JAMB UTME - Mathematics - 1980

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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Pregunta 19 Informe

Find, correct to three significant figures, the value of \(\sqrt{41830}\).

205

647

2050

6470

64.7

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Surds (radicals)

Number Bases

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Pregunta 20 Informe

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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Pregunta 21 Informe

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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Pregunta 22 Informe

(\(\frac{x^a}{x^b}\))^{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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Pregunta 23 Informe

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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Pregunta 24 Informe

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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Pregunta 25 Informe

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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Pregunta 26 Informe

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

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Pregunta 27 Informe

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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Pregunta 28 Informe

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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Pregunta 29 Informe

Simplify \(\frac{log_{10}8}{log_{10}4}\)

log10²

log10⁴

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

None of the above

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Number Bases

Logarithms

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Pregunta 30 Informe

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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Inequalities

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Pregunta 31 Informe

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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Pregunta 32 Informe

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

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Pregunta 33 Informe

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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Pregunta 34 Informe

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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Pregunta 35 Informe

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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Pregunta 36 Informe

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

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Introductory Calculus

Modular Arithmetic

Surds (radicals)

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Pregunta 37 Informe

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

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

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Pregunta 38 Informe

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

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Pregunta 39 Informe

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

169

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Logarithms

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Pregunta 40 Informe

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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Pregunta 41 Informe

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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Pregunta 42 Informe

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

45^o

90^o

60^o

15^o

30^o

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Angles

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Pregunta 43 Informe

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

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Pregunta 44 Informe

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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Pregunta 45 Informe

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