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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Integration (JAMB)

Soma maelezo ya somo kwenye Statistics (WAEC)

Integration

Statistics

Tazama Jibu

Swali 6 Ripoti

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

45^o

90^o

60^o

15^o

30^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles (WAEC)

Angles

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Swali 7 Ripoti

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

Maelezo ya Majibu

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Swali 8 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

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Swali 9 Ripoti

(\(\frac{x^a}{x^b}\))^{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}

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Number Bases

Algebraic Expressions

Tazama Jibu

Swali 10 Ripoti

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

4y = y²

4y + 9y²

4y - 9y²

-4y - 9y²

2y + y²

Maelezo ya Majibu

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Probability

Algebraic Expressions

Tazama Jibu

Swali 11 Ripoti

Write the decimal number 39 to base 2

10011 base 2

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 12 Ripoti

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

(4, 16)

(2, 4)

(4, 1)

(1, 16)

(16, 16)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Surds (radicals)

Quadratic Equations

Tazama Jibu

Swali 13 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Introductory Calculus

Modular Arithmetic

Surds (radicals)

Tazama Jibu

Swali 14 Ripoti

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Sets (WAEC)

Number Bases

Sets

Tazama Jibu

Swali 15 Ripoti

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)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 16 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Solution Of Linear Equations

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 17 Ripoti

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)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Fractions

Tazama Jibu

Swali 18 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 19 Ripoti

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

1:2

1:3

1:4

1:5

1:6

Maelezo ya Majibu

Tazama Jibu

Swali 20 Ripoti

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

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

Maelezo ya Majibu

Tazama Jibu

Swali 21 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 22 Ripoti

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\(\sqrt{a + b}\)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Surds (radicals)

Tazama Jibu

Swali 23 Ripoti

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\(\sqrt{3}\)

Maelezo ya Majibu

Tazama Jibu

Swali 24 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Inequalities (JAMB)

Soma maelezo ya somo kwenye Areas (WAEC)

Inequalities

Areas

Tazama Jibu

Swali 25 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles And Intercepts On Parallel Lines (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

Tazama Jibu

Swali 26 Ripoti

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰

Maelezo ya Majibu

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Soma maelezo ya somo kwenye Logarithms (WAEC)

Lengths And Perimeters

Logarithms

Tazama Jibu

Swali 27 Ripoti

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

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

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

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

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

Maelezo ya Majibu

Tazama Jibu

Swali 28 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Fractions

Tazama Jibu

Swali 29 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 30 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 31 Ripoti

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 32 Ripoti

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

(3, 2)

(-3, 2)

(3, -2)

(-3, -2)

(2, 2)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Indices (WAEC)

Number Bases

Indices

Tazama Jibu

Swali 33 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Triangles And Polygons

Tazama Jibu

Swali 34 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 35 Ripoti

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

log10²

log10⁴

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

None of the above

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Logarithms (WAEC)

Number Bases

Logarithms

Tazama Jibu

Swali 36 Ripoti

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Indices (WAEC)

Number Bases

Indices

Tazama Jibu

Swali 37 Ripoti

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

2cm

3cm

4cm

5cm

6cm

Maelezo ya Majibu

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Mensuration (JAMB)

Volumes

Mensuration

Tazama Jibu

Swali 38 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Trigonometry

Tazama Jibu

Swali 39 Ripoti

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 + \(\frac{5v - 1}{a}\)]

Maelezo ya Majibu

Tazama Jibu

Swali 40 Ripoti

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

Tazama Jibu

Swali 41 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sets (JAMB)

Sets

Tazama Jibu

Swali 42 Ripoti

Write down the number 0.0052048 correct to three significant figures

0.005