JAMB Mathematics 1980 past questions and answers

Find correct to three significant figures, the value of √(41830)

1. A.205
2. B.647
3. C.2050
4. D.6470
5. E.64.7

Evaluate (2⁰ + 4^-½)²

1. A.¹/₄
2. B.⁵/₄
3. C.⁹/₄
4. D.4
5. E.9

Which of the following is NOT a factor of 12⁴ − 5⁴?

1. A.7
2. B.13
3. C.17
4. D.49
5. E.169.

Rationalize the denominator of the given expression (√(1 + a) − √a)/(√(1 + a) + √a)

1. A.1 + 2a − 2√(a(1 + a))
2. B.√(a(1 + a))
3. C.2a − 2√(a(1 + a))
4. D.1 − 2a − 2√(a(1 + a))
5. E.2a − 2√(a(1 + a)) − 1.

When a dealer sells a bicycle for ₦81 he makes a profit of 8%. What did he pay for the bicycle?

1. A.₦73
2. B.₦74.52
3. C.₦75
4. D.₦75.52
5. E.₦87.48.

The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is

1. A.13
2. B.7
3. C.¹⁹/₂
4. D.10
5. E.³⁹/₄

List all integer values of x satisfying the inequality −1 < 2x − 5 ≤ 5

1. A.2, 3, 4, 5
2. B.2, 5
3. C.3, 4, 5
4. D.2, 3, 4
5. E.3.1.

Find the roots of the equation 10x² − 13x − 3 = 0

1. A.x = ³/₅ or −¹/₃
2. B.x = ³/₁₀ or −1
3. C.x = −³/₁₀ or 1
4. D.x = ¹/₅ or −³/₂
5. E.x = −¹/₅ or ³/₂

A solid cylinder of radius 3cm has a total surface area of 36πcm². Find its height

1. A.2cm
2. B.3cm
3. C.4cm
4. D.5cm
5. E.6cm.

If PN is perpendicular to QR, find the value of tan x

1. A.⁵/₉
2. B.³/₅
3. C.³/₄
4. D.⁴/₃
5. E.⁵/₃.

In the figure below, PQ∥SR, ST∥RQ, PS = 7cm, PT = 7cm, SR = 4cm. Find the ratio of the area of QRST to the area of PQRS.

1. A.56:77
2. B.56:105
3. C.28:105
4. D.28:49
5. E.56:49

In the figure below, if PT is parallel to RS, PQ = PT and angle SQT = 90°, find x

1. A.35°
2. B.50°
3. C.55°
4. D.70°
5. E.80°.

Write down the number 0.0052048 correct to three significant figures.

1. A.0.005
2. B.0.0052
3. C.0.00520
4. D.5.2048
5. E.5204.

In the figure below PS bisects angle QPR. Find the ratio SR:QR

1. A.1:2
2. B.1:3
3. C.1:4
4. D.1:5
5. E.1:6

The ratio of the areas of similar triangles is necessarily equal to

1. A.the ratio of the corresponding sides
2. B.the ratio of the squares on corresponding sides
3. C.the ratio of the corresponding heights of the triangles
4. D.half the ratio of the corresponding heights of the triangles
5. E.the ratio of the corresponding bases to the heights of the triangles.

P and Q are fixed points and X is a variable point which moves so that angle PXQ = 45°. What is the locus of X?

1. A.A pair of straight lines parallel to PQ
2. B.The perpendicular bisector of PQ
3. C.An arc of a circle passing through P and Q
4. D.A circle with diameter PQ.
5. E.The bisector of angle PXQ.

A man and wife went to buy an article costing ₦400. The woman had 10% of the cost and the man 40% of the remainder. How much did they have altogether?

1. A.₦216
2. B.₦200
3. C.₦184
4. D.₦144.
5. E.₦100.

Simplify log₁₀8/log₁₀4

1. A.log₁₀2
2. B.log₁₀4
3. C.³/₂
4. D.2
5. E.None of the above.

Make c the subject of the formula v = 1 − (a/5)(b + ³/₇c)

1. A.c = −[7b/3 + (5/a)(v − 1)]
2. B.c = −(7/3)[b + (5/a)(v − 1)]
3. C.c = (7/3)[b + (5/a)(v − 1)]
4. D.c = −(7/3)[b + (5v − 1)/a]
5. E.c = (7/3)[b − (5/a)(v − 1)]

What factor is common to all the expressions x² − x, 2x² + x − 1 and x² − 1?

1. A.x
2. B.x − 1
3. C.x + 1
4. D.No common factor
5. E.(2x − 1).

Which of the formulae below represents the general terms of the following set of numbers {−1, ²/₃, −¹/₂, ²/₅, …} for n = 1, 2, 3, 4, …?

