JAMB Mathematics Past Questions & Answers - Page 33

161.

Correct 241.34(3 x 10\(^{-3}\))\(^2\) to 4 significant figures

A.

0.0014

B.

0.001448

C.

0.0022

D.

0.002172

Correct answer is D

first work out the expression and then correct the answer to 4 s.f = 241.34..............(A)

(3 x 10-\(^3\))\(^2\)............(B)

= 3\(^2\)x\(^2\)

= \(\frac{1}{10^3}\) x \(\frac{1}{10^3}\)

(Note that x\(^2\) = \(\frac{1}{x^3}\))

= 24.34 x 3\(^2\) x \(\frac{1}{10^6}\)

= \(\frac{2172.06}{10^6}\)

= 0.00217206

= 0.002172(4 s.f)

162.

Find the derivative of the function y = 2x\(^2\)(2x - 1) at the point x = -1?

A.

18

B.

16

C.

-4

D.

-6

Correct answer is B

y = 2x\(^2\)(2x - 1)
y = 4x\(^3\) - 2x\(^2\)
dy/dx = 12x\(^2\) - 4x
at x = -1
dy/dx = 12(-1)\(^2\) - 4(-1)
= 12 + 4
= 16

163.

The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm\(^3\), then the volume of the other block is?

A.

234.00 cm3

B.

526.50 cm3

C.

166.00 cm3

D.

687cm3

Correct answer is A

Let x represent total vol. 2 : 3 = 2 + 3 = 5

\(\frac{3}{5}\)x = 351

x = \(\frac{351 \times 5}{3}\)

= 585

Volume of smaller block = \(\frac{2}{5}\) x 585

= 234.00cm\(^3\)

164.

Find the value of p if the line which passes through (-1, -p) and (-2,2) is parallel to the line 2y+8x-17=0?

A.

\(\frac{-2}{7}\)

B.

\(\frac{7}{6}\)

C.

\(\frac{-6}{7}\)

D.

2

Correct answer is D

Line:  2y+8x-17=0 

recall y = mx + c

2y = -8x + 17

y = -4x  + \(\frac{17}{2}\)

Slope m\(_1\) = 4

parallel lines: m\(_1\). m\(_2\) = -4

where Slope ( -4) = \(\frac{y_2 - y_1}{x_2 - x_1}\) at points (-1, -p) and (-2,2)

-4( \(x_2 - x_1\) ) = \(y_2 - y_1\) 

-4 ( -2 - -1) = 2 - -p

p = 4 - 2 = 2

165.

A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 91cm\(^2\), find the distance between the parallel sides

A.

13 cm

B.

4 cm

C.

6 cm

D.

7 cm

Correct answer is A

Area of Trapezium = 1/2(sum of parallel sides) * h
91 = \(\frac{1}{2}\) (5 + 9)h

cross multiply
91 = 7h
h = \(\frac{91}{7}\)
h = 13cm