JAMB Mathematics 1983 past questions and answers

If M represents the median and D the mode of the measurements 5,9,3,5,8 then (M, D) is

1. A.(6,5)
2. B.(5,8)
3. C.(5,7)
4. D.(5,5)
5. E.(7,5).

A construction company is owned by two partners X and Y and it is agreed that their profit will be divided in the ratio 4:5. At the end of the year, Y received ₦5,000 more than X. What is the total profit of the company for the year?

1. A.₦20,000
2. B.₦25,000
3. C.₦30,000
4. D.₦15,000
5. E.₦45,000.

Given a regular hexagon, calculate each interior angle of the hexagon.

1. A.60°
2. B.30°
3. C.120°
4. D.45°
5. E.135°

Solve the following equations
4x − 3 = 3x + y = 2y + 5x − 12

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

If x = 1 is a root of the equation x³ − 2x² − 5x + 6, find the other roots.

1. A.−3 and 2
2. B.−2 and 2
3. C.3 and −2
4. D.1 and 3
5. E.−3 and 1.

If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?

1. A.4:1 increase
2. B.2:1 increase
3. C.1:4 decrease
4. D.1:1 no change
5. E.3:4 decrease.

In the above figure PQR = 60°, QPR = 90°, PRS = 90°, RPS = 45°, QR = 8cm. Determine PS.

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

Given that cos z = L, where z is an acute angle, find an expression for (cot z − cosec z)/(sec z + tan z)

1. A.(1 − L)/(1 + L)
2. B.(L² − √(1 − L²))/(L² + L − 1)
3. C.−L√(1 − L)/(√(1 + L)(1 + √(1 − L²)))
4. D.√(L − 1)/(√(1 − L²) + 1 − L²)
5. E.L(L − 1)/(1 + √(1 − L²) − L²)

If 0.0000152 × 0.00042 = A × 10^B, where 1 ≤ A < 10, find A and B.

1. A.A = 9, B = 6.38
2. B.A = 6.38, B = −9
3. C.A = 6.38, B = 9
4. D.A = 6.38, B = −1
5. E.A = 6.38, B = 1.

If x + 2 and x − 1 are factors of the expressions lx³ + 2kx² + 24, find the values of l and k.

1. A.l = −6, k = −9
2. B.l = −2, k = 1
3. C.l = −2, k = −1
4. D.l = 0, k = 1
5. E.l = 6, k = 0.

In a class of 60 pupils, the statistical distribution of the number of pupils offering Biology, History, French, Geography and Additional Mathematics is as shown in the pie chart above. How many pupils offer Additional Mathematics?

1. A.15
2. B.10
3. C.18
4. D.12
5. E.28.

The value of (0.03)³ − (0.02)³ is

1. A.0.019
2. B.0.0019
3. C.0.00019
4. D.0.000019
5. E.0.000035.

y varies partly as the square of x and partly as the inverse of the square root of x. Write down the expression for y if y = 2 when x = 1 and y = 6 when x = 4.

1. A.y = 10x²/31 + 52/(31√x)
2. B.y = x² + 1/√x
3. C.y = x² + 1/x
4. D.y = x²/31 + 1/(31√x)
5. E.y = 10/31 (x² + 1/√x)

Simplify (x − 7)/(x² − 9) × (x² − 3x)/(x² − 49)

1. A.x/((x − 3)(x + 7))
2. B.(x + 3)(x + 7)/x
3. C.x/((x − 3)(x − 7))
4. D.x/((x + 3)(x + 7))
5. E.x/((x + 4)(x − 7))

The length of the sides of a right-angled triangle are (3x + 1)cm, (3x − 1)cm and x cm. Find x

1. A.2
2. B.6
3. C.18
4. D.12
5. E.0.

The scores of a set of final year students in the first semester examination in a paper are 41, 29, 55, 21, 47, 70, 70, 40, 43, 56, 73, 23, 50, 50. Find the median of the scores.

1. A.47
2. B.48½
3. C.50
4. D.48
5. E.49.

Which of the following equations represents the above graph?

1. A.y = 1 + 2x + 3x²
2. B.y = 1 + 2x + 3x²
3. C.y = 1 + 2x − 3x²
4. D.y = 1 − 2x − 3x²
5. E.y = 3x² + 2x − 1.

The above figure FGHK is a rhombus. What is the value of angle x?

1. A.90°
2. B.30°
3. C.150°
4. D.120°
5. E.60°.

PQRS is a desk of dimensions 2m × 0.8m which is inclined at 30° to the horizontal. Find the inclination of the diagonal PR to the horizontal.

1. A.23°35'
2. B.30°
3. C.15°36'
4. D.10°
5. E.10°42'.

Find x if (x_{base 4})² = 100100_{base 2}

1. A.6
2. B.12
3. C.100
4. D.210
5. E.10°42'

Simplify log₁₀ a^⅓ + ¼log₁₀a − ¹/₁₂log₁₀a⁷

1. A.1
2. B.⁷/₆ log₁₀a
3. C.0
4. D.10
5. E.a.

If w varies inversely as V and u varies directly as w³, find the relationship between u and V given that u = 1 when V = 2.

1. A.u = 8V³
2. B.u = 2∛V
3. C.V = 8/u³
4. D.V = 8u³
5. E.u = 8/V³

Solve the simultaneous equations for x
x² + y − 8 = 0
y + 5x − 2 = 0

1. A.−28, 7
2. B.6, −28
3. C.6, −1
4. D.−1, 7
5. E.3, 2.

Find the missing value in the following table
x: −2, −1, 0, 1, 2, 3
y = x³ − x + 3: ___, 3, 3, 3, 9, 27

1. A.−3
2. B.3
3. C.−9
4. D.13
5. E.9

If O is the centre of the circle in the figure above, find the value of x.

