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Higher Mathematics

Higher Mathematics. or. Everything you wanted to know about Higher Maths but …. Pick a number. answer. Question 1. How do you draw the graph of –f(x) given the graph of f(x) ?. Answer to Question 1. Reflect the graph in the x-axis. answer. Question 2. For what values is the function

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Higher Mathematics

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  1. Higher Mathematics or Everything you wanted to know about Higher Maths but …

  2. Pick a number

  3. answer Question 1 • How do you draw the graph of –f(x) given the graph of f(x) ?

  4. Answer to Question 1 • Reflect the graph in the x-axis

  5. answer Question 2 • For what values is the function f(x) = √(x-a) undefined?

  6. Answer to Question 2 • x < a

  7. answer Question 3 • If f(x) = xn then what is f’(x) ?

  8. Answer to Question 3 • nxn-1

  9. y (a,b) x answer Question 4 • What is the • general equation • of a straight • line passing • through (a,b) • with gradient m ?

  10. y (a,b) x Answer to Question 4 • y – b = m(x – a)

  11. answer Question 5 • If f(t) is the distance travelled in a certain time t seconds, then what does f’(t) represent ?

  12. Answer to Question 5 • Speed (velocity)

  13. answer Question 6 • What is an altitude of a triangle ?

  14. Answer to Question 6 • A line from a vertex, perpendicular to the opposite side

  15. answer Question 7 • What is logaa equal to ?

  16. Answer to Question 7 • 1

  17. answer Question 8 • Name the steps you take in order to differentiate functions like f(x) = x2+ 3x + 1 √x

  18. Answer to Question 8 • (i) Change roots to powers (ii) split up into 3 fractions (iii) simplify each term (iv) differentiate

  19. answer Question 9 • How do you find where a curve crosses the y-axis ?

  20. Answer to Question 9 • Let x = 0 and solve

  21. answer Question 10 • How do you draw the graph of 2f(x) given the graph of f(x) ?

  22. Answer to Question 10 • Double the y-coordinates

  23. answer Question 11 • How do you find the gradient of a line, given the angle the line makes with the positive direction of the x-axis ?

  24. y Θ x Answer to Question 11 • m = tan Θ

  25. answer Question 12 • What is the equation of a horizontal line passing through the point (a,b) ?

  26. y (a,b) x Answer to Question 12 • y = b

  27. answer Question 13 • What do you know about the gradient of two perpendicular lines ?

  28. y m1 x m2 Answer to Question 13 • They multiply together to give -1 i.e. m1xm2 = -1

  29. answer Question 14 • What is a median of a triangle ?

  30. Answer to Question 14 • A line from a vertex to the middle of the opposite side

  31. answer Question 15 • What is the gradient of a horizontal line ?

  32. y x Answer to Question 15 • 0

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

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

  35. answer Question 17 • How do you find the limit of a recurrence relation from its formula ?

  36. Answer to Question 17 • (i) let un+1 = un = L • (ii) solve equation Remember: For un+1=aun+b, a limit exists if -1<a<1

  37. answer Question 18 • How do you know when a recurrence relation of the form un+1 = aun + bconverges ?

  38. Answer to Question 18 • -1 < a < 1

  39. answer Question 19 • 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?

  40. Answer to Question 19 • (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. answer Question 20 • How do • you show • that a curve • is always decreasing?

  42. Answer to Question 20 • (i) differentiate (ii) show that f’(x) is negative and a square e.g. –(x+a)2

  43. answer Question 21 • How would you find the maximum or minimum value of a function given its equation?

  44. Answer to Question 21 • (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

  45. answer Question 22 • Which two points does the graph of y = logax always pass through ?

  46. Answer to Question 22 • (1,0) and (a,1)

  47. answer Question 23 • How do you find where a curve is decreasing ?

  48. Answer to Question 23 • (i) differentiate (ii) let f’(x) = 0 (iii) solve to find st pts (iv) draw nature table (v) read values where graph is decreasing

  49. answer Question 24 • If y is the equation of a curve, what is represented by dy/dx ?

  50. Answer to Question 24 • The gradient

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