2000 - JAMB Mathematics Past Questions and Answers - page 2

n = 3, U₃ = 4x - 2y,

U_n = a + (n+1)d,

4x - 2y = a + 2d (1)

U₉ = 10x - 8y,

10x - 8y = a + 8d (2)

Solving (1) and (2), d = 6(x-y)/6

d = x-y.

If P-1

S = a/(1+r), where a = 1/2, r = 1/2.

S = 1/2 3/2 = 1/2 x 3/2 = 1/3.

1/3 - 1 = -2/3

This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2.

Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2

y = 10x - x²

dy/dx = 10 -x

As dy/dx = 0,

10 - 2x = 0

2x = 10

x = 5

2 - x > x²

2 - x - x² > 0

(x+2)(x-1) < 0

1/α + 1/β = β+α/αβ

3x² + 5x - 2 = 0

x² + 5x/3 - 2/3 = 0

αβ = -2/3

β+α = -5/3

Thus; β+α/αβ = -2/3 -2/3 = -5/2

Make a good sketch of the question, and follow this steps.

Since ST is parallel to UV => angle USR = 50°(alternate to VUS.

Angle UST = 180° - 50° = 130° (angle on a straight line)