JAMB Mathematics 1998 past questions and answers

If 1011₂ + X₇ = 25₁₀, solve for X

1. A.14
2. B.20
3. C.24
4. D.25

Evaluate (1/0.03 ÷ 1/0.024)⁻¹ correct to 2 decimal places.

1. A.3.76
2. B.1.25
3. C.0.94
4. D.0.75

If b³ = a⁻² and c^1/3 = a^1/2b, express c in terms of a.

1. A.a^−1/2
2. B.a^1/2
3. C.a^3/2
4. D.a^−2/3

Given that log₄(y − 1) + log₄(½x) = 1 and log₂(y + 1) + log₂x = 2, solve for x and y respectively.

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

Find the value of K if K/(√3 + √2) = K√3 − 2

1. A.3
2. B.2
3. C.√3
4. D.√2

A market woman sells oil in cylindrical tins 10cm deep and 6cm in diameter at N15.00 each. If she bought a full cylindrical jug 18cm deep and 10cm in diameter for N50.00, how much did she make by selling all the oil?

1. A.N62.50
2. B.N35.00
3. C.N31.00
4. D.N25.00

A man is paid r naira per hour for normal work and double rate for overtime. If he does a 35-hour week which includes q hours of overtime, what is the weekly earning in naira.

1. A.r(35 + q)
2. B.q(35r − q)
3. C.q(35 + r)
4. D.r(35r − q)

Given the universal set U = {1, 2, 3, 4, 5, 6} and the sets P = {1, 2, 3, 4}, Q = {3, 4, 5} and R = {2, 4, 6}. Find P ∪ (Q ∪ R)′.

1. A.{4}
2. B.{1, 2, 3, 4}
3. C.{1, 2, 3, 5, 6}
4. D.{1, 2, 3, 4, 5, 6}

In the diagram above, the shaded region is

1. A.(P ∩ Q) ∪ R
2. B.(P ∩ Q) ∩ R
3. C.(P ∩ Q′) ∩ R
4. D.(R ∩ Q′) ∪ R

When the expression pm² + qm + 1 is divided by (m − 1), it has a remainder 2 and when divided by (m + 1) the remainder is 4. Find p and q respectively.

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

Factorize r² − r(2p + q) + 2pq.

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

Solve the equation √x − √(x − 2) − 1 = 0

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

Find the range of values of m for which the roots of the equation 3x² − 3mx + (m² − m − 3) = 0 are real.

1. A.−1 ≤ m ≤ 7
2. B.−2 ≤ m ≤ 6
3. C.−3 ≤ m ≤ 9
4. D.−4 ≤ m ≤ 8

make a/x the subject of formula (x + a)/(x − a) = m

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

Divide 2x³ + 11x² + 17x + 6 by 2x + 1

1. A.x² + 5x + 6
2. B.2x² + 5x + 6
3. C.2x² − 5x + 6
4. D.x² − 5x + 6

Express in partial fractions (11x + 2)/(6x² − x − 1)

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

If x is a positive real number, find the range of values for which 1/3x + ½ > 1/4x

1. A.x > −1/6
2. B.x > 0
3. C.0 < x < 4
4. D.0 < x < 1/6

The shaded area above represents

1. A.x ≥ 0, 3y + 2x ≥ 6
2. B.x ≥ 0, y ≥ 3, 3x + 2y ≥ 6
3. C.x ≥ 2, y ≥ 0, 3x + 2y ≥ 6
4. D.x ≥ 0, y ≥ 0, 3x + 2y ≥ 6

If p + 1, 2p − 10, 1 − 4p² are three consecutive terms of an arithmetic progression, find the possible values of p.

1. A.−4, 2
2. B.−3, 4/11
3. C.−11/4, 2
4. D.5, −3

The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.

1. A.1/4
2. B.1/2
3. C.1/∛3
4. D.1/∛2

The identity element with respect to the element shown in the table above is

1. A.p
2. B.q
3. C.r
4. D.s

The binary operation ∗ is defined by x∗y = xy − y − x for all real values x and y. If x∗3 = 2∗x, find x.

1. A.−1
2. B.0
3. C.1
4. D.5

The determinant of matrix
( x 1 0 )
( 1−x 2 3 )
( 1 1+x 4 )
in terms of x is.

1. A.−3x² − 17
2. B.−3x² + 9x − 1
3. C.3x² + 17
4. D.3x² − 9x + 5

Let I = (1 0 / 0 1), P = (2 3 / 4 5), Q = (u 4+u / −2v v) be 2 × 2 matrices such that PQ = I. Find (u, v)
(Rows are separated by /.)

