? What could I do to improve next time? Task 1 Tasks 2 and 3 Connect-Extend- Challenge sheet Tasks 2 and 3 Evaluation Tasks Worksheet Reflection Assessment Rubric YEAR 9 LINEAR FUNCTIONS SECTION 2 Engage Explore Explain Applying linear functions to solve real world problems. Students investigate which Fitness Centre best suits them in terms of value. The graph allows them to explore multiple scenarios in making their decision. Using the graphs to aid them, students explain which Fitness Centre is the best value for their needs. Task 1 Task 1 Elaborate Evaluate Apply linear function processes to unfamiliar problems. How does this connect to what you have learnt in class? Reflect using the learning grid and self-assessment. What have I learned? What did I do well? What did not go so well? What could I do to improve next time? Task 2 Evaluation Tasks Worksheet Reflection Assessment rubric

SECTION 1: TRIGONOMETRY (38 marks) Task 1: Trigonometry Research (9 marks) Use the internet to research the following questions. All websites used should be referenced at the end of each question. Marks will be allocated for full sentences. Ensure that you use correct punctuation, grammar and spelling. An extra 3 marks will be allocated for this. Your mark: /3 1. In your own words, give a formal definition of Trigonometry. 2 2. Explain how the word trigonometry was derived. 1 E.g. the word perimeter comes from the Greek words peri (around) and metron (measure).... 3. List 6 occupations that use trigonometry. (Sentences not required.) 3... 4. Choose one of these occupations. Describe an example of how trigonometry is used to perform a task in this occupation. Make reference to sides and angles in your description. 3............

Task 2: Access Ramps (16 marks) Just like designing the gradient (steepness) of roads, engineers need to follow guidelines when designing access ramps. Australian standards regulate that ramps have an inclined access way with a gradient steeper than 1 in 20, but not steeper than 1 in 14. (http://www.jobaccess.gov.au/content/ramps) 1. Explain what a gradient of 1 in 14 means, in terms of vertical and horizontal distances. 1...... 2. Draw a scale diagram of a ramp with a gradient of 1 in 14. 1 3. Mark the angle of elevation of the ramp on your diagram with the symbol θθ. 1 Using a protractor, carefully measure this angle to the nearest degree. 1 Angle of elevation =.. 4. Now use trigonometry to calculate the size of the angle of elevation. (Give your answer correct to the nearest degree.) 2

5. What was your measurement error? 1 Measurement error = calculated angle measured angle. 6. A ramp is to be constructed to enable access to an entry that is 90 centimetres above the ground. Use trigonometry and the angle you calculated in Question 4 to determine the minimum horizontal (base) length (b) of the ramp. 3 Give your answer in metres correct to 2 decimal places. Firstly, label the triangle with the side length and the angle to represent the situation. b.... 7. Handrails are to be constructed on both sides of the slope of the ramp from Question 6. They are to extend along the entire slope. Calculate the length of steel that is required to make the horizontal section of the handrails. Hint: use Pythagoras Theorem. Give your answer in metres correct to 2 decimal places. 3.............

8. Another access ramp has a horizontal base length of 8.5 metres and vertical height of 0.4 metres. Does this ramp meet Australian standards as described at the start of this section? Explain your answer using both clearly worked calculations and sentences. 3...............

Task 3: Clinometers (10 marks) An inclinometer, or clinometer, is an instrument for measuring angles of slope (or tilt) and elevation or depression of an object with respect to gravity. They measure both inclines and declines. In ancient times, clinometers called Astrolabes were used for navigation and locating astronomical objects. Your task is to create and use a clinometer using the instructions given to calculate the height of an everyday object. Examples are not limited to but may include: - A tree - Goal posts - A Building Things to consider when choosing an object: You need to be able to see the top of the object from your viewpoint. Flat ground is required and you must be able to measure the distance from you to the object s base. As a clinometer requires two people for best accuracy, you may team up with another student or get a guardian s help. Steps: Remove the last page of this Assignment and follow the instructions to make a clinometer (take care as your clinometer will be allocated a mark out of 2). Glue the clinometer template onto cardboard for greater strength and accuracy in measurement. Visit the Orange High website and read the Steps to using a clinometer. Follow the steps to construct the relevant diagrams and calculate the height of the object. Clinometer /2 Complete the table below 2 Eye Height (metres) Distance from object (metres) Angle Measured Angle of Elevation (90º - Angle Measured)

Draw and label a neat diagram of the object and measurements using the information collected (similar to step 5 in the link). 2 Simplify your diagram to a right- angled triangle and calculate the vertical side length of the triangle using the appropriate trigonometric ratio (steps 6 and 7). 3....... Add your solution for the triangle to your eye height to calculate the height of the object (step 8). 1...

SECTION 2: LINEAR FUNCTIONS (27 marks) Task 1: Fitness Centre (12 marks) Marks will be allocated for full sentences. Ensure that you use correct punctuation, grammar and spelling. An extra 3 marks will be allocated for this. Two of the top fitness centres in Orange have the current deals. Your mark: /3 Fitness Centre A is allowing anyone the opportunity to visit by offering classes at a cost of $12 per class. Fitness Centre B is a loyalty club where members are charged a fee of $20 per month (paid at the start of each month) and are charged $8 per class. 1. Complete a table of values for both fitness centres: Fitness Centre A 1 Number of Classes 0 1 2 3 4 5 6 7 Cost ($) Fitness Centre B 1 Number 0 1 2 3 4 5 6 7 of Classes Cost ($) 2. Graph and label both options on the grid below 3 Give the graph a title, label both axes and label the options as Fitness Centre A and B.

