JAMB UTME - Mathematics - 1980

Vraag 1 Verslag

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 Juist antwoord

28:105

28:49

56:49

Antwoorddetails

Lees lesnotitie op Mensuration (JAMB)

Lees lesnotitie op Triangles And Polygons (WAEC)

Mensuration

Triangles And Polygons

Bekijk antwoord

Vraag 2 Verslag

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 Juist antwoord

An arc of a circle passing through P and Q

A circle with diameter PQ

The bisector of angle PXQ

Antwoorddetails

Lees lesnotitie op Loci (WAEC)

Lees lesnotitie op Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

Bekijk antwoord

Vraag 3 Verslag

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 Juist antwoord

1320cm²

188cm²

188.08cm²

10cm²

Antwoorddetails

Lees lesnotitie op Areas (WAEC)

Areas

Bekijk antwoord

Vraag 4 Verslag

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 Juist antwoord

150^o

None of the above

Antwoorddetails

Lees lesnotitie op Angles And Intercepts On Parallel Lines (WAEC)

Lees lesnotitie op Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Vraag 5 Verslag

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 Juist antwoord

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

Antwoorddetails

Bekijk antwoord

Vraag 6 Verslag

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 Juist antwoord

56.2

56.3

6.5

Antwoorddetails

Lees lesnotitie op Integration (JAMB)

Lees lesnotitie op Statistics (WAEC)

Integration

Statistics

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Vraag 7 Verslag

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 Juist antwoord

3(1 - 5x)

Antwoorddetails

Lees lesnotitie op Algebraic Fractions (WAEC)

Algebraic Fractions

Bekijk antwoord

Vraag 8 Verslag

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 Juist antwoord

72^o

30^o

15^o

Antwoorddetails

Lees lesnotitie op Circles (WAEC)

Circles

Bekijk antwoord

Vraag 9 Verslag

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

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

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

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

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

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

Antwoorddetails

Lees lesnotitie op Circles (WAEC)

Circles

Bekijk antwoord

Vraag 10 Verslag

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

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

1 - cos x

sin x

1 + cos x

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

Antwoorddetails

Bekijk antwoord

Vraag 11 Verslag

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

49 Juist antwoord

169

Antwoorddetails

Lees lesnotitie op Logarithms (WAEC)

Logarithms

Bekijk antwoord

Vraag 12 Verslag

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 Juist antwoord

\(\frac{1980}{7}\)cm³

Antwoorddetails

Bekijk antwoord

Vraag 13 Verslag

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

(3, 2) Juist antwoord

(-3, 2)

(3, -2)

(-3, -2)

(2, 2)

Antwoorddetails

Lees lesnotitie op Number Bases (WAEC)

Lees lesnotitie op Indices (WAEC)

Number Bases

Indices

Bekijk antwoord

Vraag 14 Verslag

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 Juist antwoord

80^o

Antwoorddetails

Lees lesnotitie op Triangles And Polygons (WAEC)

Triangles And Polygons

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Vraag 15 Verslag

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

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

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

Antwoorddetails

Lees lesnotitie op Number Bases (WAEC)

Lees lesnotitie op Sets (WAEC)

Number Bases

Sets

Bekijk antwoord

Vraag 16 Verslag

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 Juist antwoord

c = 20 and d = -15

c = -20 and d = 15

Antwoorddetails

Lees lesnotitie op Algebraic Expressions (WAEC)

Algebraic Expressions

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Vraag 17 Verslag

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

log10²

log10⁴

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

None of the above

Antwoorddetails

Lees lesnotitie op Number Bases (WAEC)

Lees lesnotitie op Logarithms (WAEC)

Number Bases

Logarithms

Bekijk antwoord

Vraag 18 Verslag

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

8 Juist antwoord

Antwoorddetails

Lees lesnotitie op Solution Of Linear Equations (WAEC)

Lees lesnotitie op Functions And Relations (WAEC)

Lees lesnotitie op Algebraic Expressions (WAEC)

Solution Of Linear Equations

Functions And Relations

Algebraic Expressions

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Vraag 19 Verslag

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

(4, 16) Juist antwoord

(2, 4)

(4, 1)

(1, 16)

(16, 16)

Antwoorddetails

Lees lesnotitie op Surds (radicals) (WAEC)

Lees lesnotitie op Quadratic Equations (WAEC)

Surds (radicals)

Quadratic Equations

Bekijk antwoord

Vraag 20 Verslag

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

135^o or 315^o Juist antwoord

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

Antwoorddetails

Lees lesnotitie op Trigonometry (JAMB)

Trigonometry

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Vraag 21 Verslag

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 Juist antwoord

N144

N100

Antwoorddetails

Bekijk antwoord

Vraag 22 Verslag

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 Juist antwoord

N87.48

N75.52

Antwoorddetails

Lees lesnotitie op Positive And Negative Integers, Rational Numbers (WAEC)

Lees lesnotitie op Areas (WAEC)

Lees lesnotitie op Financial Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Areas

Financial Arithmetic

Bekijk antwoord

Vraag 23 Verslag

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

2cm

3cm Juist antwoord

4cm

5cm

6cm

Antwoorddetails

Lees lesnotitie op Volumes (WAEC)

Lees lesnotitie op Mensuration (JAMB)

