2020 - JAMB Mathematics Past Questions and Answers - page 3

(x - x)\(^2\) = 28

S.D = \(\frac{\sqrt\sum (x - x)^2}{N} = \frac{\sum d^2}{N} = \frac{\sqrt{28}}{7}\) 

= \(\sqrt{4}\) 

= 2

Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.
Prime numbers in the possible outcomes:  23, 29. 

The probability of choosing a prime number = \(\frac{\text{Number of Prime}}{\text{No. of Total Possible Outcome}}\)

= \(\frac{2}{11}\)

***

Gradient of line = \(\frac{\text{Change in y}}{\text{Change in x}}\) = \(\frac{y_2 - Y}{x_2 - x}\) 

y\(_2\)  = 0\(_1\) 

Y\(_1\)  = 4 

x\(_2\)  = 3 and x\(_1\)  = 0

\(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{3 - 0} = \frac{-4}{3}\)

The general equation of a straight line is y = m x + c , where is the gradient and the coordinates of the y-intercept.

At x = 0, y = c. y-intercept = 4 

y = 4x + \(\frac{4}{3}\) multiply through y 

3y = 4x + 23 

0.0014 x 0.011 = 0.0000154 = 1.54 x 10\(^{-5}\)

h = 30 tan 60 

= 30\(\sqrt{3}\) 

I = \(\frac{PRT}{100}\) = 1 = 1240 - 1000 = 240

R = \(\frac{240 \times 100}{100 \times 3}\)

= 8% 

The total angle in a pie chart = 360\(^o\).

Hence,

360\(^o\) - (60\(^o\) + 60\(^o\) + 67 + 50 = 237\(^o\)) 

360\(^o\) - 237 = 130\(^o\) 

Salary = \(\frac{123}{360} X \frac{N6000}{1}\) 

= N2,050

\(\frac{1}{3x}\) + \(\frac{1}{2}\)x

=> \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) 

= 4(2 + 3x) > 6x = 12x\(^2\) - 2x = 0

= 2x(6x - 1) > 0 = x(6x - 1) > 0

(-, -) = x < 0, 6x - 1 > 0.  - - - - -  - - 1

= x < 0, x < \(\frac{1}{6}\) (solution) 

(+, +) = x > 0, 6x - 1 > 0 = x > 0 - - - - -- - - - 2

x > \(\frac{1}{6}\)

Combining (1) and (2):

= x > 0, x < \(\frac{1}{6}\)

= 0 < x < \(\frac{1}{6}\) 

\(\frac{\sqrt{2}}{x + 2}\) = x - \(\frac{1}{\sqrt{2}}\)

x\(\sqrt{2}\) (x - \(\sqrt{2}\)) = x + \(\sqrt{2}\)

x\(\sqrt{2}\) - 2 = x + \(\sqrt{2}\) 

= x\(\sqrt{2}\) - x 

= 2 + \(\sqrt{2}\)

x (\(\sqrt{2}\) - 1) = 2 + \(\sqrt{2}\)

= \(\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\)

x = \(\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}\) 

= 3\(\sqrt{2}\) + 4 

a = b = a\(^2\) 

a + 2 = a\(^2\) - - - - - - - 1

a + 2 = 2 - a - - - - - - - - 2

Combining 1 & 2:

a\(^2\) = 2 - a 

a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0

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

a = 1 or - 2