Advanced level 2023 south west regional mock further mathematics 2
Advanced level 2023 south west regional mock further mathematics 2
l(i) Findthegeneralsolutionofthedifferentialequation^+(y+3)colx— e ~xcosecx. (Smirks)
(ii) Given that p and q are two statements, draw the truth table for the contrapositive of ~p => q.
(4 marks)
2(i) (a) By using the definition of cosechx > 0, in terms of cx, prove that
(4 marks)
V•
Hence or otherwise, show that
^ d(coscclf’.x) -1 -..v / 0 . (4 marks)
dx .vv1+.Y*
144
(ii) Find the Cartesian equation of the curve, whose polar equation is / ‘ = (3 marks)
25 cos20- \ ‘
3(i) (a) State De Moivre’s Theorem. (2 marks)
Hence,
1 J2L
(b) use it to show that if Z = —2(cos 0+ / sin0 ) , then ^rm12’ = 2cosfl 5–4lcos + 20isinfl
^ 1 2 3 4>
. 2 I 4 3 .
12 3 4
4 3 1 2)
(ii) Solve for Y, the equation Y ® (2 marks)
4(i) Sketch the graph of y J ( x), where y =|JT —l] f|x+ 1| — 4 . (5 marks)
(ii) Find the ged, d, of 2163 and 147. Express d in the form d – 2163.x f-147_y.
Determine whether or not the equation 2163x+147jy = 63 has a positive solution. (5 marks)
