1999 - JAMB Mathematics Past Questions and Answers - page 1

Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7

Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.

\(log_810\) = X = \(log_8{2 x 5}\)

\(log_82\) + \(log_85\) = X
Base 8 can be written as \(2^3\)
\(log_82 = y\)
therefore \(2 = 8^y\)
\(y = \frac{1}{3}\)

\(\frac{1}{3} = log_82\)

taking \(\frac{1}{3}\) to the other side of the original equation

\(log_85 = X-\frac{1}{3}\)

explanation courtesy of Oluteyu and Ifechuks

Start your solution by cross-multiplying, then collect like terms and factorize accordingly to get the unknown.

Hint: apply basic mathematics rules beginning from BODMAS to algebra, and follow solution carefully to arrive at p =(5/2), q = -(25/4) and r = -(9/2).

Then p+2q will give you \(\frac{5}{2}+2\left(\frac{-25}{4}\right)= -10\)

Hint: Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.
Then substitute the values of p and q into p+2q to get -10.

Cost price (cp) = (100/5) x N1.20 =N24.00
Selling price (sp) = 100-20 = 80
(80/4) x N1.50 = N30.00

Gain = SP-CP = N30.00-N24.00 = N6.00
Gain% = (gain/CP) x 100 = 25%

Hint: Two methods can be used;
1. Direct division (if you know division in number bases)
2. Convert both sides to base 10, divide and convert your answer back to base 6. Your answer should be 35₆

The correct answer is 1.
PROVE==> (2x9⁰) (3x9⁰ + Yx9¹) = (3x5⁰)(3x5⁰ + Yx5¹).
You multiply to get 2(3+9Y)=3(3+5Y).
You further multiply to get 6+18Y=9+15Y. ==>
Collect like terms 18Y-15Y=9-6.
3Y/3=3/3.
Y=1
Explanation Credit:

Multiply appropriately to remove decimals on both numerator and denominators. Such that you have \(\sqrt{\frac{(2300x750)}{(345x125)}}
Dividing, => \sqrt400 = 20\).

\(m*n = \frac{m}{n}-\frac{n}{m}
= \frac{-3}{4} - \frac{4}{-3}
= \frac{-3}{4} + \frac{4}{3}
= \frac{(-9+16)}{12}
= \frac{7}{12}\)