Volumes

Mensuration

Bekijk antwoord

Vraag 24 Verslag

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 Juist antwoord

75^o

Antwoorddetails

Lees lesnotitie op Sets (JAMB)

Sets

Bekijk antwoord

Vraag 25 Verslag

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

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

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

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

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

Antwoorddetails

Bekijk antwoord

Vraag 26 Verslag

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

x^-a2

x^b2

x^{a2 - b2}

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

x^{b2 - a2}

Antwoorddetails

Lees lesnotitie op Number Bases (WAEC)

Lees lesnotitie op Algebraic Expressions (WAEC)

Number Bases

Algebraic Expressions

Bekijk antwoord

Vraag 27 Verslag

Write the decimal number 39 to base 2

10011 base 2 Juist antwoord

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

Antwoorddetails

Lees lesnotitie op Number Bases (WAEC)

Number Bases

Bekijk antwoord

Vraag 28 Verslag

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 Juist antwoord

Antwoorddetails

Lees lesnotitie op Matrices And Determinants (JAMB)

Lees lesnotitie op Triangles And Polygons (WAEC)

Matrices And Determinants

Triangles And Polygons

Bekijk antwoord

Vraag 29 Verslag

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

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

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

\(\sqrt{3}\)

4\(\sqrt{3}\)

Antwoorddetails

Bekijk antwoord

Vraag 30 Verslag

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

2 Juist antwoord

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

Antwoorddetails

Lees lesnotitie op Indices (WAEC)

Indices

Bekijk antwoord

Vraag 31 Verslag

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰ Juist antwoord

Antwoorddetails

Lees lesnotitie op Lengths And Perimeters (WAEC)

Lees lesnotitie op Logarithms (WAEC)

Lengths And Perimeters

Logarithms

Bekijk antwoord

Vraag 32 Verslag

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 Juist antwoord

3.69

10.5

Antwoorddetails

Lees lesnotitie op Modular Arithmetic (WAEC)

Lees lesnotitie op Logarithms (WAEC)

Modular Arithmetic

Logarithms

Bekijk antwoord

Vraag 33 Verslag

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

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

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

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

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

Antwoorddetails

Bekijk antwoord

Vraag 34 Verslag

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

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

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

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

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

Antwoorddetails

Lees lesnotitie op Surds (radicals) (WAEC)

Surds (radicals)

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Vraag 35 Verslag

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

x + 1

x - 1

No common factor Juist antwoord

(2x - 1)

Antwoorddetails

Lees lesnotitie op Algebraic Expressions (WAEC)

Algebraic Expressions

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Vraag 36 Verslag

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

205 Juist antwoord

647

2050

6470

64.7

Antwoorddetails

Lees lesnotitie op Surds (radicals) (WAEC)

Lees lesnotitie op Number Bases (JAMB)

Surds (radicals)

Number Bases

Bekijk antwoord

Vraag 37 Verslag

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

1:2

1:3

1:4 Juist antwoord

1:5

1:6

Antwoorddetails

Bekijk antwoord

Vraag 38 Verslag

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

45^o

90^o

60^o

15^o

30^o Juist antwoord

Antwoorddetails

Lees lesnotitie op Angles (WAEC)

Angles

Bekijk antwoord

Vraag 39 Verslag

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

Antwoorddetails

Lees lesnotitie op Quadratic Equations (WAEC)

Quadratic Equations

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Vraag 40 Verslag

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

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

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

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

Antwoorddetails

Lees lesnotitie op Number Bases (WAEC)

Lees lesnotitie op Indices (WAEC)

Number Bases

Indices

Bekijk antwoord

Vraag 41 Verslag

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520 Juist antwoord

5.2048

5204

Antwoorddetails

Lees lesnotitie op Fractions, Decimals And Approximations (WAEC)

Lees lesnotitie op Modular Arithmetic (WAEC)

Fractions, Decimals And Approximations

Modular Arithmetic

Bekijk antwoord

Vraag 42 Verslag

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

<2, 3, 4, 5

3, 4, 5 Juist antwoord

2, 3, 4

3, 4

Antwoorddetails

Lees lesnotitie op Inequalities (JAMB)

Lees lesnotitie op Areas (WAEC)

Inequalities

Areas

Bekijk antwoord

Vraag 43 Verslag

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 Juist antwoord

Antwoorddetails

Lees lesnotitie op Introductory Calculus (WAEC)

Lees lesnotitie op Modular Arithmetic (WAEC)

Lees lesnotitie op Surds (radicals) (WAEC)

Introductory Calculus

Modular Arithmetic

Surds (radicals)

Bekijk antwoord

Vraag 44 Verslag

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 Juist antwoord

x varies directly as w

x varies inversely as w

x varies directly as square root of w

Antwoorddetails

Bekijk antwoord

Vraag 45 Verslag

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

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

Antwoorddetails

Lees lesnotitie op Circles (WAEC)

Circles

Bekijk antwoord

Vraag 46 Verslag

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

4 Juist antwoord

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

Antwoorddetails

Lees lesnotitie op Quadratic Equations (WAEC)

Quadratic Equations

Bekijk antwoord

Vraag 47 Verslag

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

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

(-1)ⁿ\(\frac{n}{2n - 1}\)

Antwoorddetails

Lees lesnotitie op Algebraic Fractions (WAEC)

Algebraic Fractions

Bekijk antwoord

Vraag 48 Verslag

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

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