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

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

3. Solution 1 Know to differentiate Differentiate Derivative equal to zero Factorise and solve Find y coordinates Nature Table State nature of TPs 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. Solution 2 Prepare to integrate Integrate Substitute Answer ans:

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

7. Solution 3a Construct a right angled triangle and use Pythagoras Find sin x and cos x Formula for sin2 x Substitute and answer ans: X 1 3

8. Solution 3b Formula for cos2 x Substitute and answer ans: Note

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

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

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

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

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

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

15. 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 marks (3) y x -3 2 O Sketch the graph of the related function

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

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 (a) 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 For correct multiplier For recurrence relation ans:

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

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

21. Solution 8a Use synthetic division Complete division Calculate k ans: -212k-8 -212k-8 -26 -4k-12 1-32k+6-4k-20

22. Solution 8b Find quotient Factorise fully ans: -21-10-8 -2 6 8 1-3-4 0

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

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

25. Solution 9 Use the discriminant Find values of a, b and c Substitute and simplify Calculate value of p 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 marks (4) and x t y Find the maximum possible value of t

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

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

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 are defined on the set of real numbers. marks (1,2,3) and (a) Evaluate (b) Find an expression for (c) For what value(s) of x does

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

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