1 / 11

Practice NAB Unit 3

Practice NAB Unit 3. Outcome 1. 1. ( a ) A, B and C have coordinates (1, 2, 3), (4, –4, 12) and (5, –6, 15). (i) Write down the components of AC (ii) Hence show that the points A, B and C are collinear. i) AC = c – a. ii) BC = c – b. ( ). ( ). ( ). ( ). 5 -6 15.

floyd
Download Presentation

Practice NAB Unit 3

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. Practice NAB Unit 3

  2. Outcome 1 1. (a) A, B and C have coordinates (1, 2, 3), (4, –4, 12) and (5, –6, 15). (i) Write down the components of AC (ii) Hence show that the points A, B and C are collinear. i) AC = c – a ii) BC = c – b ( ) ( ) ( ) ( ) 5 -6 15 4 -4 12 5 -6 15 1 2 3 – – ( ) ( ) = 1 -2 3 = 4 -8 12 Thus AC = 4BC with common point C, therefore collinear (could also have used AB)

  3. KL = 2LM l – k = 2(m – l) l – k = 2m – 2l 3l = 2m + k ( ) ( ) -1 0 3 5 -3 6 + = 2 ( ) 9 -6 15 3l = coordinates L (3,-2,5) ( ) 3 -2 5 l =

  4. a) 2(3) + -1(0) + 2(4) = 14 b) cosϴ = PQ . PR PQ = √22 + (-1)2 + 22 PQ PR = √9 = 3 cosϴ = 14 PQ = √32 + 02 + 42 3(5) = √25 = 5 ϴ = cos-1(14/15) ϴ = 21.00 Threshold 9 out of 12

  5. Outcome 2 3. (a) Differentiate –3sin x with respect to x. → -3cosx dy/dx =-½sinx (b) Given y = ½cosx, find dy/dx

  6. 4. Find f/(x) when, f(x) = (x + 3)-5 let y = U-5 where U = x + 3 dy/dU = -5U-6dU/dx = 1 dy/dx = -5U-6.1 = -5(x + 3)-6

  7. 5) a) Find ∫4cosx dx → 4sinx + c b) Integrate –¾sinx with respect to x → ¾cosx + c

  8. 3 ∫ c) Evaluate (x – 1)4 dx 2 [ ] 3 = (x – 1)5 1(5) 2 – (2 – 1)5 = (3 – 1)5 5 5 = 31/5 units2 Threshold 8 out of 11

  9. Outcome 3 6. (a) Simplify loga12 + loga2. loga24 (b) Simplify 5 log82 – log8 4. = log825 – log84 = log832 – log84 = log88 = 1

  10. loge4 7) a) If x = loge7 find an approximation for x x = 1.40 (using calculator) (b) Given that log10y = 3.4, write down an expression for the exact value of y. y = 103.4 (c) If y = 102.9, find an approximation for y. 794.3 (using calculator) Threshold 5 out of 8

  11. Outcome 4 8) Express 2cosx + 3sinx in the form kcos(x-α) where k>0 and 0≤α<3600 2cosx + 3sinx kcos(x – α) = kcosxcosα + ksinx sinα equating coefficients kcosα = 2, ksinα= 3 k = √(22 + 32) tanα = 3/2 tan-1(3/2) = 56.30 Quad i → α = 56.30 →√13cos(x – 56.30) = √13 Threshold 3 out of 5

More Related