utec paper one .pdf

(a) #t=—2 point C that divides AB in the ratio 3:1. (05 marks) (b) x+2 (05 marks) Given that x3 = (y — 3x)* show that; 2x . = 3y — 3z. — & CamScanner x and y suchthat xZ + yZ = 7 + 3i. (05 marks) Solve the equation Sin3@ = Cos@ for 0° < 6 < 180°. (05 marks) Answer ALL questions in this section V3 dx | Find the equation of the tangent tothe curve y=1+2sinx at x= rs (b) Externally (OS marks) 3x +7. find the remainder when P(x) is divided by; (O5 marks) CamScanner that < OPQ = 45°, find the locus of P(x, y). (05 marks) SECTION A (40 MARKS) Given that z = 1+ 3i find the real numbers, When a polynomial P(x) is divided by x? — 4, the remainder is A(3,5) and B(—5,-—1) are points on a line. Find the coordinates of O(0,0) and Q(4,0) are fixed points. P(x, y) is a variable point. Given (OS marks) Evaluate; J 0 Ja. af without using tables. (a) Internally 11. (a) Find the termin x7? in the expansion of; Hence solve the equation V3Sin@ + Cos@ = v2, (b) Prove the Cosine rule a? = b* + c? —2bc CosA for any triangle ABC. Hence solve the triangle in which b = 5cm, c = 8cm and A = 60°. (06 marks) (b) A right circular cone has a slant length of 9/3cm. Calculate the (12 marks) CamScanner maximum volume of the cone; and state the corresponding values of CamScanner I ft! ss wm 9. a) Express V3 Sin@ + Cos@ inthe form Rsin(@+ a). (03 marks) SECTION B (60. MARKS) ns EX «60 (07 marks) to 4 dpls. (05 marks) evaluate; (x? os =) (04 marks) (ii) V7 to 4dps (08 marks) (i) 15 to 3dps 10. ¥(a) | Use the math