AQA Level 2 Further Maths June 2016 Paper 1 (non-calculator) · old spec 8360

20 questions · 70 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.

1. Question 1 (3 marks)

   y = x²(x – 10)

   Work out dfracdydx

   (3 marks)

2. Question 2 (3 marks)

   4( 1 – 2a , a ) = ( b , 12 )

   Work out the values of a and b.

   (3 marks)

3. Question 3 (3 marks)

   The nth term of a sequence is 3n/(5n + 12)

   (a)

   Work out the position of the term that has a value of 1/2

   (2 marks)

   (b)

   Write down the limiting value of 3n/(5n + 12) as n to ∞

   (1 mark)

4. Question 4 (2 marks)

   The equation of a circle is (x + 5)² + (y – 8)² = 10

   (a)

   What are the coordinates of the centre of the circle?

   Circle your answer.

   (-5, -8)	(-5, 8)
   (5, 8)	(5, -8)

   (1 mark)

   (b)

   Write down the radius of the circle.

   (1 mark)

5. Question 5 (3 marks)

   A, B, C and D are points on a circle, centre O.

   Diagram: A circle with centre O. A is on the circle at the upper left, D at the upper right, C on the right and B at the bottom. AD, DC, OA, OC, AB and BC are drawn, so ABCD is a quadrilateral inside the circle. Angle AOC, on the side towards D, is 2x + 48° and angle ADC is 3x.

   Work out the value of x.

   (3 marks)

6. Question 6 (4 marks)

   mx + 4 – 2(x + p) equiv 6(x + 1) where m and p are integers.

   Work out the values of m and p.

   (4 marks)

7. Question 7 (3 marks)

   Work out the integer values of x for which x² – 20x + 96 < 0

   (3 marks)

8. Question 8 (3 marks)

   Solve (3 – √x)^(1/3) = -2

   (3 marks)

9. Question 9 (3 marks)

   Expand and simplify (x – 5)³

   (3 marks)

10. Question 10 (4 marks)

    4√(x) = 2 and y⁻² = 25

    x > 0 and y < 0

    Work out the value of x/y

    (4 marks)

11. Question 11 (3 marks)

    A(11/5, 34/5), B(2, 14/5) and C(5, 3) are points on a coordinate grid.

    Show that the line segments AB and BC are perpendicular.

    (3 marks)

12. Question 12 (4 marks)

    You are given that x² + 6x + 2 equiv (x + h)² + k

    (a)

    Work out the values of h and k.

    (2 marks)

    (b)

    Write down the coordinates of the minimum point on the curve y = x² + 6x + 2

    (1 mark)

    (c)

    Solve the equation x² + 6x + 2 = 0

    Give your answers in the form a ± √b

    (1 mark)

13. Question 13 (3 marks)

    Solve √125 + √20 = √80 + √x

    (3 marks)

14. Question 14 (5 marks)

    (a)

    (x – 3) is a factor of x³ – 8x² + ax + 42 where a is an integer.

    Show that the value of a is 1

    (2 marks)

    (b)

    Hence, factorise fully x³ – 8x² + x + 42

    (3 marks)

15. Question 15 (3 marks)

    Rationalise the denominator and simplify fully dfrac6√7 + 2

    (3 marks)

16. Question 16 (4 marks)

    Angle theta is obtuse and sin theta = dfrac√116

    Work out the value of cos theta

    (4 marks)

17. Question 17 (5 marks)

    The diagram shows a sketch of the cubic curve y = 1/3x³ – x² – 3x + k

    where k is a constant.

    The x-axis is a tangent to the curve at its minimum point.

    Diagram: A sketch of a cubic curve on axes with no scale. From the bottom left it crosses the negative x-axis, rises to a maximum to the left of the y-axis, falls through the positive y-axis to a minimum on the positive x-axis, where it touches the axis, then rises again.

    Work out the value of k.

    (5 marks)

18. Question 18 (2 marks)

    Factorise fully x⁴ – 81

    (2 marks)

19. Question 19 (6 marks)

    ABCD is a square.
    CDE is a straight line.

    AC is 3√2 cm and angle DEA = 60°

    Diagram: A square ABCD with B at the top left, A at the top right, C at the bottom left and D at the bottom right, and its diagonal AC, labelled 3√2 cm. CD is extended to E, and AE is drawn, making the triangle ADE. The angle at E, DEA, is 60°.

    (a)

    Show that the side of the square is 3 cm

    (2 marks)

    (b)

    Show that the perimeter of trapezium ABCE is 3(3 + √3) cm

    (4 marks)

20. Question 20 (4 marks)

    In triangle PQR, cos P = 1/3

    Diagram: Triangle PQR with P at the top, Q at the bottom left and R at the bottom right. PQ is 3n, PR is 2n and QR is w.

    Show that triangle PQR is isosceles.

    (4 marks)

Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.