91028 4 credits

1. 910284 credits Investigate relationships between tables, equations or graphs

2. Assessment specifications • Things to take notice of

3. “A grid without axes may be provided for some questions.” • This means you must LABELthe 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 data • Always ask yourself if you can have negative values e.g. you can’t pay someone for negative time on a graph

5. What to expect • Writing a rule for a linear (straight line) pattern • This means that you are adding (or subtracting) the same number

6. Using table of values

7. Example 1

8. When we substitute in ‘1’, the value of m must be ‘3’ i.e. the coefficients must add up to ‘3’

9. We can only have values from ‘1’ onwards as we don’t have a zero pattern or a negative pattern.

10. We can’t have pattern number 11/2 so we have discrete data

11. Draw the graph starting from n = 1

12. The pattern number is the input so is on the x-axis

13. The number of matches is the output so is on the y-axis

14. Do not talk about this graph having a gradient.Say instead what the increase (or decrease) is.

15. Example 2 • Timbuktu 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?

16. The distance travelled for each camel caravan

17. Do the two camel caravans meet after 10 days?What is wrong with this graph?

18. The information is just how far they travel on each of the days and does not show the total distance from each camel caravan is from Timbuktu. • We need to construct another table.

19. This is no longer linear and the distance travelled each day becomes our first difference.

20. The total distance travelled from Timbuktu to Casablanca is a quadratic function of the form D = at2 + bt + c

21. D = at2 + bt + ca = -1, c = 0, a + b + c = 60 gives b = 61

22. D = -t2 + 61t TEST the formula for t = 4D = -16 + 244 = 228

23. Similarly for the second camel caravan

24. D = at2 + bt + ca = 1.5, c = 1710, a + b + c = 1635 gives b = -76.5

25. D = 1.5t2 – 76.5t +1710 TEST the formula for t = 4D = 24 – 306 + 1710 = 1428

26. They meet after 19 days at a distance of 798 km from Timbuktu

27. What is wrong with the graph?

28. It shows negative values which do not apply.

29. Solving using the calculator • Either use EQUA- POLY • Or SOLV

30. Example 3

31. Finding differences is not working

32. Look for ratio

33. This means it is an exponential

34. It starts at 80 and increases by 1.5 times for each successive value

35. It starts at 80 and increases by 1.5 times for each successive value

37. Recognising linear data

38. An equal increase in a regular interval i.e. for every increase of ‘10’ in x, there is a 0.28 increase in ‘y’.

39. The equation is y = 0.028x + 0.27

40. Unequal intervals

41. Equation is y = 0.95x + 1.44

42. Interpreting linear graphs • Think: • Start values • Gradient (increases/decreases) • Intersection points • Relative positions

43. Writing equations for parabolas • Think • Form of the equation • Points on the curve that you know • Start values

44. Example • Zane 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 equation • y = 0.2(x + 2)(4 – x).

45. y = 0.2(x + 2)(4 – x)

46. y = 0.2(x + 2)(4 – x)x-intercepts are x = -2, x = 4Midpoint is when x = 1

47. y = 0.2(x + 2)(4 – x)when x = 1y = 1.8 m is the highest point

48. y = 0.2(x + 2)(4 – x)when x = 0y = 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.

50. 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.