1. A.2/(n + 1)
2. B.(−1)^{n + 1} × 2/(n + 1)
3. C.(−1)ⁿ × 2/(n + 1)
4. D.n/(2n − 1)
5. E.(−1)ⁿ × n/(2n + 1)

Three numbers, x, y and z, are connected by the relationships y = ⁴/₉x + 1 and z = ⁴/₉y + 1. If x = 99 find z

1. A.6⅓
2. B.20
3. C.21
4. D.176⁴/₉
5. E.None of the above.

In a school there are 35 students in Class 2A and 40 in Class 2B. The mean score for Class 2A in an English Literature examination is 60.0 and that for 2B in the same paper is 52.5. Find, to one place of decimal, the mean for the combined classes.

1. A.1.5
2. B.56.0
3. C.56.2
4. D.56.3
5. E.56.5.

A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items then the sector representing this group on the pie chart contains an angle x° at the centre of the circle where x is

1. A.36
2. B.60
3. C.70
4. D.72
5. E.75.

In triangle FGH, <G = 90°, <H = 60°, while in triangle XYZ, <X = 60° and <Y = 30°. From ΔXYZ write down the ratio equal to FG/FH

1. A.YZ/ZX
2. B.YX/YZ
3. C.ZX/YZ
4. D.YX/ZX
5. E.YZ/YX

A pentagon has four of its angles equal. If the size of the fifth angle is 60°, find the size of each of the four equal angles.

1. A.60°
2. B.108°
3. C.120°
4. D.150°
5. E.None of the above.

In the figure above, FGHJ is a circle of radius 3cm centre O. FOH, GOJ are perpendicular diameters. With G as centre, an arc of a circle is drawn to pass through F and H. Find the length of the perimeter of the lunar portion shaded.

1. A.3π(√2 − 1)cm
2. B.3π(1 + √2/2) cm
3. C.3π(1 + √2)cm
4. D.⁹/₂πcm
5. E.9πcm.

Find the product of (2√y − 3y) and (3y + 2√y)

1. A.4y + y²
2. B.4y + 9y²
3. C.4y − 9y²
4. D.−4y − 9y²
5. E.2y + y².

What will be the value of k so that the quadratic equation kx² − 4x + 1 = 0 has two equal roots?

1. A.2
2. B.3
3. C.4
4. D.8
5. E.¼

If it is given that 5^{x + 1} + 5^x = 150 then the value of x is equal to

1. A.3
2. B.4
3. C.1
4. D.2
5. E.½.

Solve the system of equation
2^{x + y} = 32
3^{3y − x} = 27

1. A.(3, 2)
2. B.(−3, 2)
3. C.(3, −2)
4. D.(−3, −2)
5. E.(2, 2).

Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm. (Take π = ²²/₇)

1. A.188.57cm²
2. B.1320cm²
3. C.188cm²
4. D.188.08cm²
5. E.100cm²

Solve the equation for all positive values of θ less than 360°, 3 tan θ + 2 = −1

1. A.135° or 315°
2. B.45 or 135°
3. C.315 or 45
4. D.315 or 180
5. E.360 or 315.

Given log 2 = 0.69, log 3 = 1.10 and log 7 = 1.90 all to a fixed base, find log 10.5 to the same base, without using tables.

1. A.1.03
2. B.2.31
3. C.3.69
4. D.10.5
5. E.1.69.

Simplify 10^{2 + log₁₀5}

1. A.500
2. B.2log₁₀5
3. C.10
4. D.25
5. E.log₁₀7.

Simplify, as much as possible 1 + 2/(1 − 5/(5 + 2/x))

1. A.2/x + 2
2. B.x + 1
3. C.10x + 6
4. D.5x + 3
5. E.(5x + 3)/(5x + 2)

Find the missing numerator: 5/(x + 1) − 3/(1 − x) − (7x − 1)/(x² − 1) = ______/(x + 1)

1. A.−1
2. B.x − 1
3. C.3(1 − 5x)/(x + 1)
4. D.3(1 − 5x)
5. E.1.

The expression x³ − 4x² + cx + d is such that x + 1 is its factor, and its value is 1 when x is −2. Find c and d.

1. A.c = 4 and d = −9
2. B.c = −4 and d = 9
3. C.c = −20 and d = −15
4. D.c = 20 and d = −15
5. E.c = −20 and d = 15.

If a function is defined by f(x + 1) = 3x² − x + 4 find f(0)

1. A.4
2. B.6
3. C.0
4. D.8
5. E.2.

The angles marked in the figure above are measured in degrees. Find x

1. A.45°
2. B.90°
3. C.60°
4. D.15°
5. E.30°.

In the figure above, PS = SR and RX is a tangent to the circle at R, <QRX is equal to 72°. Find <SPR

1. A.20°
2. B.36°
3. C.72°
4. D.30°
5. E.15°.

If x varies inversely as y, and y varies directly as the square root of z, and z varies directly as 1/w², write down in words how x varies with w.

1. A.x varies inversely as w²
2. B.x varies directly as w²
3. C.x varies directly as w
4. D.x varies inversely as w
5. E.x varies directly as square root of w.

Write the decimal number 39 to base 2

1. A.100111
2. B.110111
3. C.111001
4. D.100101
5. E.19.5.

Find the area of the shaded segment in the figure shown above

1. A.√3
2. B.4π − √3
3. C.²/₃π
4. D.2π/3 − √3
5. E.2π/3 − 2√3