Given A(2,4) , B(6,8), C(a+4, 2a + b) and CA BC, find a.
[6 marks]3 4 1 Expand by SARRUS RULE (2 0 7 ) 1 −3 −2
[4 marks]If cosθ +sinθ = √2 cosθ, show that cosθ – sinθ = √2sinθ
[4 marks]Solve the following simultaneous quations using cramer’s rule. x+ y+z =4, 2x-3y+4z=33, 3x-2y-2z=2.
[6 marks]cos5x+cos3x Prove that = cot x sin5x−sin3x
[4 marks]Show that points (1, 1), (2,3) and (3,5) are collinear. x y z
[4 marks]06 Using theorems prove that [x2 y2 z2 ] = xyz(x-y)(y-z)(z-x) x3 y3 z3
[ marks]x2−x+3 Evaluate lim x→∞ 2x3+1
[4 marks]Prove that sin10° sin 30° sin50° sin70° = 1/16.
[4 marks]Solve the differential equation: dy xy = y+2 if y(1) = 1. dx
[6 marks]Solve (xy2 +x) dx + (yx2+y) dy = 0.
[4 marks]Solve the following differential equation (1+x3) dy = x2y dx
[4 marks]x−cosx dy If y = , find . x+cosx dx
[6 marks]Solve: 2xy dy = x2+ 3y2 dx
[4 marks]Evaluate lim(1+2x)1/x x→0 Q. 6 (a) Solve the following differential equation: dy 2x(logx+1) = dx siny+ycosy
[6 marks]Evaluate: ∫sin3x cos4x dx
[4 marks]Solve : L-1 ( s+4 ) s2+4s+8
[4 marks]Evaluate: ∫ 2x dx x2−7x+12
[6 marks]Find the Laplace transform of cos32t.
[4 marks]𝜋 Evaluate: ∫2sin2x dx.0
[4 marks]