Maxima & Minima Problems
1. Ans : (0,0) point of inflexion ; (-1, 1) max point ; (3/5 , 459/3125 ) min point.
2. Ans: (i) A = (0, 5) , B = (1, 7) ; M = (0.5, 6) (ii) y=-1/2x+6 1/4
3. Ans: x = 3, y = 18
4. Ans: r = 6 ; minimum surface area ; height (when r = 6) = 12 cm
5. Ans: stat value of A = 1600 m2 ; minimum value
Curves and Circles
1. Ans : (a) x^2+ y^2=25 ; (b) x^2+y^2-2x+10y+23=0
2. Ans: (a) centre (0, 0), radius = 6 ; (b) centre (1, 3), radius = 6
(c) centre (-6, 0), radius = 3
3. Ans: x^2+y^2-6x-2y+5=0
4. Ans: (i) C = (3, 4) , radius = 3 (ii) x^2+y^2+6x-8y+16=0
5. Ans: (i) x^2+y^2+10y=0 ; (ii) A = (4, -2) , B = (-3, -1)
(iii) y=7x-5 ;
Revision : Rate of Change / Matrix and Simultaneous Equations
1. Ans: dA/dt=0.0377cm^2/s (3 s.f.)
2. Ans: (b) dx/dt=28.6cm/s (3 s.f.)
3. Ans: (a) k = -5 ; (b) ; x=-4 , y=3 ; (c) k=/5 1/3.
4E2 Rules