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 Amsar da ta dace

x varies directly as w

x varies inversely as w

x varies directly as square root of w

Bayanin Amsa

Duba Amsa

Tambaya 8 Rahoto

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

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

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

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

\(\frac{YZ}{XY}\) Amsar da ta dace

Bayanin Amsa

Duba Amsa

Tambaya 9 Rahoto

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 Amsar da ta dace

28:105

28:49

56:49

Bayanin Amsa

Karanta bayanin darasi akan Mensuration (JAMB)

Karanta bayanin darasi akan Triangles And Polygons (WAEC)

Mensuration

Triangles And Polygons

Duba Amsa

Tambaya 10 Rahoto

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

1 + 2a - 2\(\sqrt{a(1 + a)}\) Amsar da ta dace

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

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

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

Bayanin Amsa

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Surds (radicals)

Duba Amsa

Tambaya 11 Rahoto

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

<2, 3, 4, 5

3, 4, 5 Amsar da ta dace

2, 3, 4

3, 4

Bayanin Amsa

Karanta bayanin darasi akan Inequalities (JAMB)

Karanta bayanin darasi akan Areas (WAEC)

Inequalities

Areas

Duba Amsa

Tambaya 12 Rahoto

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

135^o or 315^o Amsar da ta dace

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

Bayanin Amsa

Karanta bayanin darasi akan Trigonometry (JAMB)

Trigonometry

Duba Amsa

Tambaya 13 Rahoto

Write the decimal number 39 to base 2

10011 base 2 Amsar da ta dace

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Number Bases

Duba Amsa

Tambaya 14 Rahoto

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 Amsar da ta dace

3(1 - 5x)

Bayanin Amsa

Karanta bayanin darasi akan Algebraic Fractions (WAEC)

Algebraic Fractions

Duba Amsa

Tambaya 15 Rahoto

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 \(\frac{2}{n + 1}\) Amsar da ta dace

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

(-1)ⁿ\(\frac{n}{2n - 1}\)

Bayanin Amsa

Karanta bayanin darasi akan Algebraic Fractions (WAEC)

Algebraic Fractions

Duba Amsa

Tambaya 16 Rahoto

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

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

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

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

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

Bayanin Amsa

Duba Amsa

Tambaya 17 Rahoto

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 Amsar da ta dace

N144

N100

Bayanin Amsa

Duba Amsa

Tambaya 18 Rahoto

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 Amsar da ta dace

75^o

Bayanin Amsa

Karanta bayanin darasi akan Sets (JAMB)

Sets

Duba Amsa

Tambaya 19 Rahoto

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

8 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Solution Of Linear Equations (WAEC)

Karanta bayanin darasi akan Functions And Relations (WAEC)

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Solution Of Linear Equations

Functions And Relations

Algebraic Expressions

Duba Amsa

Tambaya 20 Rahoto

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 Amsar da ta dace

80^o

Bayanin Amsa

Karanta bayanin darasi akan Triangles And Polygons (WAEC)

Triangles And Polygons

Duba Amsa

Tambaya 21 Rahoto

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

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

\(\frac{4}{\sqrt{3}}\) Amsar da ta dace

\(\sqrt{3}\)

4\(\sqrt{3}\)

Bayanin Amsa

Duba Amsa

Tambaya 22 Rahoto

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 Amsar da ta dace

72^o

30^o

15^o

Bayanin Amsa

Karanta bayanin darasi akan Circles (WAEC)

Circles

Duba Amsa

Tambaya 23 Rahoto

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 Amsar da ta dace

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

Bayanin Amsa

Duba Amsa

Tambaya 24 Rahoto

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

45^o

90^o

60^o

15^o

30^o Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Angles (WAEC)

Angles

Duba Amsa

Tambaya 25 Rahoto

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

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

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

\(\frac{9}{4}\) Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Indices (WAEC)

