JAMB Mathematics 1997 past questions and answers

If (1P03)₄ = 115₁₀, find P.

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

Evaluate 64.764² − 35.236² correct to 3 significant figures.

1. A.2960
2. B.2950
3. C.2860
4. D.2850

Find the value of (0.006)³ + (0.004)³ in standard form.

1. A.2.8 × 10⁻⁹
2. B.2.8 × 10⁻⁸
3. C.2.8 × 10⁻⁷
4. D.2.8 × 10⁻⁴

Given that log_a2 = 0.693 and log_a3 = 1.097, find log_a13.5.

1. A.1.404
2. B.1.790
3. C.2.598
4. D.2.790

Simplify log₂96 − 2log₂6

1. A.2 − log₂3
2. B.3 − log₂3
3. C.log₂3 − 3
4. D.log₂3 − 2

If 8^x/2 = (2^3/8)(4^3/4), find x.

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

Simplify (2√3 + 3√5)/(3√5 − 2√3)

1. A.(19 + 4√15)/11
2. B.(19 + 4√15)/19
3. C.(19 + 2√15)/11
4. D.(19 + 2√15)/19

Find the simple interest rate per cent per annum at which N1000 accumulates to N1240 in 3 years.

1. A.6%
2. B.8%
3. C.10%
4. D.12%

A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both languages. How many students speak neither Hausa nor Igbo?

1. A.0
2. B.9
3. C.11
4. D.20

If the function f(x) = x³ + 2x² + qx − 6 is divisible by x + 1, find q

1. A.−5
2. B.−2
3. C.2
4. D.5

Solve the simultaneous equations 2/x − 3/y = 2, 4/x + 3/y = 10

1. A.x = 3/2, y = 1/2
2. B.x = 1/2, y = 3/2
3. C.x = −1/2, y = −3/2
4. D.x = 1/2, y = −3/2

Find the minimum value of x² − 3x + 2 for all real values of x.

1. A.−1/4
2. B.−1/2
3. C.1/4
4. D.1/2

Make f the subject of the formula t = √(v/(1/f + 1/g))

1. A.(gv − t²)/gt²
2. B.gt²/(gv − t²)
3. C.v/(1/t² − 1/g)
4. D.gv/(t² − g)

What value of g will make the expression 4x² − 18xy + g a perfect square?

1. A.9
2. B.9y²/4
3. C.81y²
4. D.81y²/4

Find the value of K if (5 + 2r)/((r + 1)(r − 2)) expressed in partial fraction is K/(r − 2) + L/(r + 1) where K and L are constants.

1. A.3
2. B.2
3. C.1
4. D.−1

Let f(x) = 2x + 4 and g(x) = 6x + 7 where g(x) > 0. Solve the inequality f(x)/g(x) < 1

1. A.x < −3/4
2. B.x > −4/3
3. C.x > −3/4
4. D.x > −12

Find the range of value of x which satisfies the inequality 12x² < x + 1.

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

S_n is the sum of the first n terms of a series given by S_n = n² − 1. Find the nth term.

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

The nth term of a sequence is given by 3¹⁻ⁿ. Find the sum of the first three terms of the sequence.

1. A.13/9
2. B.1
3. C.1/3
4. D.1/9

Two binary operations ∗ and ⊗ are defined as m∗n = mn − n − 1 and m ⊗ n = mn + n − 2 for all real numbers m, n. Find the value of 3 ⊗ (4 ∗ 5)

1. A.60
2. B.57
3. C.54
4. D.42

If x∗y = x + y − xy, find x, when (x∗2) + (x∗3) = 68

1. A.24
2. B.22
3. C.−12
4. D.−21

Determine x + y if (2 −3 / −1 4)(x / y) = (−1 / 8)
(The 2 × 2 matrix has rows 2, −3 and −1, 4; the column vectors are (x, y) and (−1, 8).)

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

Find the non-zero positive value of x which satisfies the equation
| x 1 0 |
| 1 x 1 | = 0
| 0 1 x |

1. A.2
2. B.√3
3. C.√2
4. D.1

Each of the base angles of an isosceles triangle is 58° and all the vertices of the triangles lie on a circle. Determine the angles which the base of the triangle subtends at the centre of the circle.

