JAMB Mathematics 1985 Past Questions

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If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of \(\frac{3p - q}{4q + r}\)

A.\(\frac{3}{2}\)
B.\(\frac{2}{3}\)
C.2
D.3
E.18

Arrange the following numbers in ascending order of magnitude \(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650

A.\(\frac{6}{7}\) < 0.865 < \(\frac{13}{15}\)
B.\(\frac{13}{15}\) < \(\frac{6}{7}\) < 0.865
C.\(\frac{6}{7}\) < \(\frac{13}{15}\) < 0.865
D.0.865 < \(\frac{6}{7}\) < \(\frac{13}{15}\)
E.

a sum of money was invested at 8% per annum simple interest. If after 4 years the money amounts to N330.00. Find the amount originally invested

A.N180.00
B.n165.00
C.N150.00
D.N250.00
E.N200.00

In the equation below, Solve for x if all the numbers are in base 2: \(\frac{11}{x}\) = \(\frac{1000}{x + 101}\)

A.101
B.11
C.110
D.111
E.10

List all integers satisfying the inequality -1 \(\leq\) 2 x -6 < 4

A.2, 3, 4, 5
B.2, 3, 4
C.2, 5
D.3, 4, 5
E.4, 5

Find correct to two decimals places 100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)

A.100.02
B.1000.02
C.100.22
D.100.01
E.100.51

John gives one-third of his money to Janet who has N105.00. He then finds that his money is reduced to one-fourth of what Janet now has. Find how much money john has at first

A.N45.00
B.N48.00
C.N52.00
D.N60.00
E.N52.00

Find x if log₉x = 1.5

A.72.0
B.27.0
C.36.0
D.3.5
E.24.5

Write h in terms of a, b, c, d if a = \(\frac{b(1 - ch)}{a - dh}\)

A.h = \(\frac{a - b}{ad}\)
B.h = \(\frac{1 - b}{ad - bc}\)
C.h = \(\frac{(a - b)^2}{ad - bc}\)
D.h = \(\frac{a - b}{ad - bc}\)
E.h = \(\frac{b - a}{ab - dc}\)

22\(\frac{1}{2}\)% of the Nigerian Naira is equal to 17\(\frac{1}{10}\)% of a foreign currency M. What is the conversion rate of the M to the Naira?

A.1M = 1\(\frac{15}{57}\)N
B.1M = 38\(\frac{1}{4}\)N
C.1M = 1\(\frac{18}{57}\)N
D.1M = 384\(\frac{3}{4}\)N
E.

Find the values of p for which the equation x² - (p - 2)x + 2p + 1 = 0

A.(21, 0)
B.(0, 12)
C.(1, 2)
D.(3, 4)
E.(4, 5)

If e^x = 1 + \(\frac{x}{2}\) + \(\frac{x^2}{1.2}\) + \(\frac{x^3}{1.2.3}\) + .....Find \(\frac{1}{e^x}\)

A.1 - \(\frac{x}{2}\) + \(\frac{x^2}{1.2^3}\) + \(\frac{x^3}{2^4.3}\) + .........
B.1 - \(\frac{x}{2}\) + \(\frac{x^2}{1.2^3}\) + \(\frac{x^4}{2.4.3}\) + ..
C.1 + \(\frac{x}{2}\) + \(\frac{x^2}{1.2}\) + \(\frac{x^3}{1.2.3}\) + \(\frac{x^4}{1.23.4}\) + .........
D.1 - x + \(\frac{x^2}{1.2^3}\) + \(\frac{x^3}{2^4.3}\) + .........
E.1 + \(\frac{x}{2}\) + \(\frac{x^2}{1.2^3}\) + \(\frac{x^4}{1.2.6}\) + .........

(\(\sqrt{2} + 4\sqrt{2}\)) (\(\sqrt{3} + \sqrt{2}\)) (\(\sqrt{3} + \sqrt{2}\)) is equal to

A.1
B.(\(\sqrt{2} + 4\sqrt{2}\))
C.(6\(\sqrt{2}\)
D.8
E.

In a restaurant, the cost of providing a particular type of food is partly constant and partially inversely proportional to the number of people. If cost per head for 100 people is 30k and the cost for 40 people is 60k, Find the cost for 50 people?

