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Advanced Math Problems and Solutions

Solve equations, show collinearity of points, sketch functions, find tangents, and tackle geometry challenges with detailed steps and explanations in this comprehensive math study session.

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Advanced Math Problems and Solutions

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  1. Higher Supported Study May 2015 Session 2 Paper 1

  2. Question 1 Solve the equation for rearrange to = 0 factorise solve equations

  3. Question 2 D, E and F have coordinates (10,- 8, -15), (1,-2,-3) and (-2,0,1) respectively. (a) (i) Show that D, E and F are collinear. (ii) Find the ratio in which E divides DF (b) G has coordinates (k,1,0). Given that DE is perpendicular to GE, find the value of k.      so EF and DE are parallel E is a common point so D, E and F are collinear  

  4. Question 3 • The diagram shows a sketch of the function y = f (x) • Copy the diagram and on it sketch • the graph of y = f (2x) • (b) On a separate diagram sketch • the graph of y = 1 - f (2x).

  5. Question 4 Two variables, x and y, are connected by the law log 4 y The graph of log 4y against x is a straight line passing through the origin and the point A(6,3). Find the value of a A(6,3) x O

  6. Question 5a The diagram shows a sketch of and the tangent to the curve at x = 2 Show that the equation of the tangent to the curve at x = 2 is y = 5x - 8

  7. Question 5a Find algebraically the coordinates of the point where this tangent meets the curve again

  8. Question 6a Angle x is acute and is such that (a) Show clearly that the exact value of is

  9. Question 6b (b) Hence show that

  10. y P (9, 3) x O Question 7 Two identical circles touch at the point P(9,3) as shown in the diagram.  One of the circles has equation Find the equation of the other circle.

  11. Question 8 Solve the equation

  12. y y (12, 0) (–4, 0) 0 0 x x Question 9

  13. Question 10 remainder = 0 so x + 1 is a factor

  14. Question 11

  15. Question 12

  16. Question 13

  17. Question 14 Sketch the graph of

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