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Session 1 Paper 2 Questions and Answers Calculator

Harris Academy Supported Study. Session 1 Paper 2 Questions and Answers Calculator. Question 1 (Unit 1 LO1 Straight Line). Triangle ABC has as its vertices A(-18,6) , B(2,4) and C(10,-8). Find the equation of the median from A to BC (b) Find the equation of the

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Session 1 Paper 2 Questions and Answers Calculator

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  1. Harris Academy Supported Study Session 1 Paper 2 Questions and Answers Calculator

  2. Question 1 (Unit 1 LO1 Straight Line) Triangle ABC has as its vertices A(-18,6) , B(2,4) and C(10,-8) . • Find the equation of the median from A to BC (b) Find the equation of the perpendicular bisector of side AC. (c) Find the coordinates of T, the point ofintersection of these lines. A B C marks 3, 4, 3

  3. mid-point of BC gradient of median equation of line Solution 1(a) (a) ans:

  4. Solution 1(b) (b) ans: • mid-point of AC • gradient of AC • perpendicular gradient • equation of line

  5. Solution 1(c) T(-3,1) ans: • solving a system of equations • x-coordinate • y-coordinate

  6. Question 2(Unit 1 LO3 Differentiation) The diagram below shows the parabola with equation and a line which is a tangent to the curve at the point T(1,5). Find the size of the angle marked θ, to the nearest degree. marks (4)

  7. Solution 2 ans: • Know to differentiate • Find gradient of tangent at x = 1 • Use m = tanθ • Complete calculations

  8. y O B A Question 3(Unit 2 LO4 Circle ) The circle in the diagram has equation .The line AB is a chord of the circle and has equation x . • Show that the coordinates of A and B are (-1, -8) and (6, -1) respectively. (b) Establish the equation of the circle which has AB as its diameter. marks (4,3)

  9. substituting into circle equation multiplying brackets and tidying up factorising and values of y corresponding values of x Solution to question 3a ans: A(-1, -8) and B(6, -1) A(-1, -8) and B(6, -1)

  10. knowing to find midpoint of AB finding radius substituting into equation Solution to question 3b ans: (25, -45)

  11. Question 4(Unit 1 LO3 Differentiation) The graph of the cubic function y = f (x) is shown in the diagram. There are turning points at (1,1) and (3,5). Sketch the graph ofy = f '(x) (3,5) y (1,1) x marks (3)

  12. 1 3 Solution 4 ans: • Interpret stationary points • Parabola • Maximum TP

  13. Harris Academy Supported Study Session 2 Paper 2 Questions and Answers Calculator

  14. Question 5 (Unit 2 LO3 Trigonometry) Solve algebraically the equation where marks 5

  15. Solution 5 ans: 1950, 16050 , 2100, 3300 • double angle formula • re-arrange to zero and factorise • find roots • answers from • answers from

  16. Question 6(Unit 1 LO3 Differentiation) An open box is designed in the shape of a cuboid with a square base. The total surface area of the base and four sides is 1200cm2 h x x (a) If the length of the base is x centimetres, show that the volume V (x) is given by (b) Find the value of x that maximises the volume of the box. marks (3,5)

  17. Solution 6 (a) ans: • Equation for surface area • Rearrange with h = ……. • Find V

  18. knowing to differentiate differentiate set derivative to zero solve for x nature table Solution 6 (b) ans: max TP at x = 20

  19. y Q P x=1 O x Question 7 (Unit 1 LO3 Differentiation Unit 2 LO1 Polynomials) Part of the curve is shown in the diagram Also shown is the tangent to the curve at the point P where • Find the equation of the tangent. (b) The tangent meets the curve again at Q. Find the coordinates of Q. marks (4,4)

  20. Solution 7(a) (a) ans: • differentiate • gradient • y-coordinate • equation

  21. form equation rearrange to zero factorise coordinates of Q Solution 7(b) (a) ans: Q (8,64)

  22. y A 4 x O Question 8(Unit 2 LO2 Integration ) The diagram shows the parabolas and • Find the coordinates of the point A (b) Calculate the area enclosed between the two curves. marks (4, 4)

  23. Form equation Rearrange to = 0 Factorise and solve Coordinates of A Solution 8a (a) ans:

  24. Integrate Substitute limits Answer y A 4 x O Solution 8b (b) ans:

  25. Harris Academy Supported Study Session 3 Paper 2 Questions and Answers Calculator

  26. P Question 9(Unit 2 LO4 Circle ) A circle, centre C, has equation C .Show that the line with equation 2y = x + 8 is a tangent to the circle and find the coordinates of the point of contact P marks (5)

  27. substitute into circle equation multiply out brackets and simplify factorise and solve for y complete proof point of contact Solution 9 ans: P(4, 6) One point of intersection so line is a tangent

  28. y (0,4) x O P Q (-2,0) Question 10(Unit 2 LO2 Integration) The diagram shows a sketch of the graph of y = (x + 2)(x – 1)(x – 2) and the points P and Q (a) Write down the coordinates of P and Q (b) Find the total shaded area marks (2,6)

  29. Solution 10a ans: • Coordinates of P • Coordinates of Q

  30. Solution 10b ans: • two integrals • multiply out brackets • integrate • integral from 0 to 1 • integral from 1 to 2 • total area

  31. Question 11(Unit 2 LO3 Trigonometry) The diagram shows a sketch of part of the graph of a trigonometric function whose equation is of the form Find the values of a, b and c y 5 x 0 π -3 marks (3)

  32. Solution 11 ans: • Interpret amplitude • Interpret period • Interpret vertical displacement

  33. Question 12(Unit 1 LO1 Straight Line) .(a) The diagram shows line OA with equations .The angle between OA and the x-axis is Find the value of a. (b) The second diagram shows lines OA and OB. The angle between these two lines is 300 . Calculate the gradient of line OB correct to 1 decimal place marks 3,1

  34. Solution 12a ans: • gradient of line • gradient = tan (angle) and apply • process

  35. Solution 12b ans: • angle = tan-1(angle)

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