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Mathematics Past Questions

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45 questions JAMB 2359 WAEC 1853 NECO 179 POST_UTME 6 CUSTOM 10

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45 questions

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Question 11

jamb 1984

A cone is formed by bending a sector of a circle having an angle of 210^o. Find the radius of the base of the cone if the diameter of the circle is 12cm.

A12cm

B7.00cm

C1.75cm

D21cm

E3.50cm

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Question 12

jamb 1984

If (x - 2) and (x + 1) are factors of the expression x³ + px² + qx + 1, what is the sum of p and q

B-3

D\(\frac{17}{3}\)

E\(\frac{2}{3}\)

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Question 13

jamb 1984

Find a factor which is common to all three binomial expressions 4a2 - 9b2, 8a3 + 27b3, (4a + 6b)2

A4a + 6b

B4a - 6b

C2a + 3b

D2a - 3b

Enone

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Question 14

jamb 1984

The quadratic equation whose roots are 1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\) is?

Ax² + (1 - \(\sqrt{13}\)x + 1 + \(\sqrt{13}\) = 0

Bx² - 2x - 12 = 0

Cx² - 2x + 12 = 0

Dx² + 12 + 2x² = 0

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Question 15

jamb 1984

If f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4 and g(y) = \(\sqrt{5 + y}\), find g [f(3)] and f[g(4)].

A3 and 4

B-3 and 4

C-3 and -4

D3 and -4

E0 and 5

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Question 16

jamb 1984

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

Ax² - 5x - 10 = 0

Bx² - 20x + 360 = 0

Cx² - 21x - 270 = 0

D3x² - 65x + 362 = 0

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Question 17

jamb 1984

If 2x + 3y = 1 and x - 2y = 11, find (x + y)

B-3

E-2

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Question 18

jamb 1984

In a racing competition, Musa covered a distance 5x km in the first hour and (x + 10)km in the next hour. He was second to Nzozi who covered a total distance of 118km in the two hours. Which of the following inequalities is correct?

A-1 < x < x < 0

B-3 < x < 3

C0 \(\leq\) x < 18

D15 < x < 18

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Question 19

jamb 1984

The table below is drawn for a graph y = x³ - 3x + 1
\(\begin{array}{c|c} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline y = x^3 - 3x + 1 & 1 & -1 & 3 & 1 & -1 & 3 & 1\end{array}\)
From x = -2 to x = 1, the graph crosses the x-axis in the range(s)

A-1 < x < 0 and 0 < x < 1

B-2 < x < -1 and 0 < x < 1

C-2 < x < -1 and -1 < x < 0

D0 < x < 1

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Question 20

jamb 1984

A straight line y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other

A(5, 6)

B(8, 8)

C(8, 5)

D(7,7)

E(7, 5)

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Question 21

jamb 1984

Factorize 6x2 - 14x - 12

A2(x + 3)(3x - 2)

B6(x - 2)(x + 1)

C2(x - 3)(3x + 2)

D6(x + 2)(x - 1)

E(3x - 4)(2x + 3)

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Question 22

jamb 1984

p varies directly as the square of q and inversely as r. If p = 36, when q = 3, when r = 4, find p when q = 5 and r = 2.

A72

B100

C90

D200

E125

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Question 23

jamb 1984

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

C\(\frac{1}{27}\)

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

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Question 24

jamb 1984

Rationalize \(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\)

A-2 \(\sqrt{35}\)

B4\(\sqrt{7}\) - 6\(\sqrt{5}\)

C-\(\sqrt{35}\)

D4\(\sqrt{7}\) - 8\(\sqrt{5}\)

E\(\sqrt{35}\)

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Question 25

jamb 1984

A trader in country where their currency 'MONI'(M) is in base five bought 103₅ oranges at M14₅ each. If he sold the oranges at M24₅ each, what will be his gain?

A103₅

B1030₅

C102₅

D2002₅

E3032₅

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Question 26

jamb 1984

A variable point p(x, y) traces a graph in a two-dimensional plane. (0, 3) is one position of P. If x increases by 1 unit, y increases by 4 units. The equation of the graph is

A-3 = \(\frac{y + 4}{x + 1}\)

B4y = -3 + x

C\(\frac{y}{x}\) = \(\frac{-3}{4}\)

D4x = y + 3

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Question 27

jamb 1984

Find, without using logarithm tables, the value of \(\frac{log_3 27 - log_{\frac{1}{4}} 64}{log_3 \frac{1}{81}}\)

A\(\frac{-3}{9}\)

B\(\frac{-3}{2}\)

C\(\frac{6}{11}\)

D\(\frac{43}{78}\)

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Question 28

jamb 1984

Bola choose at random a number between 1 and 300. What is the probability that the number is divisible by 4?

A\(\frac{1}{4}\)

B\(\frac{4}{4}\)

C\(\frac{6}{4}\)

D\(\frac{7}{4}\)

E\(\frac{37}{149}\)

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Question 29

jamb 1984

The cost of production of an article is made up as follows: Labour N70, Power N15, Materials N30, Miscellaneous N5. Find the angle of the sector representing Labour in a pie chart

A210^o

B105^o

C105^o

D175^o

E90^o

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Question 30

jamb 1984

Thirty boys and x girls sat for a test. The mean of the boys' scores and that of the girls were respectively 6 and 8. Find x if the total scores was 468

A38

B24

C36

D22

E41

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