A.15k
B.20k
C.50k
D.40k
E.45k

The factors of 9 - (x² - 3x - 1)² are

A.-(x - 4)(x + 1) (x - 1)(x - 2)
B.(x - 4)(x - 2) (x - 1)(x + 1)
C.-(x - 2)(x + 1) (x - 2) (x - 1)
D.(x - 2)(x + 2) (x - 1)(x + 1)
E.

If 3^2y + 6(3^y) = 27. Find y

A.3
B.-1
C.2
D.-3
E.1

Factorize abx² + 8y - 4bx - 2axy

A.(ax - 4)(bx - 2y)
B.(ax + b)(x - 8y)
C.(ax - 2y)(bx - 4)
D.(bx - 4)(ax - 2y)
E.(abx - 4)(x - 2y)

At what real value of x do the curves whose equations are y = x³ + x and y = x² + 1 intersect?

A.-2
B.2
C.-1
D.9
E.1

If the quadratic function 3x² - 7x + R is a perfect square, find R

A.\(\frac{49}{24}\)
B.\(\frac{49}{12}\)
C.\(\frac{49}{13}\)
D.\(\frac{49}{3}\)
E.\(\frac{49}{36}\)

Solve for (x, y) in the equation 2x + y = 4: x^2 + xy = -12

A.(6, -8): (-2, 8)
B.(3, -4): (-1, 4)
C.(8, -4): (-1, 4)
D.(-8, 6): (8, -2)
E.(-4, 3): (4, -1)

Solve the following equation \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\)

A.(\(\frac{5}{2}\), 1)
B.(5, -4)
C.(2, 1)
D.(1, \(\frac{-5}{2}\))
E.(\(\frac{-5}{2}\), 1)

Solve the simultaneous equations 2x - 3y + 10 = 10x - 6y = 5

A.x = 2\(\frac{1}{2}\), y = 3\(\frac{1}{2}\)
B.x = \(\frac{1}{2}\), y = \(\frac{3}{2}\)
C.x = 2\(\frac{1}{4}\), y = 3\(\frac{1}{2}\)
D.x = 2\(\frac{1}{3}\), y = 3\(\frac{1}{2}\)
E.x = 2\(\frac{1}{3}\), y = 2\(\frac{1}{2}\)

If f(x - 2) = 4x² + x + 7, find f(1)

A.12
B.27
C.7
D.46
E.17

In \(\bigtriangleup\) XYZ, XY = 13cm, YZ = 9cm, XZ = 11cm and XYZ = \(\theta\). Find cos\(\theta\)^o

A.\(\frac{4}{39}\)
B.\(\frac{43}{39}\)
C.\(\frac{209}{3}\)
D.\(\frac{43}{78}\)
E.

Find the missing value in the table below
\(\begin{array}{c|c} x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y = 4 - 3x - x^3 & 80 & & 18 & 8 & 4 & 0 & -10 & -32 \end{array}\)

A.-32
B.-14
C.40
D.22
E.37

The number of goals scored by a football team in 20 matches is shown below
\(\begin{array}{c|c} \text{No. of goals} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{No. of matches} & 3 & 5 & 7 & 3 & 1 & 0 \end{array}\)
What are the values of the mean and the mode respectively?

A.(1.75, 5)
B.(1.75, 2)
C.(1.75, 1)
D.(65, 74)
E.

If the hypotenuse of right angled isosceles triangle is 2, what is the length of each of the other sides?

A.\(\sqrt{2}\)
B.\(\frac{1}{2}\)
C.22
D.1
E.2 - 1

If two fair coins are tossed, what is the probability of getting at least one head?

A.\(\frac{1}{4}\)
B.\(\frac{1}{2}\)
C.1
D.\(\frac{43}{78}\)
E.\(\frac{3}{4}\)

The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm³, then the volume of the other block is

A.234.00 cm³
B.526.50 cm³
C.166.00 cm³
D.687cm³
E.

The bearing of a bird on a tree from a hunter on the ground is N72^oE. What is the bearing of the hunter from the birds?

A.S 18^o W
B.S 72^o W
C.S 72^o E
D.S 27^o E
E.S 27^o W

Without using table, calculate the value of 1 + sec² 30^o

A.2\(\frac{1}{3}\)
B.\(\frac{2}{15}\)
C.\(\frac{5}{3}\)
D.3\(\frac{1}{2}\)
E.

