AQA Level 2 Certificate Further Maths
Topic questions Pure mathematics Simultaneous equations
17 questions · 86 marks · about 2 hours
A circle has centre (2, 3) and radius 5 A straight line passes through (3, 7) and has a gradient of 2
Work out the coordinates of the two points where the circle and the straight line intersect.
Solve
Do not use trial and improvement. You must show your working.
A function f is given by
A sketch of y = f(x) is shown.
Work out the values of a and b.
Here is the graph of y = −x2 + 3x + 6 for −2 
x 5
By drawing a suitable straight line, work out approximate solutions to
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.
The equation of a circle is (x – 2)2 + (y + 3)2 = 16 The equation of a line is y = 4 – x The circle and line intersect at two points, A and B.
Show that the x-coordinates of A and B satisfy the equation 2x2 – 18x + 37 = 0
For A, the x-coordinate and y-coordinate are both positive.
Work out the coordinates of A. Give each coordinate to 2 decimal places.
A circle has centre (0, 0) and radius 5 A straight line has equation 2 y = x + 5
Work out the coordinates of the two points where the circle and straight line intersect. Do not use trial and improvement. You must show your working.
The curve y = ax3 + bx2 + 7 has a stationary point at (–2, 11)
Work out the values of a and b.
In these simultaneous equations, k is a positive constant.
3 x + 4 y = k
y = 2 kx
Solve the simultaneous equations. Give the answers in their simplest form in terms of k.
Solve the simultaneous equations
xy = – 3
Do not use trial and improvement. You must show your working.
Here is the graph of y = x2 − 6x + 5 for values of x between 0 and 6
By drawing a suitable linear graph on the grid, work out approximate solutions to
F, H, K and J are points on a circle. Chords HJ and KF intersect at L. EFG is a tangent to the circle. FH and JK are parallel.
Angle FHJ = 2 x
Give reasons why angle FKJ and angle HJK are also equal to 2 x.
Work out the values of x and y. You must show your working. Do not use trial and improvement.
A and B are points on the line y = 3 x + 2 B, C and D (5, 0) are points on the line L. O A: AC = 1: 4
Work out the x-coordinate of B.
3x2 + 2bx + 8a can be written in the form 3(x + a)2 + b + 2
Work out the two possible pairs of values of a and b.
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