JAMB UTME - Mathematics - 1980

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^o at the centre of the circle where x is

36^o

60^o

70^o

72^o Azịza ziri ezi

75^o

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Sets (JAMB)

Sets

Lee Azịza

Ajụjụ 8 Ripọtì

List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5

<2, 3, 4, 5

3, 4, 5 Azịza ziri ezi

2, 3, 4

3, 4

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Inequalities (JAMB)

Gụọ akwụkwọ nkuzi na Areas (WAEC)

Inequalities

Areas

Lee Azịza

Ajụjụ 9 Ripọtì

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

1:2

1:3

1:4 Azịza ziri ezi

1:5

1:6

Akọwa Nkọwa

Lee Azịza

Ajụjụ 10 Ripọtì

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

3\(\pi\)\(\sqrt{2 - 1}\)cm

\(\frac{9}{2}\)\(\pi\)cm

3 \(\pi\)(1 + \(\frac{2}{2}\)) Azịza ziri ezi

3(1 + \(\frac{2}{2}\))

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Circles

Lee Azịza

Ajụjụ 11 Ripọtì

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

2 Azịza ziri ezi

\(\frac{1}{2}\)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Indices (WAEC)

Indices

Lee Azịza

Ajụjụ 12 Ripọtì

Solve the equation for the positive values of \(\theta\) less than 360^o. 3 tan \(\theta\) + 2 = -1

135^o or 315^o Azịza ziri ezi

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Trigonometry (JAMB)

Trigonometry

Lee Azịza

Ajụjụ 13 Ripọtì

A cylindrical motor of height 12cm has uniform thickness of 2cm. If the diameter of its outer cross section is 10cm, Find the volume of the constituent material. (take \(\pi\) = \(\frac{22}{7}\)

\(\frac{6600}{7}\)cm³

270cm³

660cm³

\(\frac{4224}{7}\)cm³ Azịza ziri ezi

\(\frac{1980}{7}\)cm³

Akọwa Nkọwa

Lee Azịza

Ajụjụ 14 Ripọtì

Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))

[\(\frac{7}{3}\) + \(\frac{5}{a}\)(v - 1)] + b Azịza ziri ezi

[\(\frac{7b}{3}\) + \(\frac{5}{a}\)(v - 1)]

\(\frac{7}{3}\)[b + \(\frac{5}{a}\)(v - 1)]

\(\frac{7}{3}\)[b + \(\frac{5v - 1}{a}\)]

Akọwa Nkọwa

Lee Azịza

Ajụjụ 15 Ripọtì

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

x = \(\frac{3}{5}\) or -\(\frac{1}{2}\)

x = \(\frac{3}{10}\) or -1

x = \(\frac{3}{10}\) or 1

x = \(\frac{1}{5}\) or \(\frac{-3}{2}\)

x = -\(\frac{1}{5}\) or \(\frac{3}{2}\) Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Quadratic Equations (WAEC)

Quadratic Equations

Lee Azịza

Ajụjụ 16 Ripọtì

Write the decimal number 39 to base 2

10011 base 2 Azịza ziri ezi

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Number Bases

Lee Azịza

Ajụjụ 17 Ripọtì

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

4 Azịza ziri ezi

\(\frac{1}{4}\)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Quadratic Equations (WAEC)

Quadratic Equations

Lee Azịza

Ajụjụ 18 Ripọtì

If \(\theta\) = \(\frac{3}{2}\) and \(\theta\) is less than 90^o, calculate tan \(\frac{(90 - \theta)}{cos^2\theta}\)

\(\frac{1}{2}\)

\(\frac{4}{\sqrt{3}}\) Azịza ziri ezi

\(\sqrt{3}\)

4\(\sqrt{3}\)

Akọwa Nkọwa

Lee Azịza

Ajụjụ 19 Ripọtì

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

x + 1

x - 1

No common factor Azịza ziri ezi

(2x - 1)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Algebraic Expressions

Lee Azịza

Ajụjụ 20 Ripọtì

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

56.77

56.105 Azịza ziri ezi

28:105

28:49

56:49

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Mensuration (JAMB)

Gụọ akwụkwọ nkuzi na Triangles And Polygons (WAEC)

Mensuration

Triangles And Polygons

Lee Azịza

Ajụjụ 21 Ripọtì

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

\(\frac{5}{9}\)

\(\frac{3}{5}\) Azịza ziri ezi

\(\frac{3}{4}\)

\(\frac{4}{3}\)

\(\frac{5}{3}\)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Circles

Lee Azịza

Ajụjụ 22 Ripọtì

When a dealer sells a bicycle for N81 he makes a profit of 80%. What did he pay for the bicycle?

