JAMB UTME - Mathematics - 1980

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 4 Report

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰

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Lengths And Perimeters

Logarithms

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Question 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 Report

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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Question 14 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 15 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 16 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 17 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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Surds (radicals)

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Question 18 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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Inequalities

Areas

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Question 19 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 20 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 21 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

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Introductory Calculus

Modular Arithmetic

Surds (radicals)

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Question 22 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 23 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 24 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 25 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 26 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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Fractions, Decimals And Approximations

Modular Arithmetic

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Question 27 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

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Question 28 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 29 Report

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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Question 30 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 31 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 32 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 33 Report

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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Question 34 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 35 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

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Question 36 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 37 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 38 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

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Positive And Negative Integers, Rational Numbers

Areas

Financial Arithmetic

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Question 39 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 40 Report

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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Question 41 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 42 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 43 Report

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

x + 1

x - 1

No common factor

(2x - 1)

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Algebraic Expressions

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Question 44 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 45 Report

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

(4, 16)

(2, 4)

(4, 1)

(1, 16)

(16, 16)

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Surds (radicals)

Quadratic Equations

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Question 46 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 47 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 48 Report

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