2020 - JAMB Mathematics Past Questions and Answers - page 2

Given that:

log\(_{10}\)2 = 0.3010

log\(_{10}\)3 = 04771

Then,

log\(_{10} 4.5 = log_{10}\) (\(\frac{3 \times 3}{2}\))

log\(_{10}\) 3 + log\(_{10}\) 3 - log\(_{10}\)2 = 0.4471 + 0.771 - 0.3010

= 0.6532 Ans.

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234 - 4x\(^2\) = 18\(^2\) - (2x)\(^2\) = (18 - 2x)(18 + 2x)

2x + 18 = 2x + 18 = (2x + 18)

18 - 2x = 2(a - x) 

= -2(x - a) 

Rice = 75g
Margarine = 40g
Meat = 105g
Bread = 20g

Total = 240

The angle of sector represented by meat:

= \(\frac{105}{240} \times \frac{360^o}{1}\) 

= 157.5 

Lenght of arc AB = \(\frac{Q}{360}\) 2\(\pi\)r

= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x 10.5

= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)

= \(\frac{4 \times 22 \times 3}{30} \times \frac{88}{10}\) = 8.8cm 

The perimeter = 8.8 + 2r = 8.8 + 2r 

= 8.8 + 2(10.5)

= 8.8 + 21

= 29.8cm

\(\frac{27}{5} \times 3^{-3} \times \frac{1^{-1}}{5}\)

= \(\frac{27}{5} \times \frac{1}{3^3} \times \frac{1}{\frac{1}{5}}\)

\(\frac{27}{5}\) x \(\frac{1}{27}\) x \(\frac{5}{1}\) = 1

Coca-Cola = 10
Fanta = 8
Spirite = 6
Total = 24

P(Coca-Cola) = \(\frac{10}{24}\); P(not Coca-Cola) 

1 - \(\frac{10}{24}\) 

\(\frac{24 - 10}{24} = \frac{14}{24} = \frac{7}{12}\) 

PQRS is quadrilateral. Hence,

2y + 2x + QPS = 360\(^o\)

i.e. (y + x) + QPS = 360\(^o\) 

QPS = 360\(^o\) - 2 (y + x)

But x + y + 68\(^o\) = 180\(^o\)

Therefor,

x + y = 180\(^o\) - 68\(^o\) = 112\(^o\)

QPS = 360 - 2(112\(^o\))

= 360\(^o\) - 224

= 136\(^o\)

Given (-2, 0) and (0, -4),

The gradient is of a line is the difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates):

= \(\frac{-4 - 0}{0 - (-2)}\)

= \(\frac{-4}{2}\) 

= -2

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.

Equation through (5,7) parallel to the line 7x + 5y = 12

5y = 7x + 12 

y = \(\frac{-7x}{5} + \frac{12}{5}\)

Gradient = \(\frac{-7}{5}\) 

Required equation = \(\frac{y - 7}{x - 5} = \frac{-7}{5}\)

5y - 35 = -7x + 35

5y + 7x = 70

Principal = N225.00
Interest = N27.00
Year = x
Rate = 4% 

1 = \(\frac{PRT}{100}\)

27 = \(\frac{225 \times 4 \times x}{100}\) = 2700 = 900T

T = \(\frac{2700}{900}\) 

= 3 years