2000 - JAMB Mathematics Past Questions and Answers - page 1

P = {1,2,u,v,w,x}

Q = {2,3,u,v,w,5,6,y}

R = {2,3,4,v,x,y}

P - Q = {1,x}

(P - Q) ∩ R = {1,x} ∩ {2,3,4,v,x,y} = {x}

1st year, Population = 240,000 x (2/100) = 4800.

Being the 2nd year population = 240,000 x 4800 = 244800.

Increase in Pop. in 2nd year = 244800 x (2/100) = 4896

Jan 2000, Pop. = 244800 + 4896 = 249,696

Rationalize (\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}) and equate to (m +n\sqrt{6}). Such that m = -2, and n = 1.

Use a venn diagram:

60-3x+3x+50-3x = 94-x.

110-3x+x = 94

-2x = 94-110

=>-2x = -16, this x = -8.

Members that like only one game:

= 60 - 3x + 50 - 3x

= 60 - 3x8 + 50 - 3x8

= 60 - 24 + 50 - 24

= 36 + 26 = 62

Amount A = P(1+r)ⁿ;

A = N150,000, r = 25%, n = 3.

150,000 = P(1+0.25)³ = P(1.25)³

P = 150,000/1.25³ =N76,800.00

314₁₀ - 256₇ = 340_x,

Convert 256₇ and 340_x to base 10, such that:

314 - 139 = 3x² + 4x

=> 3x² + 4x - 175 = 0 (quadratic)

Factorising, (x - 7) (3x + 25) = 0,

either x = 7 or x = -25/3 ( but x cannot be negative)

Therefore, x = 7.

Start by expanding 3(2ⁿ⁺¹) - 4(2^n-1) 2ⁿ⁺¹ - 2ⁿ:

3 x 2ⁿ x 2¹ - 2² x 2ⁿ x 2^-1 2ⁿ x 2 -2ⁿ

Solving the equation above gives;

2ⁿ x 2¹ x 2 2ⁿ = 2 x 2 = 4

Covert everything to base 10 and collect like terms, such that:

210P - 42P = 434 + 406

168P = 840

P = 840/168 = 5

a * b = a^b

a * 2 = a² = 2 - a

a² + 2a - a - 2 = 0

a(a+2) - 1(a+2) = 0

(a-1)(a+2) = 0

a = 1, -2