N73

N74.52

N75 Azịza ziri ezi

N87.48

N75.52

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Positive And Negative Integers, Rational Numbers (WAEC)

Gụọ akwụkwọ nkuzi na Areas (WAEC)

Gụọ akwụkwọ nkuzi na Financial Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Areas

Financial Arithmetic

Lee Azịza

Ajụjụ 23 Ripọtì

A solid cylinder of radius 3cm has a total surface area of 36\(\pi\)cm2. Find its height

2cm

3cm Azịza ziri ezi

4cm

5cm

6cm

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Volumes (WAEC)

Gụọ akwụkwọ nkuzi na Mensuration (JAMB)

Volumes

Mensuration

Lee Azịza

Ajụjụ 24 Ripọtì

(\(\frac{x^a}{x^b}\))^{a + b} by (\(\frac{x^{a + b}}{x^{a - b}}\))^{\(\frac{a^2}{b}\)}

x^-a2

x^b2

x^{a2 - b2}

\(\frac{1}{x^{a2 + b2}}\) Azịza ziri ezi

x^{b2 - a2}

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Number Bases

Algebraic Expressions

Lee Azịza

Ajụjụ 25 Ripọtì

Find the area of the shades segments in the figure

\(\sqrt{3}

4 \(\pi - \sqrt{3}\)

-\(\frac{2}{3} \pi\)

\(\frac{2\pi}{3}\) -3 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Introductory Calculus (WAEC)

Gụọ akwụkwọ nkuzi na Modular Arithmetic (WAEC)

Gụọ akwụkwọ nkuzi na Surds (radicals) (WAEC)

Introductory Calculus

Modular Arithmetic

Surds (radicals)

Lee Azịza

Ajụjụ 26 Ripọtì

Which of the formula below represents the general terms of the following set of numbers(-1, \(\frac{2}{3}\), -\(\frac{1}{2}\), \(\frac{2}{5}\)......) for n = 1, 2, 3, 4.......?

\(\frac{2}{n + 1}\)

(-1)^{n + 1} \(\frac{2}{n + 1}\)

(-1)ⁿ \(\frac{2}{n + 1}\) Azịza ziri ezi

\(\frac{n}{2n - 1}\)

(-1)ⁿ\(\frac{n}{2n - 1}\)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Fractions (WAEC)

Algebraic Fractions

Lee Azịza

Ajụjụ 27 Ripọtì

Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm. (take \(\pi\) = \(\frac{22}{7}\))

188.57cm² Azịza ziri ezi

1320cm²

188cm²

188.08cm²

10cm²

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Areas (WAEC)

Areas

Lee Azịza

Ajụjụ 28 Ripọtì

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

the ratio of the corresponding sides

the ratio of the squares of corresponding sides Azịza ziri ezi

the ratio of the corresponding heights of the triangles

half the ratio of the corresponding heights of the triangles

the ratio of the corresponding bases to the heights of the triangles

Akọwa Nkọwa

Lee Azịza

Ajụjụ 29 Ripọtì

Find the missing numerator \(\frac{5}{x + 1}\) - \(\frac{3}{1 - x}\) - \(\frac{7x - 1}{x^2 - 1}\) = \(\frac{?}{x + 1}\).

-1

x - 1

\(\frac{3(1 - 5x)}{x + 1}\)

1 Azịza ziri ezi

3(1 - 5x)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Fractions (WAEC)

Algebraic Fractions

Lee Azịza

Ajụjụ 30 Ripọtì

Three numbers, x, y and z are connected by the relationships y = \(\frac{4x}{9}\) + 1. If x = 99, find z

6\(\frac{1}{3}\)

21 Azịza ziri ezi

176\(\frac{4}{9}\)

None of the above

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Solution Of Linear Equations (WAEC)

Gụọ akwụkwọ nkuzi na Simple Operations On Algebraic Expressions (WAEC)

Solution Of Linear Equations

Simple Operations On Algebraic Expressions

Lee Azịza

Ajụjụ 31 Ripọtì

If x varies inversely as y, and y varies directly as the square root of z, and z varies directly \(\frac{1}{w^2}\) write down in words how x varies with w

x varies inversely as w²

x varies directly as w² Azịza ziri ezi

x varies directly as w

x varies inversely as w

x varies directly as square root of w

Akọwa Nkọwa

Lee Azịza

Ajụjụ 32 Ripọtì

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

A pair of straight lines parallel to PQ

The perpendicular bisector of PQ Azịza ziri ezi

An arc of a circle passing through P and Q

A circle with diameter PQ

The bisector of angle PXQ

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Loci (WAEC)

Gụọ akwụkwọ nkuzi na Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

Lee Azịza

Ajụjụ 33 Ripọtì

Rationalize the denominator of the given expression \(\frac{\sqrt{1 + a} - \sqrt{a}}{1 + a + \sqrt{a}}\)

