AQA Level 2 Further Maths June 2024 Paper 1 (non-calculator)
23 questions · 80 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)
Work out the value of √(t/20) where t = 2.42 × 10³
(2 marks)
Question 2 (1 mark)
Factorise x² – y²
(1 mark)
Question 3 (1 mark)
The nth term of a sequence is (3n + 4)/n
Circle the limiting value of (3n + 4)/n as n to ∞
1 3 4 7
(1 mark)
Question 4 (2 marks)
The equations of two straight lines are
y – 3x = 4 and 6y = 18x – 5
Show that the lines are parallel.
(2 marks)
Question 5 (3 marks)
y = (4x³ + x⁷)/(x⁴)
Work out dfracdydx
(3 marks)
Question 6 (3 marks)
Points A (–12, 1) and B (12, –1) lie on a circle.
AB is a diameter of the circle.Work out the equation of the circle.
(3 marks)
Question 7 (3 marks)
A point P (x, y) is transformed using the transformation represented by ( 4 & 0 , -2 & 3 )
The image of P is (–8, 7)
Work out the values of x and y.
(3 marks)
Question 8 (3 marks)
Solve by factorising 2x³ – 9x² – 5x = 0
(3 marks)
Question 9 (3 marks)
ABCDEFGH is a cuboid.
Diagram: A cuboid ABCDEFGH. The top face is ABCD with B at the front left, C at the front right, A behind B and D behind C. F, G, H and E are below B, C, D and A. AB is 3 cm, BF is 12 cm and FG is 4 cm.
Work out the length AG.
(3 marks)
Question 10 (5 marks)
A function f is given by
beginaligned f(x) &= -1/2x + 21 && 0 ≤ x ≤ 2 \\ &= ax² + bx && 2 < x ≤ 6 endaligned
A sketch of y = f(x) is shown.
Diagram: A sketch of y = f(x). A straight line goes down gently from the y-axis to the point P. From P a curve rises to a maximum and then falls to the point Q (6, 12).
Work out the values of a and b.
(5 marks)
Question 11 (6 marks)
(a)
(3x – 7) is a factor of 3x³ – 4x² – 13x + 14
Work out the other two linear factors.
(3 marks)
(b)
(x – 2) is a factor of ax⁴ – 3ax³ + 5x – 22
Work out the value of a.
(3 marks)
Question 12 (3 marks)
In triangle ABC, cos A = 3/4
Diagram: Triangle ABC with A at the top, B at the bottom left and C at the bottom right. AB is 12 cm and AC is 10 cm.
Work out the length BC.
(3 marks)
Question 13 (4 marks)
A garden patio is made from two rectangles.
All lengths are in metres.Diagram: An L-shaped patio made from two rectangles. The left rectangle is 7 wide and x tall. The right rectangle is 8 wide and x – 3 tall, joined along the bottom.
The area of the patio is less than 51 m²
Work out the range of possible values of x.
Give your answer in the form a < x < b where a and b are both integers.
You must show your working.(4 marks)
Question 14 (4 marks)
(a)
Write 2x² – 16x + 7 in the form k(x + m)² + n where k, m and n are integers.
(3 marks)
(b)
Solve (x – 1)² – 5 = 0
(1 mark)
Question 15 (3 marks)
(a)
Matrix mathbfM represents a reflection in the line y = -x
Write down matrix mathbfM
(1 mark)
(b)
mathbfN = ( 0 & 1 , -1 & 0 )
Describe geometrically the single transformation represented by mathbfN²
(2 marks)
Question 16 (4 marks)
A, B, C and D are points on a circle, centre O.
angle OBC : angle ODC = 5 : 3Diagram: A circle with centre O. A is at the top; B, C and D are on the lower part of the circle, with C between B and D. Chords AB, AD, BC and CD are drawn, and radii OB and OD. Angle BAD is 52°.
Work out the size of angle OBC.
You must show your working.(4 marks)
Question 17 (3 marks)
Show that 21x/(3x² – 2x – 8) – 7/(x – 2) simplifies to k/(3x² – 2x – 8) where k is an integer.
(3 marks)
Question 18 (4 marks)
Rationalise the denominator and simplify fully
dfrac3√5 + √3√5 – √3
(4 marks)
Question 19 (5 marks)
The equation of a curve is y = x³ – 3x² + 5
Work out the stationary points of the curve and determine their nature.
You must show your working.(5 marks)
Question 20 (4 marks)
Here is the graph of y = -x² + 3x + 6 for -2 ≤ x ≤ 5
Diagram: A graph with x from –3 to 6 and y from –6 to 12. The curve y = –x squared + 3x + 6 is drawn from x = –2, where y = –4, up through (0, 6) to its highest point at about (1.5, 8.25), and down to x = 5, where y = –4.
By drawing a suitable straight line, work out approximate solutions to
x² – 7/2x – 3 = 0
(4 marks)
Question 21 (5 marks)
(2^(x + 3))^(4x + 1) = 8^(x – 1)
Work out the possible values of x.
(5 marks)
Question 22 (4 marks)
f(x) = (3sin xcos x + sin² x)/(12cos² x + 4sin xcos x)
Simplify f(x) and hence solve f(x) = -dfrac√34 for 90° < x < 180°
You must show your working.(4 marks)
Question 23 (5 marks)
The nth term of a quadratic sequence is an² – 5n + c where a and c are integers.
The first four terms of the sequence are
2 x 16 y
Work out the values of x and y.
(5 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.