JAMB Mathematics 1992 past questions and answers

Find n if 34_n = 10011₂

1. A.5
2. B.6
3. C.7
4. D.8

The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?

1. A.1/25
2. B.1/4
3. C.4
4. D.25

Evaluate log_b aⁿ if b = a^1/n.

1. A.n²
2. B.n
3. C.1/n
4. D.1/n

What is the value of x satisfying the equation 4^2x/4^3x = 2?

1. A.−2
2. B.−½
3. C.½
4. D.2

Simplify 5√18 − 3√72 + 4√50

1. A.17√4
2. B.4√17
3. C.17√2
4. D.12√4

If x = 3 − √3, find x² + 36/x²

1. A.9
2. B.18
3. C.24
4. D.27

If x = (all prime factors of 44) and y = (all prime factors of 60), the element of x∪y and x∩y respectively are

1. A.{2, 4, 3, 5, 11} and {4}
2. B.{4, 3, 5, 11} and {3, 4}
3. C.{2, 5, 11} and {2}
4. D.{2, 3, 5, 11} and {2}

If U = {0, 2, 3, 6, 7, 8, 9, 10} is the universal set E = {0, 4, 6, 8, 10} and F = {x : x² = 2⁶, x is odd}. Find (E∩F)′ where ′ means the complement of a set

1. A.{0}
2. B.U
3. C.{8}
4. D.ϕ

Make t the subject of formula s = ut + ½ at²

1. A.1/a[u ± √(u² − 2as)]
2. B.1/a[−u ± √(u² − 2as)]
3. C.1/a[u ± √(u² + 2as)]
4. D.1/a[−u ± √(u² + 2as)]

Factorize 9p² − q² + 6qr − 9r²

1. A.(3p − 3q + r)(3p − q − 9r)
2. B.(6p − 3q − 3r)(3q − p − 4r)
3. C.(3p − q + 3r)(3p + q − 3r)
4. D.(3q − p + 3r)(3q − p + 3r)

Solve the equation y − 11√y + 24 = 0

1. A.8, 3
2. B.64, 9
3. C.6, 4
4. D.9, −8

A man invested the sum of N280.00 partly at 5% and partly at 4%. If the total interest is N12.80 per annum, find the amount invested at 5%.

1. A.₦14.00
2. B.₦120.00
3. C.₦140.00
4. D.₦160.00

If x + 1 is a factor of x³ + 3x² + kx + 4, find the value of k.

1. A.6
2. B.−6
3. C.8
4. D.−8

Resolve 3/(x² + x − 2) into partial fractions

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

Find all values of x satisfying the inequality −11 ≤ 4 − 3x ≤ 28

1. A.−5 ≤ x ≤ 8
2. B.5 ≤ x ≤ 8
3. C.−8 ≤ x ≤ 5
4. D.−5 < x ≤ 8

The sketch above is the curve of y = ax² + bx + c. Find a, b and c respectively

1. A.1, 0, −4
2. B.−2, 2, −4
3. C.0, 1, −4
4. D.2, −2, −4

Find the sum to the infinity of the following series 3 + 2 + 4/3 + 8/9 + 16/27 + ...

1. A.1270
2. B.190
3. C.18
4. D.9

What is the n-th term of the sequence 2, 6, 12, 20, .......?

1. A.4n − 2
2. B.2(3ⁿ⁻¹)
3. C.n² + n
4. D.n² + 3n + 2

For an arithmetical sequence, the first term is 2 and the common difference is 3. Find the sum of the first 11 terms.

1. A.157
2. B.187
3. C.197
4. D.200

If the binary operation * is defined by m * n = mn + m + n for any real number m and n, find the identity element e under the operation

1. A.e = 1
2. B.e = −1
3. C.e = −2
4. D.e = 0

Use the matrices below to answer questions 22 and 23.
P = [x 3 0; 2 y 3; 4 2 z] (rows: x, 3, 0 / 2, y, 3 / 4, 2, z)
Q = [x 2 4; 3 y 2; 0 3 z] (rows: x, 2, 4 / 3, y, 2 / 0, 3, z)
When P^T is the transpose of P, calculate |P^T| when x = 0, y = 1 and z = 2

1. A.48
2. B.24
3. C.−24
4. D.−48

Use the matrices below to answer questions 22 and 23.
P = [x 3 0; 2 y 3; 4 2 z] (rows: x, 3, 0 / 2, y, 3 / 4, 2, z)
Q = [x 2 4; 3 y 2; 0 3 z] (rows: x, 2, 4 / 3, y, 2 / 0, 3, z)
PQ is equivalent to

1. A.PP^T
2. B.PP⁻¹
3. C.QP
4. D.PP

In the fig. above, TŜP = 105° and PR̂Q = 20°, find PQ̂R

1. A.130°
2. B.120°
3. C.75°
4. D.30°

In the fig. above, PQR is a semicircle while PQ and QR are chords. QS is the perpendicular from Q to the diameter PR. What is the expression for QS?

