1994 - JAMB Mathematics Past Questions and Answers - page 4

Sin(-690^o) = Sin(-360 -3300

sin - 360 = sin 0

∴ sin(-690^o) = sin(330^o)

Negative angles are measured in clockwise direction

The acute angle equivalent of sin(-330^o) = sin(30^o)

sin(-330^o) = sin(30^o)

= (\frac{1}{2})

= 0.5

y = 3t³ + 2t² - 7t + 3

(\frac{dy}{dt}) = 9t² + 4t - 7

When t = -1

(\frac{dy}{dt}) = 9(-1)² + 4(-1) - 7

= 9 - 4 -7

= 9 - 11

= -2

Equation of curve;

y = 2x² - 2x + 3

gradient of curve;

(\frac{dy}{dx}) = differential coefficient

(\frac{dy}{dx}) = 4x - 2, for gradient to be 2

∴ (\frac{dy}{dx}) = 2

4x - 2 = 2

4x = 4

∴ x = 1

When x = 1, y = 2(1)² - 2(1) + 3

= 2 - 2 + 3

= 5 - 2

= 3

coordinate of the point where the curve; y = 2x² - 2x + 3 has gradient equal to 2 is (1, 3)

(\int^{1}_{-1})(2x + 1)²dx

= (\int^{1}_{-1})(4x² + 4x + 1)dx

= (\int^{1}_{-1})[(\frac{4x^3}{3}) + 2x² + c]

= [(\frac{4}{3}) + 3 + c] - [4 + (\frac{1}{3}) + c]

= (\frac{8}{3}) + 3 + -1 - C

= (\frac{8}{3}) + 2

= (\frac{14}{3})

= (\frac{42}{3})

x = (\frac{\sum x}{N})

= (\frac{18}{3})

= 6

(\begin{array}{c|c} x & x - x & x - x \ \hline 4 & -2 & 2\ 5 & 1 & 1\ 9 & 3 & 3\ \hline & & 6\end{array})

M.D = (\frac{|x - x|}{N})

= (\frac{6}{3})

= 2

Median = L + [(\frac{\frac{N}{2} - f}{fm})]h

N = Sum of frequencies

L = lower class boundary of median class

f = sum of all frequencies below L

fm = frequency of modal class and

h = class width of median class

Median = 11 + [(\frac{\frac{50}{2} - 21}{20})]5

= 11 + ((\frac{25 - 21}{20}))5

= 11 + ((\frac{(4)}{20}))

11 + 1 = 12

(\begin{array}{c|c} x & f & fx & \bar{x} - x & (\bar{x} - x)^2 & f(\bar{x} - x)^2 \ \hline 1 & 2 & 2 & -2 & 4 & 8\ 2 & 1 & 2 & -1 & 1 & 1\ 3 & 2 & 6 & 0 & 0 & 0\ 4 & 1 & 4 & 1 & 1 & 1\ 2 & 2 & 10 & 2 & 4 & 8\ \hline & 8 & 24 & & & 18 \end{array})

x = (\frac{\sum fx}{\sum f})

= (\frac{24}{8})

= 3

Variance (6²) = (\frac{\sum f(\bar{x} - x)^2}{\sum f})

= (\frac{18}{8})

= (\frac{9}{4})

40 = 20 - x + x + 35 - x

40 = 55 - x

x = 55 - 40

= 15

∴ P(both) (\frac{15}{40})

= (\frac{3}{8})

y = x³ - 27, y = -27 (\to) (0, -27)

when y = 0, x = 3 (3, 0)