Presentation is loading. Please wait.

Presentation is loading. Please wait.

1.1 Question 1 How do you find the equation of a perpendicular bisector of a straight line ?

Similar presentations


Presentation on theme: "1.1 Question 1 How do you find the equation of a perpendicular bisector of a straight line ?"— Presentation transcript:

1 1.1 Question 1 How do you find the equation of a perpendicular bisector of a straight line ?

2 Answer to Question 1 (i)find the midpoint of the line (ii)find the gradient of the line (iii)find the gradient perpendicular to the given line (iv)Use midpoint and gradient in y-b = m(x-a) M(a,b)

3 1.1 Question 2 How do you find the midpoint of a line joining two points ?

4 Answer to Question 2 Add the coordinates and divide by two x 1 + x 2, y 1 + y 2 2 () x y (x 2,y 2 ) (x 1,y 1 )

5 1.1 Question 3 How do you find the altitude AN of ΔABC ?

6 Answer to Question 3 (i)find the gradient of BC (ii)find the gradient of AN, perpendicular to BC (iii)use y-b=m(x-a), using A as (a,b) A N B C

7 2.1 Question 4 How do you show that x-1 is a factor of the function f(x)=x 3 -3x+2 ?

8 Answer to Question 4 (i)rewrite the function as f(x)=x 3 +0x 2 -3x+2 (ii)use synthetic division with 1 on the outside (iii)show that remainder = 0

9 1.2 Question 5 For what values is this function undefined ? f(x)= x (x+2)(x-3)

10 Answer to Question 5 -2 and 3

11 1.2 Question 6 How do you draw the graph of 2f(x) given the graph of f(x) ?

12 Answer to Question 6 Double the y-coordinates

13 2.3 Question 7 How do you find the exact value of sin (α-β), given that sinα = 4 / 5 and cosβ = 12 / 13 ?

14 Answer to Question 7 (i) draw triangles for α and β (ii) work out cosα and sinβ (iii) expand formula for sin(α-β) (iv) insert exact values α 4 5 12 13 β

15 2.1 Question 8 What is the turning point of y=2(x-a) 2 +b ? Max or min ?

16 Answer to Question 8 (i)(a,b) minimum (a,b)

17 1.2 Question 9 How do you draw the graph of f(-x) given the graph of f(x) ?

18 Answer to Question 9 Reflect the graph in the y-axis

19 1.2 Question 10 How do you draw a graph of the form y = cos(x+a) or y = sin(x+a) ?

20 Answer to Question 10 Move the graph of y=cosx or y=sinx a units to the LEFT Move the graph of y=cosx or y=sinx a units to the LEFT

21 1.3 Question 11 Name the steps you take in order to differentiate functions like f(x) = x 2 + 3x + 1 √x

22 Answer to Question 11 (i)Change roots to powers (ii) split up into 3 fractions (iii) simplify each term (iv) differentiate

23 1.3 Question 12 If f(t) is the distance travelled in a certain time t seconds, then what does f ’ (t) represent ?

24 Answer to Question 12 Speed (velocity)

25 2.2 Question 13 Given f’(x) and a point on the curve, how do you find f(x) ?

26 Answer to Question 13 (i)integrate (ii)substitute in a given point to work out value of C

27 1.1 Question 14 What do you know about the gradients of two parallel lines?

28 Answer to Question 14 They are the same

29 1.1 Question 15 How do you find the equation of a tangent to a curve at the point when x = a ?

30 Answer to Question 15 (i)Differentiate (ii)fit a into f ’ (x) to get the gradient (m) (iii)fit a into f(x) to get the tangent point (a,b) (iv)use y-b=m(x-a)

31 1.3 Question 16 How do you find the rate of change of a function at a particular point ?

32 Answer to Question 16 (i) differentiate (ii) fit in given x value

33 1.3 Question 17 If y is the equation of a curve, what is represented by dy/dx ?

34 Answer to Question 17 The gradient

35 1.3 Question 18 How do you find where a curve is increasing ?

36 Answer to Question 18 (i)differentiate (ii)let f’(x) = 0 (iii)solve to find stationary points (iv)draw nature table (v)read values for which graph is increasing

37 1.3 Question 19 How would you find the maximum or minimum value of a function given its equation?

38 Answer to Question 19 (i) differentiate (ii) let f’(x) = 0 (iii) solve to find the stationary points (iv) draw the nature table (v) read off max or min

39 1.4 Question 20 Given a rec. relation in the form u n+1 = au n + b and 3 consecutive terms, how do you find the values of a and b?