1. A.QS = PS.SR
2. B.QS = √(PS.SR)
3. C.QS = √2 √(PS.SR)
4. D.QS = (1/√2) √(PS.SR)

Determine the distance on the earth's surface between two towns P(Lat. 60°N, Long. 20°E) and Q(Lat. 60°N, Long. 25°W) (Radius of the earth = 6400km)

1. A.800π/9 km
2. B.800√3π/9 km
3. C.800πkm
4. D.800√3πkm

If in the diagram above, FG is parallel to KM, find the value of x

1. A.75°
2. B.95°
3. C.105°
4. D.125°

X is a point due east of Y on a coast. Z is another point on the coast but 6√3km due south of Y. If the distance XZ is 12km, calculate the bearing of Z from X.

1. A.240°
2. B.210°
3. C.150°
4. D.60°

The above diagram is a circle with centre O. Find the area of the shaded portion.

1. A.9πcm²
2. B.9(π − 2)cm²
3. C.18πcm²
4. D.36πcm²

The locus of a point which is equidistant from two given fixed points is the

1. A.perpendicular bisector of the straight line joining them.
2. B.parallel line to the straight line joining them
3. C.transverse to the straight line joining them
4. D.angle bisector of 90° which the straight line joining them makes with the horizontal.

What is the perpendicular distance of a point (2,3) from the line 2x − 4y + 3 = 0?

1. A.√5/2
2. B.√5/−20
3. C.5/√13
4. D.0

Find the equation of the line through (5, 7) parallel to the line 7x + 5y = 12

1. A.5x + 7y = 120
2. B.7x + 5y = 70
3. C.x + y = 7
4. D.15x + 17y = 90.

Given that θ is an acute angle and sin θ = m/n, find cot θ

1. A.√((n² − m²)/m)
2. B.√((n + m)(n − m))/m
3. C.m/√(n² − m²)
4. D.√(n/(n² − m²))

In the fig. above, if XZ is 10cm, calculate RY in cm

1. A.10
2. B.10(1 − 1/√3)
3. C.10(1 − √3)
4. D.10(1 − 1/√2)

Evaluate lim_x→2 (x − 2)(x² + 3x − 2)/(x² − 4)

1. A.0
2. B.2
3. C.3
4. D.4

If y = x sin x, find d²y/dx²

1. A.2cos x − x sin x
2. B.sin x + x cos x
3. C.sin x − x cos x
4. D.x sin x − 2 cos x

Obtain a maximum value of the function f(x) = x³ − 12x + 11

1. A.−5
2. B.−2
3. C.2
4. D.27

A student blows a balloon and its volume increases at a rate of π(20 − t²)cm³ s⁻¹ after t seconds. If the initial volume is 0 cm³, find the volume of the balloon after 2 seconds.

1. A.37.00π
2. B.37.33π
3. C.40.00π
4. D.42.67π

Evaluate the integral ∫_π/12^π/4 2 cos 2x dx

1. A.−½
2. B.−1
3. C.½
4. D.1

A storekeeper checked his stock of five commodities and arrived at the following statistics:
Commodity: F, G, H, K, M
Quantity: 215, 113, 108, 216, 68
What angle will commodity H represent on a pie chart?

1. A.216°
2. B.108°
3. C.68°
4. D.54°

x: 2, 4, 6, 8
f: 4, y, 6, 5
If the mean of the above frequency distribution is 5.2, find y

1. A.6.0
2. B.5.2
3. C.5.0
4. D.4.0

No. of children: 0, 1, 2, 3, 4, 5, 6
No. of families: 7, 11, 6, 7, 7, 5, 3
Find the mode and median respectively of the distribution above.

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

If the scores of 3 students in a test are 5, 6 and 7, find the standard deviation of their scores.

1. A.2/3
2. B.2/(3√3)
3. C.√(2/3)
4. D.√3/2

Sample variance can be defined as S² = (1/n) Σ (x_i − x̄)² and S² = (1/(n − 1)) Σ (x_i − x̄)² where n is the number of sample observations. There is no difference practically between the above definitions when

1. A.n ≠ 35
2. B.n > 35
3. C.n < 35
4. D.n = 5

Two perfect dice are thrown together. Determine the probability of obtaining a total score of 8.

1. A.1/12
2. B.5/36
3. C.1/6
4. D.7/36

The probability of an event P is 3/4 while that of another event Q is 1/6. If the probability of both P and Q is 1/12, what is the probability of either P or Q?

1. A.1/96
2. B.1/8
3. C.5/6
4. D.11/12

Five people are to be arranged in a row for a photograph. How many arrangements are there if a married couple in the group insists on sitting next to each other?

1. A.48
2. B.24
3. C.20
4. D.10

A student has five courses to take from Mathematics and Physics. There are 4 courses in Mathematics and 3 in Physics which he can choose from at will. In how many ways can he choose his courses such that he takes exactly two courses in Physics.

1. A.11
2. B.12
3. C.10
4. D.7