JAMB UTME - Mathematics - 1980

Frage 1 Bericht

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

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

(-1)ⁿ\(\frac{n}{2n - 1}\)

Antwortdetails

Lies die Unterrichtsnotiz zu Algebraic Fractions (WAEC)

Algebraic Fractions

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Frage 2 Bericht

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

x + 1

x - 1

No common factor Richtige Antwort

(2x - 1)

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Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 3 Bericht

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

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

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

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

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

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Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Surds (radicals)

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Frage 4 Bericht

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 Richtige Antwort

150^o

None of the above

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Lies die Unterrichtsnotiz zu Angles And Intercepts On Parallel Lines (WAEC)

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Frage 5 Bericht

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

x^-a2

x^b2

x^{a2 - b2}

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

x^{b2 - a2}

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Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Number Bases

Algebraic Expressions

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Frage 6 Bericht

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 Richtige Antwort

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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Frage 7 Bericht

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 Richtige Antwort

c = 20 and d = -15

c = -20 and d = 15

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Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 8 Bericht

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

45^o

90^o

60^o

15^o

30^o Richtige Antwort

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Lies die Unterrichtsnotiz zu Angles (WAEC)

Angles

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Frage 9 Bericht

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

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

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

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

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

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Frage 10 Bericht

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 Richtige Antwort

N87.48

N75.52

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Lies die Unterrichtsnotiz zu Positive And Negative Integers, Rational Numbers (WAEC)

Lies die Unterrichtsnotiz zu Areas (WAEC)

Lies die Unterrichtsnotiz zu Financial Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Areas

Financial Arithmetic

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Frage 11 Bericht

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

4 Richtige Antwort

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

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Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Quadratic Equations

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Frage 12 Bericht

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 Richtige Antwort

\(\frac{1980}{7}\)cm³

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Frage 13 Bericht

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

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

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

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

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Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Indices (WAEC)

Number Bases

Indices

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Frage 14 Bericht

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

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Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Quadratic Equations

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Frage 15 Bericht

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 Richtige Antwort

75^o

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Lies die Unterrichtsnotiz zu Sets (JAMB)

Sets

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Frage 16 Bericht

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 Richtige Antwort

56.2

56.3

6.5

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Lies die Unterrichtsnotiz zu Integration (JAMB)

Lies die Unterrichtsnotiz zu Statistics (WAEC)

Integration

Statistics

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Frage 17 Bericht

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

49 Richtige Antwort

169

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Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Logarithms

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Frage 18 Bericht

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 Richtige Antwort

3(1 - 5x)

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Lies die Unterrichtsnotiz zu Algebraic Fractions (WAEC)

Algebraic Fractions

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Frage 19 Bericht

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 Richtige Antwort

An arc of a circle passing through P and Q

A circle with diameter PQ

The bisector of angle PXQ

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Lies die Unterrichtsnotiz zu Loci (WAEC)

Lies die Unterrichtsnotiz zu Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

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Frage 20 Bericht

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 Richtige Antwort

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Lies die Unterrichtsnotiz zu Introductory Calculus (WAEC)

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Introductory Calculus

Modular Arithmetic

Surds (radicals)

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Frage 21 Bericht

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

2cm

3cm Richtige Antwort

4cm

5cm

6cm

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Lies die Unterrichtsnotiz zu Volumes (WAEC)

Lies die Unterrichtsnotiz zu Mensuration (JAMB)

Volumes

Mensuration

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Frage 22 Bericht

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

205 Richtige Antwort

647

2050

6470

64.7

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Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Lies die Unterrichtsnotiz zu Number Bases (JAMB)

Surds (radicals)

Number Bases

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Frage 23 Bericht

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520 Richtige Antwort

5.2048

5204

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Lies die Unterrichtsnotiz zu Fractions, Decimals And Approximations (WAEC)

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Fractions, Decimals And Approximations

Modular Arithmetic

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Frage 24 Bericht

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

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

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

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Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Sets (WAEC)

Number Bases

Sets

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Frage 25 Bericht

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 Richtige Antwort

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

None of the above

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Lies die Unterrichtsnotiz zu Solution Of Linear Equations (WAEC)

Lies die Unterrichtsnotiz zu Simple Operations On Algebraic Expressions (WAEC)

Solution Of Linear Equations

Simple Operations On Algebraic Expressions

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Frage 26 Bericht

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

135^o or 315^o Richtige Antwort

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

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Lies die Unterrichtsnotiz zu Trigonometry (JAMB)

Trigonometry

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Frage 27 Bericht

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

(4, 16) Richtige Antwort

(2, 4)

(4, 1)

(1, 16)

(16, 16)

Antwortdetails

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Surds (radicals)

Quadratic Equations

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Frage 28 Bericht

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 Richtige Antwort

x varies directly as w

x varies inversely as w

x varies directly as square root of w

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Frage 29 Bericht

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

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

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

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

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

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

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Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 30 Bericht

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

4y = y²

4y + 9y²

4y - 9y² Richtige Antwort

-4y - 9y²

2y + y²

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Lies die Unterrichtsnotiz zu Probability (WAEC)

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Probability

Algebraic Expressions

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Frage 31 Bericht

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 Richtige Antwort

N144

N100

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Frage 32 Bericht

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 Richtige Antwort

72^o

30^o

15^o

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Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 33 Bericht

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰ Richtige Antwort

Antwortdetails

Lies die Unterrichtsnotiz zu Lengths And Perimeters (WAEC)

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Lengths And Perimeters

Logarithms

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Frage 34 Bericht

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

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

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

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

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

Antwortdetails

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Frage 35 Bericht

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

1:2

1:3

1:4 Richtige Antwort

1:5

1:6

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Frage 36 Bericht

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

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

1 - cos x

sin x

1 + cos x

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

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Frage 37 Bericht

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 Richtige Antwort

80^o

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Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Triangles And Polygons

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Frage 38 Bericht

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

8 Richtige Antwort

Antwortdetails

Lies die Unterrichtsnotiz zu Solution Of Linear Equations (WAEC)

Lies die Unterrichtsnotiz zu Functions And Relations (WAEC)

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Solution Of Linear Equations

Functions And Relations

Algebraic Expressions

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Frage 39 Bericht

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

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

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

\(\sqrt{3}\)

4\(\sqrt{3}\)

Antwortdetails

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Frage 40 Bericht

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 Richtige Antwort

28:105

28:49

56:49

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Lies die Unterrichtsnotiz zu Mensuration (JAMB)

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Mensuration

Triangles And Polygons

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Frage 41 Bericht

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 Richtige Antwort

3.69

10.5

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Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Modular Arithmetic

Logarithms

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Frage 42 Bericht

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

log10²

log10⁴

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

None of the above

Antwortdetails

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Number Bases

Logarithms

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Frage 43 Bericht

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

<2, 3, 4, 5

3, 4, 5 Richtige Antwort

2, 3, 4

3, 4

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Lies die Unterrichtsnotiz zu Inequalities (JAMB)

Lies die Unterrichtsnotiz zu Areas (WAEC)

Inequalities

Areas

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Frage 44 Bericht

Write the decimal number 39 to base 2

10011 base 2 Richtige Antwort

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

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Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Number Bases

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Frage 45 Bericht

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

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

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Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 46 Bericht

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

(3, 2) Richtige Antwort

(-3, 2)