A level north west regional mock gce 2022 further mathematics 2
A level north west regional mock gce 2022 further mathematics 2
1 (a) With respect to the origin, O, the p0ints A „ . Cartesian coordinates
(2,3,0).(2,4, 3),(0.4, 0) and (2, l, j), re’ ’C“d L
Find (i) AB*AC
(ii) The area of triangle ABC
(iii) The distance of the point D from plan(, ABC
(b) Find the set of real values of .t forwhich 8coshA.+ 4sinh;t =7
2 (a) A linear transformer T: -» 9?3|las matrix M
Find the kernel of T
(b) Given that I„ =J0‘x 0 ~ 2x) dx where n is a positive integer, show that ( n+3)I„ = «1
Hence, evaluate I
where M—
(4 marks)
3. A curve C is given by the polar equation r •-= 8ocot £cosec#, (i) Find the Cartesian equation of the curve C Hence, (ii) Show that the point A with parametric equations x= at 2 (iii) Find the equation of the normal to the curve C at the point A. (2 marks) y = lat’Jl }’>es on cun’e C- (2 marks)
4 A real-valued function is given by f (x) = In
x-1
(i) Find llie domain of /
(ii) Evaluate the one-sided limits of / at the boundaries of its domain. Hence, state the equations
of the 3 asymptotes to the curve y =/(x)
(iii) Find the coordinates of the points where the graph of y = fix) crosses the coordinate axes. (2 marks)
(iv) Find fix) and explain why the graph of }’ = fix ) has no turning point.
(v) Find fix) and explain why the graph of y- fix) has no inflexion point.
(vi) Determine the intervals, in the domain of f ,where the graph is concave up or down.
(vii) Determine the centre of symmetry of the curve y = fix).
(viii) Sketch the cun’e y= fix)
