1 / 21

Topic i. numbers & algebra

Topic i. numbers & algebra. Subtopic: SEQUENCES. FACT:. In a 60 kph speed zone , the risk of casualty crash doubles for every 5 kph over the speed limit. FACT:.

klaus
Download Presentation

Topic i. numbers & algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topic i. numbers & algebra Subtopic: SEQUENCES

  2. FACT: In a 60 kph speedzone, therisk of casualtycrashdoubles forevery 5 kph overthespeedlimit.

  3. FACT: In averageconditions, a car travelling at 60 km/h willtakeabout 45 metres to stop in anemergencybrakingsituation. A car brakingfrom 65 km/h willstillbemoving at closeto 32 km/h after 45 metres travelled.

  4. EXAMPLE 1. CRASH DATA

  5. Howmuchspeeddoesthe driver succeed in losingbeforeimpact?

  6. Each 5 kph added to the initial speed results in an approximately 20% decrease in the amount of speed the driver manages to lose by braking. WHY IS THIS????

  7. Each 5 kph added to the initial speed results in an approximately 20% decrease in the amount of speed the driver manages to lose by braking. WHY IS THIS???? - 18% - 32% - 25% - 19% - 29% - 17%

  8. EXAMPLE 2. PROFIT A companybegandoingbusinessfouryears ago. Itsprofitsforthelastfouryearshavebeen$11 million, $15 million, $ 19 millionand $23 million. IfthePATTERNcontinuestheexpectedprofit in 30yearsisgoingtobe $127 million WHY????

  9. EXAMPLE 3. SQUARES & SQUARE NUMBERS HOW MANY POINTS WILL THE NEXT FIGURE HAVE? WHY??? WHAT ARE THESE SQUARES REPRESENTING????

  10. All of the above are …

  11. SEQUENCES

  12. SEQUENCES But … WHAT IS A SEQUENCE?

  13. DEFINITION A SEQUENCEis a set of quantitiesarranged in a definiteorder. Forexample: • 1, 2, 3, 4, 5, … • 1, 4, 9, 16, 25, … • 1, 8, 27, 64, 125, … • -10, -8, -6, -4, -2, …

  14. TWO TYPES OF SEQUENCES • Arithmetic Sequence • Geometric Sequence

  15. TWO TYPES OF SEQUENCES ArithmeticSequence 1, 3, 5, 7, 9, … 11, 15, 19, 23, … GeometricSequence 2, 6, 18, 54, 162 200, 20, 2, 0.2

  16. Howtodistinguishanarithmetic series? An arithmetic sequence will always have a common difference between successive terms. For example: • 2, 4, 6, 8, 10, … COMMON DIFFERENCE of 2 • 1, 4, 7, 11, 14, … COMMON DIFFERENCE of 3

  17. GETTING BACK TO THE PROFIT EXAMPLE … How can youcalculatethe 27thterm? Moreover, how can youcalculatethenthterm? Tip: Whatisthecommondifference?

  18. GETTING BACK TO THE PROFIT EXAMPLE … The common difference is 4. 15 – 11 = 4 19 – 15 = 4 Therefore we know that we need to multiply the nth by 4

  19. GETTING BACK TO THE PROFIT EXAMPLE … But … 4(1) = 4, 4(2) = 8 and 4(3) = 12 … Ifweadd + 7 we’llgettheresult. Hence, in 30 yearstheprofitwillbe 30(4) + 7 =

  20. HOW WOULD YOU CALCULATE THE Nth TERM???

  21. HOW WOULD YOU CALCULATE THE Nth TERM??? Tip: Look forit in yourbooklet!!!!!

More Related