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Session 1 Paper 1 Questions and Answers Non Calculator

Harris Academy Supported Study. Session 1 Paper 1 Questions and Answers Non Calculator. Question 1 (Unit 1 LO3 Differentiation). Find the stationary points of the function and determine their nature. marks (7). Know to differentiate Differentiate Derivative equal to zero

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Session 1 Paper 1 Questions and Answers Non Calculator

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

  2. Question 1(Unit 1 LO3 Differentiation) Find the stationary points of the function and determine their nature. marks (7)

  3. Know to differentiate Differentiate Derivative equal to zero Factorise and solve Find y coordinates Nature Table State nature of TPs Solution 1 ans: Max TP at (-2,20) Min TP at (2,-12) Max TP at (-2,20) Min TP at (2,-12)

  4. Question 2 (Unit 2 LO2 Integration) Evaluate marks (4)

  5. Prepare to integrate Integrate Substitute Answer Solution 2 ans:

  6. Question 3 (Unit 2 LO3 Trigonometry) If x is an acute angle such that find exact values for (a) (b) marks (4,2)

  7. Solution 3a ans: • Construct a right angled triangle and use Pythagoras • Find sin x and cos x • Formula for sin2x • Substitute and answer 1 X 3

  8. Formula for cos2x Substitute and answer Solution 3b ans: Note

  9. Question 4 (Unit 2 LO3 Trigonometry) Solve marks (4)

  10. Use double angle formula Factorise and form equations Solve Solve Solution 4 ans:

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

  12. Question 5 (Unit 1 LO1 Straight Line) The line with equation meets the x and the yaxes at the points A and B respectively (a) Determine the coordinates of A and B (b) Find the equation of the perpendicular bisector of AB. marks (2,4)

  13. Coordinates of A Coordinates of B Solution 5a ans:

  14. Rearrange to y =…… and find gradient Perpendicular gradient Midpoint of AB Find equation of line Solution 5b ans:

  15. y O 2 x -3 Question 6 (Unit 1 LO2 Functions and graphs) The diagram below shows part of the graph of . The function has stationary points at and as shown Sketch the graph of the related function marks (3)

  16. Reflection in x-axis Move 3 units up Annotate graph y 3 O 2 x y 6 (2,3) O x Solution 6

  17. Question 7(Unit 1 Recurrence Relations) A doctor administers 40ml of a drug to Mr Sick each week. Over the same period 80% of the drug in the bloodstream is removed. If the level in the bloodstream rises above 55ml the drug becomes toxic • Write down a recurrence relation to model this situation. (b) Find a limit and explain what it means in the context of the question. marks (2,4)

  18. Solution 7a ans: • For correct multiplier • For recurrence relation

  19. justify limit use limit formula calculate limit explanation Solution 7b ans:

  20. Question 8 (Unit 2 LO1 Polynomials) (a) For what value of kis a factor of ? (b) Hence fully factorise the expression when k takes this value marks (3,2)

  21. Solution 8a ans: • Use synthetic division • Complete division • Calculate k

  22. Find quotient Factorise fully Solution 8b ans:

  23. Harris Academy Supported Study Session 3 Paper 1 Questions and Answers Non Calculator

  24. Question 9 (Unit 2 LO1 Polynomials) For what value of p does the equation have equal roots? marks (4)

  25. Use the discriminant Find values of a, b and c Substitute and simplify Calculate value of p Solution 9 ans:

  26. Question 10 (Unit 2 LO4 Circle) A block of wood of thickness t has to pass between two rollers The equations of the two circles are y and x Find the maximum possible value of t t marks (4)

  27. Find centre and radius of small circle Find centre and radius of large circle Calculate distance between centres Calculate distance, t Solution 10 ans:

  28. Question 11 (Unit 1 LO3 Differentiation) Part of the graph of is shown in the diagram The tangent to the curve at the point where x = 1 is also shown y o x 1 Find the equation of the tangent at the point where x = 1 marks (5)

  29. Solution 11 ans: • knowing to differentiate • differentiate • gradient at x = 1 • y coordinate • equation

  30. Question 12 (Unit 1 LO2 Functions and graphs) The functions and are defined on the set of real numbers. (a) Evaluate (b) Find an expression for (c) For what value(s) of x does marks (1,2,3)

  31. Evaluate h(f (3)) Solution 12a ans: Solution 12b ans: • Apply h • Apply f

  32. Equation Rearrange to ..... = 0 Factorise and solve Solution 12c ans:

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