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Prelim revision Question 1

Prelim revision Question 1. How do you get the gradient of a line with an equation like 3x + 2y = 5 ?. Ans to Prelim revision Question 1. (i) Rearrange into the form y = m x + c (ii) read off gradient = m. Prelim revision Question 2.

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Prelim revision Question 1

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  1. Prelim revision Question 1 • How do you get the gradient of a line with an equation like 3x + 2y = 5 ? C

  2. Ans to Prelim revision Question 1 • (i) Rearrange into the form y = mx + c (ii) read off gradient = m

  3. Prelim revision Question 2 • What is the equation of a horizontal line passing through the point (a,b) ? C

  4. y (a,b) x Ans to Prelim revision Question 2 • y = b

  5. Prelim revision Question 3 • How do you remember the exact trig ratio values of 30o, 45o and 60o ? C

  6. 60o 1 2 30o √3 45o √2 1 45o 1 Ans to Prelim revision Question 3 • Draw reference triangles • Use SOH CAH TOA

  7. Prelim revision Question 4 • How do you find the length of a line joining two points ? C

  8. y B(x2,y2) A(x1,y1) x Ans to Prelim revision Question 4 • √(x2 – x1)2 + (y2 –y1)2

  9. Prelim revision Question 5 • What are the two formulae used to find the area of a triangle ? C

  10. A b c height C B B a s e a Ans to Prelim revision Question 5 • Area = ½base x height • Area = ½bcsinA

  11. Prelim revision Question 6 • What is a median of a triangle ? 1.1

  12. Ans to Prelim revision Question 6 • A line from a vertex to the middle of the opposite side

  13. Prelim revision Question 7 • What is the equation of a vertical line passing through (a,b) ? 1.1

  14. y (a,b) x Ans to Prelim revision Question 7 • x = a

  15. Prelim revision Question 8 • What do you know about the gradient of two perpendicular lines ? 1.1

  16. y m1 x m2 Ans to Prelim revision Question 8 • They multiply together to give -1 i.e. m1xm2 = -1

  17. Prelim revision Question 9 • How do you draw the graph of 3-f(x) given the graph of f(x) ? 1.2

  18. Ans to Prelim revision Question 9 • Reflect the graph in the x-axis, then move it up 3

  19. Prelim revision Question 10 • How do you draw the graph of f(x+1) given the graph of f(x) ? 1.2

  20. Ans to Prelim revision Question 10 • Move the graph 1 unit to the left

  21. Prelim revision Question 11 • How do you draw the graph of f(x-1) given the graph of f(x) ? 1.2

  22. Ans to Prelim revision Question 11 • Move the graph 1 unit to the right

  23. Prelim revision Question 12 • What is the Converse of Pythagoras’ Theorem ? C

  24. C a b B A c Ans to Prelim revision Question 12 • If a2 = b2 + c2 then ΔABC is right-angled at A

  25. Prelim revision Question 13 • How do you change from radians to degrees ? 1.2

  26. Ans to Prelim revision Question 13 • Divide by πand multiply by 180

  27. Prelim revision Question 14 • How do you find f(g(x)) for given functions f(x) and g(x) ? 1.2

  28. Ans to Prelim revision Question 14 • Substitute g(x) into f(x) i.e. each x in f(x) is replaced by the entire function g(x)

  29. Prelim revision Question 15 • Which two points does the graph y = ax always pass through ? 1.2

  30. Ans to Prelim revision Question 15 • (0,1) and (1,a)

  31. Prelim revision Question 16 • How do you draw a graph of the form • y = cos bx • or y = sin bx ? 1.2

  32. Ans to Prelim revision Question 16 • Draw the normal graph but fit in b cycles between 0 and 2 π

  33. Prelim revision Question 17 • What is the turning point of y = b-3(x-a)2 ? • and is it max or min ? 1.2

  34. Ans to Prelim revision Question 17 • (a,b) • Maximum (a,b)

  35. Prelim revision Question 18 • For what values of a function is the function said to be undefined ? 1.2

  36. Ans to Prelim revision Question 18 • When you fit in a value of x and you cannot get an answer • Remember you can’t divide by zero, or square root a negative number.

  37. Prelim revision Question 19 • How do you write functions like 2x2 + 12x + 3 ? in the form a(x+b)2+c 1.2

  38. Ans to Prelim revision Question 19 • (i) multiply out a(x+b)2+c • (ii) compare with given function • (iii) find a, b and c

  39. Prelim revision Question 20 • For what values is the function f(x) = √(x-a) undefined? 1.2

  40. Ans to Prelim revision Question 20 • x < a

  41. Prelim revision Question 21 • How do you draw a graph of the form y = acosx or y = asinx ? 1.2

  42. Ans to Prelim revision Question 21 • Draw y = cosx or y = sinx graph shape with a maximum of a and a minimum of -a

  43. Prelim revision Question 22 • How do you show that a curve is always increasing? 1.3

  44. Ans to Prelim revision Question 22 • (i) Differentiate • (ii) show that f’(x) is always > 0

  45. Prelim revision Question 23 • How do you find x2 + 1 √x ∫ dx ? 2.2

  46. Ans to Prelim revision Question 23 (i) change root to power (ii) split up into fractions (iii) simplify each term (iv) integrate each term (v) REMEMBER+C

  47. Prelim revision Question 24 • How do you find where a curve is decreasing ? 1.3

  48. Ans to Prelim revision Question 24 (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. Prelim revision Question 25 • How do you find the limit of a recurrence relation from its formula ? 1.4

  50. Ans to Prelim revision Question 25 • (i) let un+1 = un = L giving L=aL+b • (ii) solve equation Remember: For un+1=aun+b, a limit only exists if -1<a<1

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