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Core 1 Revision Day

Further Mathematics Support Programme www.furthermaths.org.uk. Core 1 Revision Day. Let Maths take you Further…. Outline of the Day. 10:00 11:00 Algebra 11:00 11:15 Break 11:15 12:15 Co-ordinate Geometry 12:15 1:00pm Lunch 1:00 2:00 Curve Sketching and Indices

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Core 1 Revision Day

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  1. Further Mathematics Support Programme www.furthermaths.org.uk Core 1 Revision Day Let Maths take you Further…

  2. Outline of the Day 10:00 11:00 Algebra 11:00 11:15 Break 11:15 12:15 Co-ordinate Geometry 12:15 1:00pm Lunch 1:00 2:00 Curve Sketching and Indices 2:00 3:00 Calculus 3:00pm Home time!

  3. ALGEBRA

  4. Key Topics

  5. For AS-core you should know: • How to solve quadratic equations by factorising, completing the square and “the formula”. • The significance of the discriminant of a quadratic equation. • How to solve simultaneous equations (including one linear one quadratic). • How to solve linear and quadratic inequalities. QUICK QUIZ

  6. Quick Quiz

  7. Question 1 The expression (2x-5)(x+3) is equivalent to: A) 2x2 + x - 15 B) 2x2 - x - 15 C) 2x2 + 11x - 15 D) 2x2 - 2x - 15 E) Don’t know (2x-5)(x+3) = 2x2 +6x – 5x -15 = 2x2 +x – 15

  8. Question 2 The discriminantof the quadratic equation 2x2 +5x-1=0 is: A) 17 B) 33 C) 27 D) -3 E) I don’t know b2 – 4ac = 52 – 4 x 2 x (-1) = 25 + 8 =33

  9. Question 3 Consider the simultaneous equations: x + 3y = 5 3x – y =5 The correct value of x for the solution is: A) x=1 B) x= -1 C) x=2 D) x= -2 E) I don’t know 3 x (2) 9x –3 y =15 (3) + x + 3y = 5 (1) 10x = 20 x=2

  10. Worked Exam Questions

  11. Take away 16 since the -4 in the bracket will give us an extra 16. Worked Example Write the expression x2 -8x – 29 in the form (x+a)2 + b, where a and b are constants. Hence find the roots of the equation x2 -8x – 29 = 0. Express the roots in the form c±d√5 where c and d are constants to be determined. So a=-4 and b=-45. Don’t forget the plus and minus. A very common error through out A-level! We must complete the question

  12. Worked Example Solve the simultaneous equations x – 2y = 1, x2 + y2 = 29. 1) 2) Equation 1 does not have any squared terms, so it is easier to expression x in terms of y You must know how to solve quadratic equations with ease! You could use the formula if you wanted!

  13. Worked Example a) Find the set of values of x for which 6x+3>5-2x. b) Find the set of values of x for which 2x2 -7x > >-3. c) Hence, or otherwise, find the set of values of x for which 6x+3>5-2x and 2x2 -7x > >-3. ½ 3 ¼ ½ 3

  14. Questions for you to try now...

  15. Question for you to try Question 1

  16. Question for you to try Question 2

  17. Question for you to try Question 3

  18. Answers to selected questions

  19. Solutions Question 1 For part (i) your values of a and b are: A) a =30, b = 2; B) a = 120, b = 2; C) a = 30, b = 5; D) a = 120, b = 5; E) None of these.

  20. Worked Solution Question 1 a=30 and b=2

  21. Solutions Question 2 The formula for r is given by: A) B) C) D) E) None of these.

  22. Solutions Question 3 The set of values for x is: A) -3<x<1 B) -3>x>1 C) -3<x or x>1 D) -3>x or x>1 E) None of these.

  23. More practice for you.

  24. C1(AQA) Jan 2006 Question 1

  25. C1(AQA) Jan 2007 Question 3

  26. C1(AQA) Jan 2007 Question 7

  27. C1(Edexcel) Jan 2006 Question 1

  28. C1(Edexcel) Jan 2006 Question 5

  29. C1(Edexcel) Jun 2006 Question 2

  30. C1(Edexcel) Jun 2006 Question 6

  31. C1(Edexcel) Jun 2006 Question 8

  32. C1(Edexcel) Jan 2007 Question 2

  33. C1(Edexcel) Jan 2007 Question 5

  34. C1(Edexcel) Jun 2007 Question 1

  35. C1(Edexcel) Jun 2007 Question 6

  36. C1(Edexcel) Jun 2007 Question 7

  37. C1(Edexcel) Jan 2008 Question 2

  38. C1(Edexcel) Jan 2008 Question 3

  39. C1(Edexcel) Jan 2008 Question 8

  40. COORDINATE GEOMETRY

  41. Key Topics

  42. For AS-core you should know: • How to calculate and interpret the equation of a straight line. • How to calculate the distance between two points, the midpoint of two points and the gradient of the straight line joining two points. • Relationships between the gradients of parallel and perpendicular lines. • How to calculate the point of intersection of two lines. • Calculating equations of circles and how to interpret them. • Circle Properties. QUICK QUIZ

  43. Gradient = change in y = y2 – y1 change in x x2 – x1 y = mx + c m = gradient c = y intercept

  44. Distance between two points Equation of a circle: Centre: (a, b) Radius: r

  45. Quick Quiz

  46. Question 1 A straight line has equation 10y = 3x + 15. Which of the following is true? A) The gradient is 0.3 and the y-intercept is 1.5 B)The gradient is 3 and the y-intercept is 15 C)The gradient is 15 and the y-intercept is 3 D)The gradient is 1.5 and the y-intercept is 0.3 E) Don’t know y = 3/10 x + 15/10 y = 0.31 x + 1.5

  47. Question 2 A is the point (1, 5), B is the point (4, 7) and C is the point (5, 2). Triangle ABC is A) right-angled B) scalene with no right angle C) equilateral D) isosceles E) Don’t know The sides are all different lengths

  48. Question 3 • A circle has the equation (x + 3)² + (y − 1)² = 4. Which of the following statements is false? A) The y coordinate of the centre is −1 B) The radius of the circle is 2 C) The x coordinate of the centre is −3 D)The point (−3,−1) lies on the circle E) Don’t know The equation represents a circle with centre (-3, 1) and radius 2. So the statement isincorrect

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