1. A.(−5/2, −1)
2. B.(−5/2, 3/2)
3. C.(−5/6, 1)
4. D.(5/2, 2/3)

In the diagram above, PR is a diameter of the circle PQRS. PST and QRT are straight lines. Find ∠QSR

1. A.20°
2. B.25°
3. C.30°
4. D.35°

In the diagram above, PQ||ST and ∠PQR = 120°. ∠RST = 130°. Find the angle marked x

1. A.50°
2. B.65°
3. C.70°
4. D.80°

In the figure above, PQST is a parallelogram and TSR is a straight line. If the area of ΔQRS is 20cm², find the area of the trapezium PQRT

1. A.35cm²
2. B.65cm²
3. C.70cm²
4. D.140cm²

TQ is tangent to a circle XYTR, ∠YXT = 32°, ∠RTQ = 40°. Find ∠YTR

1. A.108°
2. B.121°
3. C.140°
4. D.148°

A chord of a circle radius √3cm subtends an angle of 60° on the circumference of the circle. Find the length of the chord.

1. A.3/2cm
2. B.3/2cm
3. C.√3cm
4. D.3cm

A cylindrical drum of diameter 56cm contains 123.2 litres of oil when full. Find the height of the drum in centimetres. (π = 22/7)

1. A.12.5
2. B.25.0
3. C.45.0
4. D.50.0

The locus of all points at a distance 8cm from a point N passes through points T and S. If S equi-distant from T and N, find the area of triangle STN.

1. A.4√3cm²
2. B.16√3cm²
3. C.32cm²
4. D.64cm²

If the distance between the points (x, 3) and (−x, 2) is 5. Find x.

1. A.6.0
2. B.2.5
3. C.√6
4. D.3

The midpoint of the segment of the line y = 4x + 3 which lies between the x-axis and the y-axis is

1. A.(−3/2, 3/2)
2. B.(−2/3, 3/2)
3. C.(3/8, 3/2)
4. D.(−3/8, 3/2)

In the diagram above QTR is a straight line and ∠PQT = 30°. Find the sine of ∠PTR

1. A.8/15
2. B.2/3
3. C.3/4
4. D.15/16

For what value of x does 6 sin(2x − 25)° attain its maximum value in the range 0° ≤ x ≤ 180°?

1. A.12½
2. B.32½
3. C.57½
4. D.147½

From the top of a vertical mast 150m high, two huts on the same ground level are observed. One due East and the other due West of the mast. Their angles of depression are 60° and 45° respectively. Find the distance between the huts.

1. A.150(1 + √3)m
2. B.50(3 + √3)m
3. C.150√3m
4. D.50/√3m

If y = 243(4x + 5)⁻², find dy/dx when x = 1

1. A.−8/3
2. B.3/8
3. C.9/8
4. D.−8/9

Differentiate x/cos x with respect to x.

1. A.1 + x sec x tan x
2. B.1 + sec²x
3. C.cos x + x tan x
4. D.sec x + x sec x tan x

Evaluate ∫₂^π (sec²x − tan²x)dx.

1. A.π/2
2. B.π − 2
3. C.π/3
4. D.π + 2

Find the equation of the curve which passes through the point (2, 5) and whose gradient at any point is given by 6x − 5.

1. A.6x² − 5x + 5
2. B.6x² + 5x + 5
3. C.3x² − 5x − 5
4. D.3x² − 5x + 3

If m and n are the mean and median respectively of the set of numbers 2, 3, 9, 7, 6, 7, 8, 5, find m + 2n to the nearest whole number.

1. A.19
2. B.18
3. C.13
4. D.12

Average hourly earnings (N): 5–9, 10–14, 15–19, 20–24
No. of workers: 17, 32, 25, 24
Estimate the mode of the above frequency distribution.

1. A.12.2
2. B.12.7
3. C.12.9
4. D.13.4

Find the variance of the number k, k + 1, k + 2

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

Find the positive value of x if the standard deviation of the numbers 1, x + 1, 2x + 1 is √6

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

A bag contains 16 red and 20 blue balls only. How many white balls must be added to the bag so that the probability of randomly picking a red ball is equal to 2/5?

1. A.4
2. B.20
3. C.24
4. D.40

The pie chart above shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is N7200?

1. A.1000
2. B.2000
3. C.3000
4. D.4000

In a recent zonal championship games involving 10 teams, teams X and Y were given probabilities 2/5 and 1/3 respectively of winning the gold in the football event. What is the probability that either team will win the gold?

1. A.2/15
2. B.7/15
3. C.11/15
4. D.13/15

If x, y can take values from the set {1, 2, 3, 4}, find the probability that the product of x and y is not greater than 6.

1. A.5/8
2. B.5/16
3. C.1/2
4. D.7/8