What is the probability that a number chosen at random from the intergers between 1 and 10 inclusive is either a prime or a multiple of 3?

A.\(\frac{7}{10}\)
B.\(\frac{3}{5}\)
C.\(\frac{4}{5}\)
D.\(\frac{3}{10}\)
E.

Find the area of a regular hexagon inscribed in a circle of radius 8cm

A.16\(\sqrt{3}\) cm³
B.96\(\sqrt{3}\) cm³
C.192\(\sqrt{3}\) cm³
D.16\(\sqrt{3}\) cm²
E.33cm²

If cos \(\theta\) = \(\frac{\sqrt{3}}{2}\) and \(\theta\) is less than 90^o. Calculate cos\(\frac{90 - \theta}{sin^2\theta}\)

A.\(\frac{4}{\sqrt{3}}\)
B.\(\sqrt{\frac{3}{2}}\)
C.\(\sqrt{\frac{76}{2}}\)
D.4\(\sqrt{\frac{76}{2}}\)
E.

A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?

A.5kg
B.16kg
C.19kg
D.6kg
E.

PRSQ is a trapezium of area 14cm² in which PQ||RS. If PQ = 4cm and SR = 3cm, Find the area of SQR in cm²

A.7.0
B.6.0
C.5.2
D.5.0
E.

A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?

A.\(\frac{2}{3}\)
B.\(\frac{2}{15}\)
C.\(\frac{1}{2}\)
D.\(\frac{1}{3}\)
E.

Two points X and Y both on latitude 60^oS have longitude147^oE and 153^oW respectively. Find to the nearest kilometer the distance between X and Y measured along the parallel of latitude(Take 2\(\pi\)R = 4 x 10⁴km, where R is the radius of the earth)

A.16667km
B.28850km
C.8333km
D.2233km
E.

In a class of 120 students, 18 of them scored an A grade in mathematics. If the section representing the A grade students on a pie chart has angle Z^o at the centre of the circle, what is Z?

A.15
B.27
C.50
D.52
E.54

If a{\(\frac{x + 1}{x - 2} - \frac{x - 1}{x + 2}\)} = 6x. Find a in its simplest form

A.x² - 1
B.x² + 1
C.x² + 4
D.x² - 4
E.1

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In \(\bigtriangleup\) XYZ, XKZ = 90^O, XK = 15cm, XY = 35cm and YK = 8cm. Find the area of \(\bigtriangleup\)XYZ

A.190 sq.cm
B.20 sq.cm
C.210 sq.cm
D.160sq.cm
E.320sq.cm

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In the figure, MNQP is a cyclic quadrilateral. MN and Pq are produced to meet at X and NQ and MP are produced to meet at Y. If MNQ = 86^o and NQP = 122^o find (x^o, y^o)

A.28^o, 36^o
B.36^o, 28^o
C.43^o, 61^o
D.61^o, 43^o
E.36^o, 43^o

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In the figure POQ is the diameter of the circle PQR. If PSR = 145^o, find x^o

A.25^o
B.35^o
C.45^o
D.125^o
E.

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In the figure, GHIJKLMN is a cube of side a. Find the length of HN.

A.\(\sqrt{3a}\)
B.3a
C.3a²
D.a\(\sqrt{2}\)
E.a\(\sqrt{3}\)

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In the figure, PQ is the tangent from P to the circle QRS with SR as its diameter. If QRS = \(\theta\)^oand RQP = \(\phi\)^o, which of the following relationships between \(\theta\)^o and \(\phi\)^o is correct

A.\(\theta\)^o + \(\phi\)^o = 90²
B.\(\phi\)^o = 90² - 2\(\theta\)^o
C.\(\theta\)^o = \(\phi\)^o
D.\(\phi\)^o = 2\(\theta\)^o
E.\(\theta\)^o + 2\(\phi\)^o

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In the figure, the area of the shaded segment is

A.3\(\pi\)
B.9\(\frac{\sqrt{3}}{4}\)
C.3 \(\pi - 3 \frac{\sqrt{3}}{4}\)
D.\(\frac{(\sqrt{3 - \pi)}}{4}\)
E.\(\pi + \frac{9 \sqrt{3}}{4}\)

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In the figure, find angle x

A.100^o
B.120^o
C.60^o
D.110^o
E.140^o