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Math Equations & Calculations Assistant

Get step-by-step solutions to various math equations and calculations, including finding equations of lines, graph plotting, differentiation, integration, and solving trigonometric equations.

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Math Equations & Calculations Assistant

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  1. Question 1 How do you find the equation of a perpendicular bisector of a straightline ? 1.1

  2. M (a,b) 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)

  3. Question 2 How do you find the midpointof a line joining two points ? 1.1

  4. y (x2,y2) (x1,y1) x Answer to Question 2 Add the coordinates and divide by two x1+ x2 , y1+ y2 22 ( )

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

  6. A B N C 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)

  7. Question 4 How do you show that x-1 is a factor of the function f(x)=x3-3x+2 ? 2.1

  8. Answer to Question 4 (i) rewrite the function as f(x)=x3+0x2-3x+2 (ii) use synthetic division with 1 on the outside (iii) show that remainder = 0

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

  10. Answer to Question 5 -2 and 3

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

  12. Answer to Question 6 Double the y-coordinates

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

  14. α 5 4 β 13 12 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

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

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

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

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

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

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

  21. Question 11 Name the steps you take in order to differentiate functions like f(x) = x2+ 3x + 1 √x 1.3

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

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

  24. Answer to Question 12 Speed (velocity)

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

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

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

  28. Answer to Question 14 They are the same

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

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

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

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

  34. Answer to Question 17 The gradient

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

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

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

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

  41. Question 21 How do you find the value of a in the polynomial x3+ax2+4x+3 given either a factor of the polynomial, or the remainder when the polynomial is divided by a number ? 2.1

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

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

  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. Question 23 How do you solve equations of the form sin2xo = 0.5 ? (0≤x≤360) 2.3

  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. Question 24 How do you solve equations like cos2xo-5sinxo = 0 ? (0≤x≤360) 2.3

  48. Answer to Question 24 (i) fit in 1-2sin2xo for cos2xo (ii) factorise (iii) solve equation

  49. Question 25 How do you find a unit vectorparallelto a given vector ? 3.1

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

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