1. A.128°
2. B.116°
3. C.64°
4. D.58°

From the figure above, FK//GR and FH = GH, ∠RFK = 34° and ∠FGH = 47°. Calculate the angle marked x

1. A.42°
2. B.52°
3. C.64°
4. D.72°

The figure above shows circles of radii 3cm and 2cm with centre at X and Y respectively. The circles have a transverse common tangent of length 25cm. Calculate XY.

1. A.√630cm
2. B.√626cm
3. C.√615cm
4. D.√600cm

A chord of a circle of diameter 42cm subtends an angle of 60° at the centre of the circle. Find the length of the minor arc.

1. A.22cm
2. B.44cm
3. C.110cm
4. D.220cm

An arc of a circle subtends an angle 70° at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.

1. A.22cm²
2. B.44cm²
3. C.66cm²
4. D.88cm²

Find the volume of the prism above.

1. A.990cm³
2. B.880cm³
3. C.550cm³
4. D.495cm³

A cone with the sector angle of 45° is cut out of a circle of radius r cm. Find the base radius of the cone.

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

A point P moves so that it is equidistant from point L and M. If LM is 16cm, find the distance of P from LM when P is 10cm from L.

1. A.12cm
2. B.10cm
3. C.8cm
4. D.6cm

The angle between the positive horizontal axis and a given line is 135°. Find the equation of the line if it passes through the point (2, 3)

1. A.x − y = 1
2. B.x + y = 1
3. C.x + y = 5
4. D.x − y = 5

Find the distance between the point Q(4, 3) and the point common to the lines 2x − y = 4 and x + y = 2.

1. A.3√10
2. B.3√5
3. C.√26
4. D.√13

The angle of elevation of a building from a measuring instrument placed on the ground is 30°. If the building is 40m high, how far is the instrument from the foot of the building?

1. A.20/√3 m
2. B.40/√3 m
3. C.20√3m
4. D.40√3m

In a triangle XYZ, if ∠XYZ is 60°, XY = 3cm and YZ = 4cm. Calculate the length of the side XZ.

1. A.√23cm
2. B.√13cm
3. C.2√5cm
4. D.2√3cm

In the figure above, XYZ is a triangle with XY = 5cm, XZ = 2cm and XZ is produced to E marking the angle YZE = 150°. If the angle XYZ = θ calculate the value of sin θ.

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

Differentiate (6x³ − 5x² + 1)/3x² with respect to x

1. A.2 + 2/(3x³)
2. B.2 + 1/(6x)
3. C.2 − 2/(3x³)
4. D.2 − 1/(6x)

d/dx cos (3x² − 2x) is equal to

1. A.−sin (6x − 2)
2. B.−sin (3x² − 2x)
3. C.(6x − 2)sin(3x² − 2x)
4. D.−(6x − 2)sin(3x² − 2x)

Find the gradient of the curve y = 2√x − 1/x at the point x = 1

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

Integrate 1/x + cos x with respect to x

1. A.−1/x + sin x + k
2. B.ln x + sin x + k
3. C.ln x − sin x + k
4. D.−1/x sin x + k

The pie chart above shows the income of a civil servant in a month. If his monthly income is N6 000, find his monthly basic salary.

1. A.N2 000
2. B.N2 600
3. C.N3 100
4. D.N3 450

In an examination, the result of a certain school is as shown in the histogram above. How many candidates did the school present?

1. A.12
2. B.16
3. C.18
4. D.19

Age: 20, 25, 30, 35, 40, 45
No. of people: 3, 5, 1, 1, 2, 3
Find the median age of the frequency distribution in the table above.

1. A.20
2. B.25
3. C.30
4. D.35

The following are the scores of ten students in a test of 20 marks: 15, 16, 17, 13, 16, 8, 5, 16, 19, 17. What is the modal score?

1. A.13
2. B.15
3. C.16
4. D.19

Find the standard deviation of the following data −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5.

1. A.2
2. B.3
3. C.√10
4. D.√π

Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where Σd² = 60.

1. A.2
2. B.3
3. C.4
4. D.6

In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?

1. A.17/30
2. B.11/30
3. C.6/30
4. D.5/30