3. (a) How much does it cost to attend 2 classes at Fitness Centre B? 1.. (b) How many classes need to be attended for the cost of each Fitness Centre to be the same? 1.... (c) Determine the cost per month to attend 8 classes at Fitness Centre B. 1... (d) If you were choosing between the two fitness centres, which would you choose? Why? 1...... (e) Fitness Centre A is losing customers. To compete with Fitness Centre B they create a new deal. They claim that the cost to attend 10 classes at their centre is half that of Fitness Centre B. They also have a monthly fee of $20. Under this deal what would be the new cost of each class? 3.

Task 2: Triangles On the Cartesian Plane (12 marks) 1. (a) Plot the points A(-2, 1) and B(4, 5) on the number plane below. 1 Draw a right-angled triangle joining these two points. (b) Write the coordinates of the midpoint of A and B. 1..... (c) Determine the gradient of the line joining points A and B. 1...... (d) Calculate the length of the interval joining points A and B, correct to 1 decimal place. 1............... (e) Calculate the area of the right-angled triangle. 1..

2. For the linear function (straight line graph) below: (a) Write the y-intercept... 1 (b) Determine the gradient. 1....... (c) Write the equation of the graph in gradient-intercept form. (yy = mmmm + bb ) 1 (d) Calculate the area of the triangle formed by the x and y axes and the straight line graph. 1......

3. Consider the following information about a linear function (straight line graph): The distance from the origin to the y-intercept of a linear (straight line) graph is twice the distance from the origin to the x-intercept. The area of the triangle formed by the line and the axes is 2.25 units 2. The line has a negative gradient. The line has a negative y-intercept. Determine the gradient and y-intercept of the line. 3 You may use the number plane below to assist you. (Use pencil so that you can make changes.) Show all of your thinking and calculations to fully communicate all steps of your answer.

SECTION 3: EVALUATION (15 marks) Activity Recording Sheet Name:... Learning obstacle tasks: TRIGONOMETRY and LINEAR FUNCTIONS 1. What were the activities asking you to FIND OUT for both tasks? 2............ 2. What STRATEGIES did you use to help solve the problems? 1 look for a pattern guess and check work backwards draw a picture make a list make a table or diagram use objects to act out the problem brainstorm use logical reasoning by eliminating some answers 3. Did you get anyone to help you solve the problems? Describe the assistance given. 1...... 4. How do you rate the problems? 1 The problems were easy to solve. The problems needed some brain power. The problems were hard to solve and needed lots of brain power.

Connect Extend Challenge Connect: How are the ideas and information connected to what you already know? Extend: What ideas did you get that extend your thinking in new directions? Challenge: (6 Marks) What is challenging or confusing for you? What questions do you have? What puzzles you?

Worksheet Reflection Reflection What have I learned? What did I do well? 2 What did not go so well? What could I do to improve next time? 2

Assessment Rubric Name: Date: / /20 Criteria Look beyond Look within Look at 1. Above the standard: expert 2. At the standard: practitioner Problem solving Look beyond Look within Look at Reasoning and proof in support of conclusions, opinions and claims. Look within Look at Communication Look beyond Look within Look at Connections Representations A B C/D E An efficient strategy is chosen and progress towards a solution is evaluated. Adjustments in strategy, if necessary, are made along the way, and/or alternative strategies are considered. Note: The expert must achieve a correct answer. Deductive arguments are used to justify decisions and may result in more formal proofs. Precise mathematical language and symbolic notation are used to consolidate mathematical thinking and to communicate ideas. Mathematical connections or observations are used to extend the solution. Abstract or symbolic mathematical representations are constructed to analyse relationships and to extend thinking. A correct strategy is chosen based on the mathematical situation in the task. Evidence of solidifying prior knowledge and applying it to the problem-solving situation is present. Note: The practitioner must achieve a correct answer. A systematic approach and/or justification of correct reasoning are present. Communication of an approach is evident through a methodical, organised, coherent, sequenced and labelled response. Mathematical connections or observations are clearly recognised. Appropriate and accurate mathematical representations are constructed and refined to solve problems or portray solutions. 3. Approaching the standard: moving forward A partially correct strategy is chosen, or a correct strategy for solving only part of the task is chosen. Evidence of drawing on some relevant previous knowledge is present, showing some relevant engagement in the task. Some correct reasoning or justification for reasoning is present with trial and error or unsystematic trying of several cases. Communication of an approach is evident through verbal/written accounts and explanations, use of diagrams or objects, writing and mathematical symbols. Some attempt is made to relate the task to other subjects or to own interests and experiences. An attempt is made to construct mathematical representations to record and communicate problem solving. 4. Ungraded below standard: travelling required No strategy is evident, or a strategy is chosen that will not lead to a solution. Little or no engagement in the task is present. No correct reasoning or justification for reasoning is present. No awareness of audience or purpose is communicated. Little or no communication of an approach is evident. No connections are made. No attempt is made to construct mathematical representations. Numerical grade [ / 80]; Letter grade [ ] (A = 90 100%; B = 70 89%; C = 40 69%; D = 10 39%; E = 0-9%) Comments:...