AQA A Level Further Maths
The matrix M is defined as
where k is a constant.
State any restrictions on the value of k
The matrix M is defined as
where c is a real number.
The linear transformation T is represented by the matrix M
Show that, for one particular value of c, the image under T of every point lies in the plane
State the value of c for which this occurs.
It is given that M is a non-singular matrix.
State any restrictions on the value of c
Using your answer from part (b)(ii), solve
A is a non-singular 2 
2 matrix and AT is the transpose of A
State the restriction on the possible values of k
The matrix M is defined as
where k is a constant.
State any restrictions on the value of k
Using your answer to part (a)(i), solve
Roberto is solving this mathematics problem:
Roberto’s solution is as follows:
Sketch the curve C1
Explain what Roberto has done wrong.
Find the area enclosed by C1
P and Q are distinct points on C1 for which r is a maximum. P is above the initial line.
Find the polar coordinates of P and Q
T maps C1 onto a curve C2
T maps P onto the point P
Find the polar coordinates of P
Find the area enclosed by C2
Fully justify your answer.
State any restrictions on the value of p.
The equations below represent three planes.
Find, in terms of p, the coordinates of the point of intersection of the three planes.
In the case where p 
2, show that the planes are mutually perpendicular.
Which of the following matrices is singular?
Circle your answer.
Three planes have equations
The planes do not meet at a unique point.
Show that k 4
5 is one possible value of k, and find the other possible value of k.
For each value of k found in part (a), identify the configuration of the given planes.
In each case fully justify your answer, stating whether or not the equations of the planes form a consistent system.
Argand Diagram which represent the roots of the equation in part (a).
Find the exact area of the shape formed by joining the transformed points.
Three planes have equations
where k is a real constant.
The planes do not meet at a unique point.
Find the possible values of k.
For each value of k found in part (a), identify the configuration of the given planes.
Fully justify your answer, stating in each case whether or not the equations of the planes form a consistent system.
Memes
Laugh now. Cry in the exam hall later. Then come back and do a past paper.
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