2008 - JAMB Mathematics Past Questions and Answers - page 4

(y=\frac{x^7 - x^5}{x^4}\

y = \frac{x^7}{x^4} \div \frac{x^5}{x^4}\

y = x^3 - x \

\frac{dy}{dx} = 3x^2 - 1)

sin x - x cos x

dy/dx = cos x - [1.cos x + x -sin x]

= co x - [cos x - x sin x]

= cos x - cos x + x sin x

= x sin x

y = x(1+x)

= x + x²

dy/dx = 1 + 2x

As dy/dy → 0

1 + 2x = 0

2x = -1

X = -¹/₂

Y = x(1+x)

= -¹/₂(1 - ¹/₂) at x = -¹/₂

= -¹/₂(¹/₂)

= -¹/₄

(\int_1 ^2(6x^2-2x)dx=[\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\

= [2x^3 - x^2]_1^2)

= [2(2)³ - (2)²] – [2(1)³ - (1)²]

= [16-4] – [2-1]

= 12 – 1

= 11

(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\

=sin\frac{\pi}{2} - sin\frac{-\pi}{2})

= sin90 – sin-90

= sin90 – sin270

= 1 – (-1)

= 1+1

= 2

30 + 45 + 60 + 90 + 2x + x = 360^o

225 + 3x = 360

3x = 360 - 225

3x = 135

x = 45^o

Ratio of least to most = 3:12

= ³/₁₂

= ¹/₄

(Mean = \frac{t+2t-1+t-2+2t-14t+2t+2}{6}\

Mean = \frac{12t-2}{6}\

=\frac{2(6t-1)}{6}\

=\frac{6t-1}{3}\

=\frac{6t}{3}- \frac{1}{3}\

=2t-\frac{1}{3})

4, 4, 1, 0, 4, 4, 2, 0

Arrange in ascending order:

0, 0, 1, 1, 2, 4, 4, 4, 4

Position of median = N+1 / 2 = 9+1 / 2 = 5th

Median = 2

x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1

Range = 3x+2 - (x-3)

= 3x+2 - x - 3

= 2x + 5