Number Bases

Indices

Duba Amsa

Tambaya 26 Rahoto

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

x^-a2

x^b2

x^{a2 - b2}

\(\frac{1}{x^{a2 + b2}}\) Amsar da ta dace

x^{b2 - a2}

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Number Bases

Algebraic Expressions

Duba Amsa

Tambaya 27 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Matrices And Determinants (JAMB)

Karanta bayanin darasi akan Triangles And Polygons (WAEC)

Matrices And Determinants

Triangles And Polygons

Duba Amsa

Tambaya 28 Rahoto

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

2 Amsar da ta dace

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

Bayanin Amsa

Karanta bayanin darasi akan Indices (WAEC)

Indices

Duba Amsa

Tambaya 29 Rahoto

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520 Amsar da ta dace

5.2048

5204

Bayanin Amsa

Karanta bayanin darasi akan Fractions, Decimals And Approximations (WAEC)

Karanta bayanin darasi akan Modular Arithmetic (WAEC)

Fractions, Decimals And Approximations

Modular Arithmetic

Duba Amsa

Tambaya 30 Rahoto

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 Amsar da ta dace

\(\frac{1980}{7}\)cm³

Bayanin Amsa

Duba Amsa

Tambaya 31 Rahoto

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 Amsar da ta dace

c = 20 and d = -15

c = -20 and d = 15

Bayanin Amsa

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 32 Rahoto

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰ Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Lengths And Perimeters (WAEC)

Karanta bayanin darasi akan Logarithms (WAEC)

Lengths And Perimeters

Logarithms

Duba Amsa

Tambaya 33 Rahoto

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

log10²

log10⁴

\(\frac{3}{2}\) Amsar da ta dace

None of the above

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Logarithms (WAEC)

Number Bases

Logarithms

Duba Amsa

Tambaya 34 Rahoto

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 \(\frac{3}{2}\) Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Quadratic Equations (WAEC)

Quadratic Equations

Duba Amsa

Tambaya 35 Rahoto

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 Amsar da ta dace

56.2

56.3

6.5

Bayanin Amsa

Karanta bayanin darasi akan Integration (JAMB)

Karanta bayanin darasi akan Statistics (WAEC)

Integration

Statistics

Duba Amsa

Tambaya 36 Rahoto

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 Amsar da ta dace

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

None of the above

Bayanin Amsa

Karanta bayanin darasi akan Solution Of Linear Equations (WAEC)

Karanta bayanin darasi akan Simple Operations On Algebraic Expressions (WAEC)

Solution Of Linear Equations

Simple Operations On Algebraic Expressions

Duba Amsa

Tambaya 37 Rahoto

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

\(\frac{1 - cos x}{sin x}\) Amsar da ta dace

1 - cos x

sin x

1 + cos x

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

Bayanin Amsa

Duba Amsa

Tambaya 38 Rahoto

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

2cm

3cm Amsar da ta dace

4cm

5cm

6cm

Bayanin Amsa

Karanta bayanin darasi akan Volumes (WAEC)

Karanta bayanin darasi akan Mensuration (JAMB)

Volumes

Mensuration

Duba Amsa

Tambaya 39 Rahoto

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

4y = y²

4y + 9y²

4y - 9y² Amsar da ta dace

-4y - 9y²

2y + y²

Bayanin Amsa

Karanta bayanin darasi akan Probability (WAEC)

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Probability

Algebraic Expressions

Duba Amsa

Tambaya 40 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Introductory Calculus (WAEC)

Karanta bayanin darasi akan Modular Arithmetic (WAEC)

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Introductory Calculus

Modular Arithmetic

Surds (radicals)

Duba Amsa

Tambaya 41 Rahoto

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 + \(\frac{2}{2}\)) Amsar da ta dace

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

Bayanin Amsa

Karanta bayanin darasi akan Circles (WAEC)

Circles

Duba Amsa

Tambaya 42 Rahoto

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

(3, 2) Amsar da ta dace

(-3, 2)