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Further Mathematics Past Questions

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799 questions JAMB 2 WAEC 795 CUSTOM 2

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Question 181

waec 2017

A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \(-3 \Delta -1\).

A\(-4\sqrt{3}\)

B\(\frac{-4\sqrt{3}}{3}\)

C\(\frac{-3\sqrt{3}}{4}\)

D\(\frac{-3\sqrt{3}}{4}\)

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Question 182

waec 2017

If \(log_{y}\frac{1}{8}\) = 3, find the value of y.

A-2

B-\(\frac{1}{2}\)

C\(\frac{1}{2}\)

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Question 183

waec 2016

A ball falls from a height of 18m above the ground. Find the speed with which the ball hits the ground. \([g = 10ms^{-2}]\)

A9\(ms^{-1}\)

B9.49\(ms^{-1}\)

C13.42\(ms^{-1}\)

D18.97\(ms^{-1}\)

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Question 184

waec 2016

A man of mass 80kg stands in a lift. If the lift moves upwards with acceleration 0.5\(ms^{-2}\), calculate the reaction from the floor of the lift on the man. \([g = 10ms^{-2}]\)

A760N

B800N

C805N

D840N

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Question 185

waec 2016

A force 10N acts in the direction 060° and another force 6N acts in the direction 330°. Find the y component of their resultant force.

A\((3 + 3\sqrt{3})N\)

B\((-3 + 5\sqrt{3})N\)

C\((5 + 3\sqrt{3})N\)

D\((5 + 5\sqrt{3})N\)

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Question 186

waec 2016

A body of mass 10kg moving with a velocity of 5\(ms^{-1}\) collides with another body of mass 15kg moving in the same direction as the first with a velocity of 2\(ms^{-1}\). After collision, the two bodies move together with a common velocity v\(ms^{-1}\).

A3.2

B5.3

C7.0

D8.0

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Question 187

waec 2016

Find the unit vector in the direction of \(-2i + 5j\).

A\(\frac{1}{\sqrt{29}}(2i + 5j)\)

B\(\frac{1}{\sqrt{29}}(-2i + 5j)\)

C\(\frac{1}{29}(2i - 5j)\)

D\(\frac{1}{29}(-2i - 5j)\)

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Question 188

waec 2016

Given that \(r = 3i + 4j\) and \(t = -5i + 12j\), find the acute angle between them.

A14.3°

B55.9°

C59.5°

D75.6°

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Question 189

waec 2016

A box contains 14 white balls and 6 black balls. Find the probability of first drawing a black ball and then a white ball without replacement.

A0.21

B0.22

C0.30

D0.70

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Question 190

waec 2016

A fair coin is tossed 3 times. Find the probability of obtaining exactly 2 heads.

A\(\frac{1}{8}\)

B\(\frac{3}{8}\)

C\(\frac{5}{8}\)

D\(\frac{7}{8}\)

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Question 191

waec 2016

Find the variance of 11, 12, 13, 14 and 15.

C\(\sqrt{2}\)

D13

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Question 192

waec 2016

Given that \(n = 10\) and \(\sum d^{2} = 20\), calculate the Spearman's rank correlation coefficient.

A0.121

B0.733

C0.879

D0.979

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Question 193

waec 2016

Find an expression for y given that \(\frac{\mathrm d y}{\mathrm d x} = x^{2}\sqrt{x}\)

A\(\frac{1x^{\frac{2}{7}}}{7} + c\)

B\(\frac{2x^{\frac{3}{2}}}{7} + c\)

C\(\frac{2x^{\frac{7}{2}}}{7} + c\)

D\(\frac{1x^{\frac{7}{2}}}{7} + c\)

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Question 194

waec 2016

The radius of a circle increases at a rate of 0.5\(cms^{-1}\). Find the rate of change in the area of the circle with radius 7cm. \([\pi = \frac{22}{7}]\)

A11\(cm^{2}s^{-1}\)

B22\(cm^{2}s^{-1}\)

C33\(cm^{2}s^{-1}\)

D44\(cm^{2}s^{-1}\)

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Question 195

waec 2016

Find the minimum value of \(y = 3x^{2} - x - 6\).

A\(-6\frac{1}{6}\)

B\(-6\frac{1}{12}\)

C\(-6\)

D\(0\)

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Question 196

waec 2016

Find the gradient to the normal of the curve \(y = x^{3} - x^{2}\) at the point where x = 2.

A\(\frac{-1}{8}\)

B\(\frac{1}{8}\)

C\(\frac{-1}{24}\)

D\(1\)

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Question 197

waec 2016

Find \(\lim\limits_{x \to 3} \frac{2x^{2} + x - 21}{x - 3}\).

D13

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Question 198

waec 2016

The lines \(2y + 3x - 16 = 0\) and \(7y - 2x - 6 = 0\) intersect at point P. Find the coordinates of P.

A(4, 2)

B(4, -2)

C(-4, 2)

D(-4, -2)

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Question 199

waec 2016

Points E(-2, -1) and F(3, 2) are the ends of the diameter of a circle. Find the equation of the circle.

A\(x^{2} + y^{2} - 5x + 3 = 0\)

B\(x^{2} + y^{2} - 2x - 6y - 13 = 0\)

C\(x^{2} + y^{2} - x + 5y - 6 = 0\)

D\(x^{2} + y^{2} - x - y - 8 = 0\)

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Question 200

waec 2016

Find the equation of the line which passes through (-4, 3) and parallel to line y = 2x + 5.

Ay = 2x + 11

By = 3x - 5

Cy = 2x - 11

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