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

75^o

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Sets

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Question 19 Report

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

1:2

1:3

1:4

1:5

1:6

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Question 20 Report

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

An arc of a circle passing through P and Q

A circle with diameter PQ

The bisector of angle PXQ

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Loci

Euclidean Geometry

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Question 21 Report

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

72^o

30^o

15^o

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Circles

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Question 22 Report

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

135^o or 315^o

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

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Read lesson note on Trigonometry (JAMB)

Trigonometry

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Question 23 Report

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

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

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Read lesson note on Indices (WAEC)

Indices

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Question 24 Report

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

56.2

56.3

6.5

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Read lesson note on Integration (JAMB)

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Integration

Statistics

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Question 25 Report

A pentagon has four of its angles equal. If the size of the fifth angle is 60^o, Find the size of each of the four equal angles.

60^o

108^o

120^o

150^o

None of the above

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Read lesson note on Angles And Intercepts On Parallel Lines (WAEC)

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Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Question 26 Report

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

c = 20 and d = -15

c = -20 and d = 15

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Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 27 Report

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

2cm

3cm

4cm

5cm

6cm

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Volumes

Mensuration

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Question 28 Report

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

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

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Quadratic Equations

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Question 29 Report

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

x varies directly as w

x varies inversely as w

x varies directly as square root of w

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Question 30 Report

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

\(\frac{1980}{7}\)cm³

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Question 31 Report

Evaluate \((2^{0} + 4^{-\frac{1}{2}})^{2}\)

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

\(\frac{5}{4}\)

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

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Read lesson note on Number Bases (WAEC)

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Number Bases

Indices

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Question 32 Report

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

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

1 - cos x

sin x

1 + cos x

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

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Question 33 Report

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

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

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

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

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

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

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Circles

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Question 34 Report

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

N144

N100

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Question 35 Report

In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90^o, Find x

35^o

50^o

55^o

70^o

80^o

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Triangles And Polygons

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Question 36 Report

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

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

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Circles

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Question 37 Report

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

<2, 3, 4, 5

3, 4, 5

2, 3, 4

3, 4

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Read lesson note on Inequalities (JAMB)

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Inequalities

Areas

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Question 38 Report

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

x^-a2

x^b2

x^{a2 - b2}

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

x^{b2 - a2}

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Read lesson note on Number Bases (WAEC)

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Number Bases

Algebraic Expressions

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Question 39 Report

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

3.69

10.5

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Modular Arithmetic

Logarithms

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Question 40 Report

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

-1

x - 1

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

3(1 - 5x)

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Algebraic Fractions

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Question 41 Report

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

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

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

None of the above

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Solution Of Linear Equations

Simple Operations On Algebraic Expressions

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Question 42 Report

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰

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Lengths And Perimeters

Logarithms

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Question 43 Report

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

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

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

\(\sqrt{3}\)

4\(\sqrt{3}\)

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Question 44 Report

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

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

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

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

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

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Question 45 Report

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

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Read lesson note on Matrices And Determinants (JAMB)

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Matrices And Determinants

Triangles And Polygons

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Question 46 Report

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520

5.2048

5204

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Read lesson note on Fractions, Decimals And Approximations (WAEC)

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Fractions, Decimals And Approximations

Modular Arithmetic

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Question 47 Report

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

1320cm²

188cm²

188.08cm²

10cm²

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Areas

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Question 48 Report

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

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

(-1)ⁿ\(\frac{n}{2n - 1}\)

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Algebraic Fractions

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Question 49 Report

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