1. A.50
2. B.260
3. C.100
4. D.65
5. E.130.

Find the angle of the sectors representing each item in a pie chart of the following data
6, 10, 14, 16, 26

1. A.15°, 25°, 35°, 40°, 65°
2. B.60°, 100°, 140°, 160°, 260°
3. C.6°, 10°, 14°, 16°, 26°
4. D.30°, 50°, 70°, 80°, 130°
5. E.None of the above.

The score of 16 students in a Mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65, 70. What is the sum of the median and modal scores?

1. A.125
2. B.130
3. C.140
4. D.150
5. E.137.5.

The letters of the word 'MATRICULATION' are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel.

1. A.⁷/₁₃
2. B.⁵/₁₃
3. C.⁶/₁₃
4. D.⁸/₁₃
5. E.⁴/₁₃

Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures.

1. A.4.46
2. B.4.48
3. C.4.47
4. D.4.49
5. E.4.50

If a rod of length 250cm is measured as 25cm long in error, what is the percentage error in measurement?

1. A.55
2. B.10
3. C.5
4. D.4
5. E.2.

If (²/₃)^m (³/₄)ⁿ = ²⁵⁶/₇₂₉, find the values of m and n.

1. A.m = 4; n = 2
2. B.m = −4, n = −2
3. C.m = −4, n = 2
4. D.m = 4, n = −2
5. E.m = −2, n = 4.

Without using tables find the numerical value of log₇ 49 + log₇ (¹/₇)

1. A.1
2. B.2
3. C.3
4. D.7
5. E.0.

Factorize completely 81a⁴ − 16b⁴

1. A.(3a + 2b)(2a − 3b)(9a² + 4b²)
2. B.(3a − 2b)(2a − 3b)(4a² − 9b²)
3. C.(3a − 2b)(3a + 2b)(9a² + 4b²)
4. D.(3a − 2b)(2a − 3b)(9a² + 4b²)
5. E.(3a − 2b)(2a − 3b)(9a² − 4b²).

One interior angle of a convex hexagon is 170° and each of the remaining interior angles is equal to x°. Find x.

1. A.120°
2. B.110°
3. C.105°
4. D.102°
5. E.100°.

PQRS is a cyclic quadrilateral in which PQ = PS. PT is a tangent to the circle and PQ makes an angle of 50° with the tangent as shown in the figure below. What is the size of QRS?

1. A.50°
2. B.40°
3. C.110°
4. D.80°
5. E.100°.

A ship H leaves a port P and sails 30km due South. Then it sails 60km due West. What is the bearing of H from P?

1. A.26° 34'
2. B.243° 26'
3. C.116° 34'
4. D.63° 26'
5. E.240°.

In a sample survey of a university community, the following table shows the percentage distribution of the number of members per household.
No. of members per household: 1, 2, 3, 4, 5, 6, 7, 8 (Total)
Number of households: 3, 12, 15, 28, 21, 10, 7, 4 (100)
What is the median?

1. A.4
2. B.3
3. C.5
4. D.4.5
5. E.None.

On a square paper of length 2.524375cm is inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram correct to 3 significant figures.

1. A.6.00cm²
2. B.6.10cm²
3. C.6cm²
4. D.6.09cm²
5. E.4.00cm².

If f(x) = 1/(x − 1) + (x − 1)/(x² − 1), find f(1 − x)

1. A.1/x + 1/(x − 2)
2. B.x + 1/(2x − 1)
3. C.−1/x − 1/(x − 2)
4. D.−1/x − 1/(2x − 1)
5. E.1/x + 1/(x² − 1)

In the figure below find PRQ

1. A.66½°
2. B.62½°
3. C.125°
4. D.105°
5. E.65°.

Simplify ∛(27a⁻⁹/8)

1. A.9a⁻²/2
2. B.9a⁻³/2
3. C.3/(2a³)
4. D.2/(3a²)
5. E.3a²/2

The farm yields of four crops on a piece of land in Ondo are represented on the pie chart above. What is the angle of the sector occupied by Okro in the chart?

1. A.91⅓°
2. B.19⅓°
3. C.33⅓°
4. D.11°
5. E.91°.

PQR is the diameter of a semicircle RSP with centre at Q and radius of length 3.5cm. If QPT = QRT = 60°, find the perimeter of the figure PTRS (π = ²²/₇)

1. A.25cm
2. B.18cm
3. C.36cm
4. D.29cm
5. E.25.5cm.

In triangle PQR, QR = 3cm, PR = √3cm, PQ = 2√3cm and PQR = 30°. Find angles P and R.

1. A.P = 60° and R = 90°
2. B.P = 30° and R = 120°
3. C.P = 90° and R = 60°
4. D.P = 60° and R = 60°
5. E.P = 45° and R = 105°.

In the above diagram, if PS = SR and PQ∥SR, what is the size of PQR?

1. A.25°
2. B.50°
3. C.55°
4. D.65°
5. E.75°.

Find the mean of the following 24.57, 25.63, 24.32, 26.01, 25.77.

1. A.25.12
2. B.25.30
3. C.25.26
4. D.25.50
5. E.25.73.

In the figure above, PT is a tangent to the circle with centre at O. If PQT = 30°, find the value of PTO.

1. A.30°
2. B.15°
3. C.24°
4. D.12°
5. E.60°.

A man drove for 4 hours at a certain speed, he then doubled his speed and drove for another 3 hours. Altogether he covered 600 kilometres. At what speed did he drive for the last 3 hours?

1. A.120km/hr
2. B.60km/hr
3. C.600/7km/hr
4. D.50km/hr
5. E.100km/hr.