Ultimate Exam Question Finder
Every question from real past papers, each with its mark scheme, a worked solution and a shadow: the same question with new numbers.
AQA Level 2 Further Maths June 2017 Paper 1 (non-calculator) · old spec 8360
18 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.
Question 1 (2 marks)
On the grid below, draw a straight line through (2, 1) with gradient 3/4
Diagram: A blank grid with x from –6 to 6 and y from –5 to 5, with axes through O.
(2 marks)
Question 2 (3 marks)
A curve has equation y = ax² + 3x where a is a constant.
When x = -1, the gradient of the curve is -5
Work out the value of a.
(3 marks)
Question 3 (4 marks)
(a)
On the axes below, sketch the graph of y = x² + 7x – 18
Label all points of intersection with the axes.
You do not need to work out the coordinates of any stationary points.Diagram: Blank axes: an x-axis and a y-axis crossing at O, with no scale.
(3 marks)
(b)
Work out the equation of the line of symmetry of the graph of y = x² + 7x – 18
(1 mark)
Question 4 (3 marks)
A straight line passes through the points (-4, 7), (6, -5) and (8, t)
Use an algebraic method to work out the value of t.
You must show your working.(3 marks)
Question 5 (3 marks)
(x + 4)(x² – kx – 5) is expanded and simplified.
The coefficient of the x² term is twice the coefficient of the x term.
Work out the value of k.
(3 marks)
Question 6 (3 marks)
Factorise fully (x + 6)⁴ + (x + 6)³(3x + 4)
Do not attempt to expand the brackets.
(3 marks)
Question 7 (6 marks)
The function f is given by f(x) = √(2x – 5)
(a)
Which of these inequalities is a possible domain for f(x)?
Circle the inequality.x ≥ 0 x ≥ 2/5 x ≥ 2 x ≥ 5/2 (1 mark)
(b)
Work out x when f(x) = 1.2
(2 marks)
(c)
Work out the value of f(25/8)
Give your answer as a fraction in its simplest form.
(3 marks)
Question 8 (4 marks)
The first four terms of a quadratic sequence are 10 33 64 103 …
Work out an expression for the nth term.
(4 marks)
Question 9 (5 marks)
Here is a rectangle.
Diagram: A rectangle. The top side is labelled (2x – 3) cm and the right-hand side is labelled (x + 1) cm.
(a)
Show that the area of the rectangle is 2x² – x – 3 cm²
(1 mark)
(b)
The area of the rectangle is greater than 7 cm²
Work out the range of possible values of x.
Give your answer as an inequality.(4 marks)
Question 10 (4 marks)
Circle C_1 has centre L and equation (x – 3)² + y² = 36
Circle C_2 has centre M and equation (x – h)² + y² = 64 where h is a constant.
The circles intersect at N.
LN is perpendicular to MN.
Diagram: Axes with O at the origin. Circle C1 has its centre L on the x-axis, a little to the right of O. Circle C2, bigger, has its centre M further right on the x-axis. The circles cross at N, above the x-axis; LN and MN are drawn, with a right angle at N.
Work out the value of h.
(4 marks)
Question 11 (4 marks)
Simplify fully x/(x – 3) + 6/((x – 3)(x – 5))
(4 marks)
Question 12 (4 marks)
The transformation matrix mathbfM represents a 90° clockwise rotation about the origin.
(a)
Write down the matrix mathbfM.
(1 mark)
(b)
Describe fully the single transformation represented by mathbfM².
(2 marks)
(c)
Write down the matrix for the single transformation represented by mathbfM².
(1 mark)
Question 13 (3 marks)
Solve x^(-1/4) = 0.2
(3 marks)
Question 14 (4 marks)
In the diagram, BCD is a straight line.
AD = 2√3 cm
Diagram: Triangle ABD with a right angle at B, A above B, and D to the right of B. C is on BD, between B and D, and AC is drawn. Angle ACB is 45° and angle ADB is 30°. AD is 2√3 cm.
Work out the exact length of CD.
Give your answer in the form a + b√3 where a and b are integers.
(4 marks)
Question 15 (4 marks)
The continuous curve y = f(x) has exactly three stationary points.
The three stationary points are
a minimum point P at (a, b) where a < 0 and b < 0
a point of inflection Q at (0, 3)
a maximum point R at (c, d) where c > 0 and d > 3
The curve cuts the x-axis at three distinct points.
On the axes below, sketch the curve.
Label the points P, Q and R on your sketch.Diagram: Blank axes: an x-axis and a y-axis crossing at O, with no scale.
(4 marks)
Question 16 (4 marks)
Here is a triangle.
Diagram: A triangle with a long horizontal base labelled y cm. The left-hand side is 6 cm; the angle at the top, between the 6 cm side and the third side, is 120°. The angle at the right-hand end of the base, opposite the 6 cm side, is x°.
sin x° = dfrac1√12
Work out the value of y.
(4 marks)
Question 17 (5 marks)
(a)
Factorise 2x² + 7x + 5
(2 marks)
(b)
Hence, or otherwise, work out the value of theta between 0° and 360° for which
2sin² theta + 7sin theta + 5 = 0
(3 marks)
Question 18 (5 marks)
Simplify fully dfrac24 – √3004√3 – 5
Give your answer in the form a√b where a and b are integers.
(5 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.