1 / 40

Unit 2 revision Q 1

Unit 2 revision Q 1. How do you find the root of an equation between two given values to 1 dp ?. Answer to Unit 2 revision Q 1. iteration. Unit 2 revision Q 2. How do you find where a curve crosses the x-axis ?. Answer to Unit 2 revision Q 2. Let y = 0 or f(x) = 0 and solve for x.

wyatt
Download Presentation

Unit 2 revision Q 1

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. Unit 2 revision Q 1 • How do you find the root of an equation between two given values to 1 dp ? 2.1

  2. Answer to Unit 2 revision Q 1 • iteration

  3. Unit 2 revision Q 2 • How do you find where a curve crosses the x-axis ? 2.1

  4. Answer to Unit 2 revision Q 2 • Let y = 0 or f(x) = 0 and solve for x

  5. Unit 2 revision Q 3 • How do you solve equations like 100 x2 4 - =0? 2.1

  6. Answer to Unit 2 revision Q 3 • (i) multiply by the denominator of the fraction (here x2) • (ii) factorise and solve

  7. Unit 2 revision Q 4 • What is the condition for equal roots ? 2.1

  8. Answer to Unit 2 revision Q 4 • b2 – 4ac = 0

  9. Unit 2 revision Q 5 • What is the quadratic formula and explain when it is used ? 2.1

  10. Answer to Unit 2 revision Q 5 • x = -b±√(b2-4ac) 2a • It is used to find roots of a quadratic equation when it is difficult to factorise.

  11. Unit 2 revision Q 6 • How do you solve quadratic inequations like x2+5x-6 ≥ 0 ? 2.1

  12. Answer to Unit 2 revision Q 6 • (i) factorise • (ii) draw graph • (iii) read x values where graph is on or above x-axis

  13. Unit 2 revision Q 7 • How do you solve quadratic inequations like x2 - 5x + 6 < 0 ? 2.1

  14. Answer to Unit 2 revision Q 7 • (i) factorise • (ii) draw graph • (iii) read x values where graph is below x-axis

  15. Unit 2 revision Q 8 • What is the condition for no real roots ? 2.1

  16. Answer to Unit 2 revision Q 8 • b2 – 4ac < 0

  17. Unit 2 revision Q 9 • How do you find where a curve crosses the y-axis ? 2.1

  18. Answer to Unit 2 revision Q 9 • Substitute x=0 into equation to find y value

  19. Unit 2 revision Q 10 • What is the condition for real roots ? 2.1

  20. Answer to Unit 2 revision Q 10 • b2 – 4ac ≥ 0

  21. Unit 2 revision Q 11 • How do you find where a line and a circle intersect ? 2.4

  22. Answer to Unit 2 revision Q 11 • Rearrange line to get x = … or y = … • Substitute into circle equation and solve

  23. Unit 2 revision Q 12 • How do you factorise a cubic expression like x3-2x2-x+2 ? 2.1

  24. factor 1 -2 -1 2 Remainder=0 Answer to Unit 2 revision Q 12 • Synthetic division using factors of last number

  25. Unit 2 revision Q 13 • How do you find ∫ x3 dx ? b a 2.2

  26. Answer to Unit 2 revision Q 13 [ ] • x3+1 3+1 then 1/4[(b4) - (a4)] b a

  27. Unit 2 revision Q 14 • How do you integrate xn ? 2.2

  28. Answer to Unit 2 revision Q 14 • xn+1 n+1 + C

  29. Unit 2 revision Q 15 • How do you calculate the area under a curve ? 2.2

  30. Answer to Unit 2 revision Q 15 • (i) integrate • (ii) substitute in two limits and subtract to find area

  31. Unit 2 revision Q 16 • How do you find the exact values of sin(A+B), cos(A-B) etc. given that • cosA = 3/5 and • sinB = 12/13 ? 2.3

  32. A 5 3 13 12 Answer to Unit 2 revision Q 16 • (i) draw two Δs • (ii) find missing sides • (iii) expand formula • (iv) substitute in values from Δs using SOH CAH TOA B

  33. Unit 2 revision Q 17 • How do you solve equations like • Cos2xo - 5cosxo = 2 ? (0 ≤ x ≤ 360) 2.3

  34. Answer to Unit 2 revision Q 17 • (i) Substitute 2cos2xo-1 for cos2xo • (ii) Make RHS=0 and then factorise (use c for cos xo if you like) • (iii) solve for cos xo and hence for x

  35. Unit 2 revision Q 18 • What is the centre and radius of a circle of the form • x2+y2+2gx+2fy+c=0 ? 2.4

  36. Answer to Unit 2 revision Q 18 • Centre (-g,-f) • Radius √(g2+f2-c)

  37. Unit 2 revision Q 19 • What is the centre and radius of a circle with equation x2 + y2 = r2 ? 2.4

  38. Answer to Unit 2 revision Q 19 • (i) centre (0,0) • (ii) radius = r

  39. Unit 2 revision Q 20 • What is the centre and radius of a circle of the form • (x-a)2+(y-b)2 = r2 ? 2.4

  40. y r C (a,b) x Answer to Unit 2 revision Q 20 • Centre (a,b) • Radius = r

More Related