Presentation on theme: "Investigate relationships between tables, equations or graphs"— Presentation transcript:
1Investigate relationships between tables, equations or graphs creditsInvestigate relationships between tables, equations or graphs
2Assessment specifications Things to take notice of
3“A grid without axes may be provided for some questions.” This means you must LABEL the axes otherwise your graph has no meaning. Draw big graphs not little ones i.e. use the whole grid.
4“Candidates may be required to understand the difference between graphs representing situations involving continuous data from graphs representing situations involving discrete data.”Always ask yourself if you can have half of the value e.g. you can’t buy half a cell phone- this is discrete dataAlways ask yourself if you can have negative values e.g. you can’t pay someone for negative time on a graph
5What to expect Writing a rule for a linear (straight line) pattern This means that you are adding (or subtracting) the same number
12The pattern number is the input so is on the x-axis
13The number of matches is the output so is on the y-axis
14Do not talk about this graph having a gradient Do not talk about this graph having a gradient. Say instead what the increase (or decrease) is.
15Example 2Timbuktu and Casablanca are linked by a camel route which is 1710 km long. One camel caravan leaves Timbuktu for Casablanca and travels 60 km on the first day, 58 km on the second, 56 km on the next day and so on. Another caravan leaves Casablanca for Timbuktu and travels 75 km on the first day, 72 km on the second, 69 on the next day, and so on. A. How many days does it take before the two caravans meet? B. How far from Timbuktu do the two caravans meet?
42Interpreting linear graphs Think:Start valuesGradient (increases/decreases)Intersection pointsRelative positions
43Writing equations for parabolas ThinkForm of the equationPoints on the curve that you knowStart values
44ExampleZane is throwing screwed up pieces of paper into a rubbish bin. The graph below shows the height of a piece of paper above the floor.The height of the piece of paper above the floor is y, in metres, and the horizontal distance of the piece of paper from Zane is x, in metres.The graph has the equationy = 0.2(x + 2)(4 – x).
46y = 0.2(x + 2)(4 – x) x-intercepts are x = -2, x = 4 Midpoint is when x = 1
47y = 0.2(x + 2)(4 – x) when x = 1 y = 1.8 m is the highest point
48y = 0.2(x + 2)(4 – x) when x = 0 y = 1.6 m is the initial height
49(b)Zane decides to increase the difficulty by moving further from the rubbish bin. He stands 5.3 m from the nearest side of a rubbish bin that is 30 cm in height.
50This time he releases the piece of paper 2. 0 metres above the floor This time he releases the piece of paper 2.0 metres above the floor. It reaches a maximum height of 3.0 m above the floor when it has travelled 2 metres from Zane.
51Form an equation to model the path of the piece of paper and use it to determine whether Zane gets the piece of paper into the rubbish bin.
52You must justify your answer with clear mathematical reasoning, including showing exactly how you used the equation to obtain your answer.
53There are two forms of the equation that you should consider:
54As you are not given any intercepts, it is better to choose the first equation.
55You have one unknown (k) so you need 1 point You have one unknown (k) so you need 1 point. In this case, when x = 0, y = 2
56You have one unknown (k) so you need 1 point You have one unknown (k) so you need 1 point. In this case, when x = 0, y = 2
60A rugby player places the ball on the ground 46 metres from the goal posts. He steps back, runs towards the ball and kicks it towards the goal posts.For the goal to count, the ball must pass over a bar 3 metres above the ground between the goal posts – in other words, the ball must be at least 3 metres high after it has travelled 46 metres from where it was kicked.The ball’s path through the air can be modelled with a parabola.
6124 m46 mMaximum height 36 mGoal 3 m highDiagram is NOT drawn to scale.
62The highest point the ball reaches is 36 metres. It reaches this point when it has travelled 24 metres horizontally.Write the equation of the ball’s path. Use it to determine if the goal is scored by stating how high the ball is when it reaches the bar.You must show the equation you have formed and the calculations used to support your answer.
63Consider both forms of the equation. Maximum height 36 mGoal 3 m highDiagram is NOT drawn to scale.
64Either form will get you the answer. Maximum height 36 mGoal 3 m highDiagram is NOT drawn to scale.
65For the first equation use the point (0, 36) For the second equation use the point (24,0) 24 m46 mMaximum height 36 mGoal 3 m highDiagram is NOT drawn to scale.
66You could also have if your axis was taken as shown 24 m46 mMaximum height 36 mGoal 3 m highDiagram is NOT drawn to scale.
67When x = 46 all equations will give the same answer
68ExampleHamish has made a small water rocket as a science project. This is a soft-drink bottle that is pressurised with, say, a bike pump. It then flies through the air. The graph shows the height of the rocket for one of Hamish’s launches. The rocket is launched from the top of a fence post at H.
70How high does the rocket get at the top of the curve? The graph has the equation h = 0.04(d + 3)(15 – d) where h is the height of the rocket above the ground, and d is the horizontal distance from the rocket’s starting point. Both h and d are measured in metres.How high does the rocket get at the top of the curve?
71How high does the rocket get at the top of the curve? The graph has the equation h = 0.04(d + 3)(15 – d) where h is the height of the rocket above the ground, and d is the horizontal distance from the rocket’s starting point. Both h and d are measured in metres.How high does the rocket get at the top of the curve?The midpoint of d = -3 and d = 15 is d = 6Substitute this into the equation.
72Here is the diagram of a suspension bridge over a river Here is the diagram of a suspension bridge over a river. The bridge has been modelled with straight lines and a parabola.Diagram is NOT drawn to scale.RPABriverSQ