JAMB UTME - Mathematics - 1980

Question 1 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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Integration

Statistics

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Question 2 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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Algebraic Expressions

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Question 3 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

56.105

28:105

28:49

56:49

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Mensuration

Triangles And Polygons

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Question 4 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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Trigonometry

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Question 5 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 6 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 7 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

Answer Details

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Inequalities

Areas

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Question 8 Report

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

N87.48

N75.52

Answer Details

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Positive And Negative Integers, Rational Numbers

Areas

Financial Arithmetic

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Question 9 Report

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

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

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

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

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

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Read lesson note on Surds (radicals) (WAEC)

Surds (radicals)

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Question 10 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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Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Question 11 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 12 Report

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

\(\frac{19}{2}\)

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

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Number Bases

Sets

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Question 13 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 14 Report

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 \(\frac{FG}{FH}\)

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

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

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

\(\frac{YZ}{XY}\)

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Question 15 Report

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 16 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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Number Bases

Algebraic Expressions

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Question 17 Report

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

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

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

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

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Number Bases

Indices

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Question 18 Report

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

4y = y²

4y + 9y²

4y - 9y²

-4y - 9y²

2y + y²

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Probability

Algebraic Expressions

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Question 19 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 20 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 21 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 22 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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Matrices And Determinants

Triangles And Polygons

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Question 23 Report

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

Answer Details

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Introductory Calculus

Modular Arithmetic

Surds (radicals)

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Question 24 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 25 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 26 Report

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

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Quadratic Equations

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Question 27 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

Answer Details

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Loci

Euclidean Geometry

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Question 28 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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Indices

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Question 29 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 30 Report

Find the solution of the equation x + 2\(\sqrt{x - 8}\) = 0

(4, 16)

(2, 4)

(4, 1)

(1, 16)

(16, 16)

Answer Details

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Surds (radicals)

Quadratic Equations

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Question 31 Report

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

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

Answer Details

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Quadratic Equations

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Question 32 Report

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520

5.2048

5204

Answer Details

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Fractions, Decimals And Approximations

Modular Arithmetic

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Question 33 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)

Answer Details

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Algebraic Fractions

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Question 34 Report

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

2cm

3cm

4cm

5cm

6cm

Answer Details

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Volumes

Mensuration

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Question 35 Report

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

(3, 2)

(-3, 2)

(3, -2)

(-3, -2)

(2, 2)

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Number Bases

Indices

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Question 36 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 37 Report

If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).

Answer Details

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Solution Of Linear Equations

Functions And Relations

Algebraic Expressions

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Question 38 Report

The angles marked in the figure are measured in degrees. Find x.

45^o

90^o

60^o

15^o

30^o

Answer Details

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Angles

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Question 39 Report

Write the decimal number 39 to base 2

10011 base 2

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

Answer Details

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Number Bases

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Question 40 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

Answer Details

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Modular Arithmetic

Logarithms

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Question 41 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 42 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 43 Report

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

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