1 + 2a - 2\(\sqrt{a(1 + a)}\) Azịza ziri ezi

\(\sqrt{1(1 + a)}\)

2a - 2\(\sqrt{a(1 + a)}\)

1 + 2a - 2\(\sqrt{a + b}\)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Surds (radicals) (WAEC)

Surds (radicals)

Lee Azịza

Ajụjụ 34 Ripọtì

Find the product of (2\(\sqrt{y - 3y}\)) and (3y = 2y)

4y = y²

4y + 9y²

4y - 9y² Azịza ziri ezi

-4y - 9y²

2y + y²

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Probability (WAEC)

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Probability

Algebraic Expressions

Lee Azịza

Ajụjụ 35 Ripọtì

In triangle FGB, < G = 90^o, < H = 60^o, while in triangle XYZ, < X = 60^o and < Y = 30^o. Form XYZ write down the ratio equal to \(\frac{FG}{FH}\)

\(\frac{YX}{ZX}\)

\(\frac{YX}{YZ}\)

\(\frac{ZX}{YZ}\)

\(\frac{YZ}{XY}\) Azịza ziri ezi

Akọwa Nkọwa

Lee Azịza

Ajụjụ 36 Ripọtì

fG is a given straight line and H is a fixed point. The construction marks shown in the diagram indicate the

perpendicular bisector of the line

perpendicular bisector of th eline JK

perpendicular bisector of the line HI

perpendicular from H to the line FG Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Matrices And Determinants (JAMB)

Gụọ akwụkwọ nkuzi na Triangles And Polygons (WAEC)

Matrices And Determinants

Triangles And Polygons

Lee Azịza

Ajụjụ 37 Ripọtì

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

\(\frac{19}{2}\) Azịza ziri ezi

\(\frac{39}{4}\)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Gụọ akwụkwọ nkuzi na Sets (WAEC)

Number Bases

Sets

Lee Azịza

Ajụjụ 38 Ripọtì

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰ Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Lengths And Perimeters (WAEC)

Gụọ akwụkwọ nkuzi na Logarithms (WAEC)

Lengths And Perimeters

Logarithms

Lee Azịza

Ajụjụ 39 Ripọtì

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.

c = 4 and d = -9

c = -4 and d = 9

c = -20 and d = -15 Azịza ziri ezi

c = 20 and d = -15

c = -20 and d = 15

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Algebraic Expressions

Lee Azịza

Ajụjụ 40 Ripọtì

A man and his wife went to buy an article costing N400. The woman had 10% of the cost and the man 40% of the remainder. How much did they have altogether?

N216

N200

N184 Azịza ziri ezi

N144

N100

Akọwa Nkọwa

Lee Azịza

Ajụjụ 41 Ripọtì

Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.

1.03

2.31 Azịza ziri ezi

3.69

10.5

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Modular Arithmetic (WAEC)

Gụọ akwụkwọ nkuzi na Logarithms (WAEC)

Modular Arithmetic

Logarithms

Lee Azịza

Ajụjụ 42 Ripọtì

In the figure, PS = SR and Rx is a tangent to the circle at R, < QRX is equal to 72^o. Find

20^o

36^o Azịza ziri ezi

72^o

30^o

15^o

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Circles

Lee Azịza

Ajụjụ 43 Ripọtì

Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)

\(\frac{1 - cos x}{sin x}\) Azịza ziri ezi

1 - cos x

sin x

1 + cos x

\(\frac{1 + cos x}{sin x}\)

Akọwa Nkọwa

Lee Azịza

Ajụjụ 44 Ripọtì

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

(3, 2) Azịza ziri ezi

(-3, 2)

(3, -2)

(-3, -2)

(2, 2)

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Gụọ akwụkwọ nkuzi na Indices (WAEC)

Number Bases

Indices

Lee Azịza

Ajụjụ 45 Ripọtì

Which of the following is NOT a factor of 12\(^{4}\) - 5\(^{4}\)?

49 Azịza ziri ezi

169

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Logarithms (WAEC)

Logarithms

Lee Azịza

Ajụjụ 46 Ripọtì

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520 Azịza ziri ezi

5.2048

5204

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Fractions, Decimals And Approximations (WAEC)

Gụọ akwụkwọ nkuzi na Modular Arithmetic (WAEC)

Fractions, Decimals And Approximations

Modular Arithmetic

Lee Azịza

Ajụjụ 47 Ripọtì

In a school, there are 35 students in class 2A and 40 in class 2B. The mean score for class 2 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

2.5

56.0 Azịza ziri ezi

56.2

56.3

6.5

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Integration (JAMB)

Gụọ akwụkwọ nkuzi na Statistics (WAEC)

Integration

Statistics

Lee Azịza

Ajụjụ 48 Ripọtì