40 Answer to Question 20 (i) fit 1 st term into u n and 2 nd term into u n+1 (ii) fit 2 nd term into u n and the 3 rd term into u n+1 (iii) solve simultaneous equations

41 2.1 Question 21 How do you find the value of a in the polynomial x 3 +ax 2 +4x+3 given either a factor of the polynomial, or the remainder when the polynomial is divided by a number ?

42 Answer to Question 21 (i)do synthetic division (ii)let the expression = 0 or the remainder (iii)solve the equation

43 3.2 Question 22 How do you find ∫ (ax + b) n dx ?

44 Answer to Question 22 (i)increase power by 1 (ii)divide by new power (iii)divide by the derivative of the bracket i.e. (ax+b) n+1 a(n+1) + C

45 2.3 Question 23 How do you solve equations of the form sin2x o = 0.5 ? (0≤x≤360)

46 Answer to Question 23 (i) decide on the 2 quadrants (sin is +ve) (ii) press INV sin to get angle (iii) work out your 2 angles (iv) divide each by 2

47 2.3 Question 24 How do you solve equations like cos2x o -5sinx o = 0 ? (0≤x≤360)

48 Answer to Question 24 (i) fit in 1-2sin 2 x o for cos2x o (ii) factorise (iii) solve equation

49 3.1 Question 25 How do you find a unit vector parallel to a given vector ?

50 Answer to Question 25 (i) find the length of the given vector (ii) divide all the components by this length

51 2.4 Question 26 How do you prove that a line is a tangent to a circle ?

52 Answer to Question 26 Rearrange line to make y = or x = Substitute line into circle Prove it has equal roots using b 2 -4ac = 0 or repeated roots

53 3.1 Question 27 How do you find the angle between two vectors ?

54 Answer to Question 27 a.b a b a.b a b cos  = a b 

55 3.1 Question 28 What is a unit vector ?

56 Answer to Question 28 A vector of length 1 unit

57 3.1 Question 29 What vector is equal to AB + CD + BC ?

58 Answer to Question 29 AD

59 3.1 Question 30 If u = ai+bj+ck then what is u in component form ?

60 Answer to Question 30 U = abcabc

61 3.2 Question 31 How do you integrate sin ax ?

62 Answer to Question 31 - 1 / a cos ax + C

63 3.2 Question 32 How would you differentiate a function like y = sin 3 x ?

64 Answer to Question 32 (i) write as (sin x) 3 (ii) multiply by the power (iii) decrease power by one (iv) multiply by the derivative of the bracket i.e. 3 sin 2 x cosx (i) write as (sin x) 3 (ii) multiply by the power (iii) decrease power by one (iv) multiply by the derivative of the bracket i.e. 3 sin 2 x cosx

65 3.3 Question 33 Given experimental data, how do you find an equation in the form y=ab x or y=ax b ?

66 Answer to Question 33 (i) take logs of both sides (ii) rearrange to get a straight line equation (iii) determine type (iv) Equate and solve for a and b (i) take logs of both sides (ii) rearrange to get a straight line equation (iii) determine type (iv) Equate and solve for a and b

67 3.2 Question 34 How do you differentiate an expression like without multiplying it out ?

68 Answer to Question 34 (i) multiply by the power (ii) decrease power by 1 (iii) multiply by derivative of bracket

69 3.3 Question 35 Given an equation like m = m o e -3k and an amount by which it has been decayed, how do you find k ?

70 Answer to Question 35 (i) fit in m and m o (ii) rearrange to get e -3k = (iii) take logs to get -3k = (iv) solve for k (i) fit in m and m o (ii) rearrange to get e -3k = (iii) take logs to get -3k = (iv) solve for k

71 3.3 Question 36 What is log a x + log a y equal to ?

72 Answer to Question 36 Log a xy

73 3.3 Question 37 How do you solve equations of the form 3 x = 0.155 ?

74 Answer to Question 37 (i) take logs of both sides (ii) bring x down to front (iii) solve the equation (i) take logs of both sides (ii) bring x down to front (iii) solve the equation

75 3.3 Question 38 What is log a x n equal to ?

76 Answer to Question 38 nlog a x

77 1.3 Question 39 If y = How should you rewrite y so it is ready to differentiate?

78 Answer to Question 39

79 3.4 Question 40 How do you find the maximum or minimum values of acosx + bsinx + c ?

80 Answer to Question 40 (i) change acosx+bsinx into Rcos(x-a) (ii) max is R+c


Download ppt "1.1 Question 1 How do you find the equation of a perpendicular bisector of a straight line ?"

Similar presentations


Ads by Google