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 Ìdáhùn tó tọ́

x varies directly as w

x varies inversely as w

x varies directly as square root of w

Awọn alaye Idahun

Wo Idahun

Ibeere 11 Ìròyìn

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

1 + 2a - 2\(\sqrt{a(1 + a)}\) Ìdáhùn tó tọ́

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Surds (radicals)

Wo Idahun

Ibeere 12 Ìròyìn

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

205 Ìdáhùn tó tọ́

647

2050

6470

64.7

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Ka ìwé ẹ̀kọ́ nípa Number Bases (JAMB)

Surds (radicals)

Number Bases

Wo Idahun

Ibeere 13 Ìròyìn

Write down the number 0.0052048 correct to three significant figures

0.005

0.0052

0.00520 Ìdáhùn tó tọ́

5.2048

5204

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Fractions, Decimals And Approximations

Modular Arithmetic

Wo Idahun

Ibeere 14 Ìròyìn

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 \(\frac{3}{2}\) Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 15 Ìròyìn

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

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

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

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

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

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Wo Idahun

Ibeere 16 Ìròyìn

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 Ìdáhùn tó tọ́

\(\frac{1980}{7}\)cm³

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Wo Idahun

Ibeere 17 Ìròyìn

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 Ìdáhùn tó tọ́

56.2

56.3

6.5

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Ka ìwé ẹ̀kọ́ nípa Statistics (WAEC)

Integration

Statistics

Wo Idahun

Ibeere 18 Ìròyìn

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 Ìdáhùn tó tọ́

75^o

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Ka ìwé ẹ̀kọ́ nípa Sets (JAMB)

Sets

Wo Idahun

Ibeere 19 Ìròyìn

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 Ìdáhùn tó tọ́

3.69

10.5

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Modular Arithmetic

Logarithms

Wo Idahun

Ibeere 20 Ìròyìn

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

135^o or 315^o Ìdáhùn tó tọ́

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

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Ka ìwé ẹ̀kọ́ nípa Trigonometry (JAMB)

Trigonometry

Wo Idahun

Ibeere 21 Ìròyìn

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

49 Ìdáhùn tó tọ́

169

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Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 22 Ìròyìn

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 \(\frac{2}{n + 1}\) Ìdáhùn tó tọ́

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

(-1)ⁿ\(\frac{n}{2n - 1}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Algebraic Fractions (WAEC)

Algebraic Fractions

Wo Idahun

Ibeere 23 Ìròyìn

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 Ìdáhùn tó tọ́

1320cm²

188cm²

188.08cm²

10cm²

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Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Areas

Wo Idahun

Ibeere 24 Ìròyìn

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

8 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Functions And Relations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Solution Of Linear Equations

Functions And Relations

Algebraic Expressions

Wo Idahun

Ibeere 25 Ìròyìn

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

2 Ìdáhùn tó tọ́

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

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Ka ìwé ẹ̀kọ́ nípa Indices (WAEC)

Indices

Wo Idahun

Ibeere 26 Ìròyìn

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 Ìdáhùn tó tọ́

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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Wo Idahun

Ibeere 27 Ìròyìn

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 Ìdáhùn tó tọ́

150^o

None of the above

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Angles And Intercepts On Parallel Lines (WAEC)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

Wo Idahun

Ibeere 28 Ìròyìn

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

1:2

1:3

1:4 Ìdáhùn tó tọ́

1:5

1:6

Awọn alaye Idahun

Wo Idahun

Ibeere 29 Ìròyìn

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

4 Ìdáhùn tó tọ́

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 30 Ìròyìn

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 Ìdáhùn tó tọ́

80^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Triangles And Polygons

Wo Idahun

Ibeere 31 Ìròyìn

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 Ìdáhùn tó tọ́

N144

N100

Awọn alaye Idahun

Wo Idahun

Ibeere 32 Ìròyìn

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

4y = y²

4y + 9y²

4y - 9y² Ìdáhùn tó tọ́

-4y - 9y²

2y + y²

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Probability

Algebraic Expressions

Wo Idahun

Ibeere 33 Ìròyìn

Write the decimal number 39 to base 2

10011 base 2 Ìdáhùn tó tọ́

110111 base 2

111001 base 2

100101 base 2

19.5 base 2

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Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Number Bases

Wo Idahun

Ibeere 34 Ìròyìn

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰ Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Lengths And Perimeters (WAEC)

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Lengths And Perimeters

Logarithms

Wo Idahun

Ibeere 35 Ìròyìn

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 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Introductory Calculus (WAEC)

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Introductory Calculus

Modular Arithmetic

Surds (radicals)

Wo Idahun

Ibeere 36 Ìròyìn

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

2cm

3cm Ìdáhùn tó tọ́

4cm

5cm

6cm

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Volumes (WAEC)

Ka ìwé ẹ̀kọ́ nípa Mensuration (JAMB)

Volumes

Mensuration

Wo Idahun

Ibeere 37 Ìròyìn

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 Ìdáhùn tó tọ́

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

None of the above

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Simple Operations On Algebraic Expressions (WAEC)

Solution Of Linear Equations

Simple Operations On Algebraic Expressions

Wo Idahun

Ibeere 38 Ìròyìn

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 Ìdáhùn tó tọ́

3(1 - 5x)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Algebraic Fractions (WAEC)

Algebraic Fractions

Wo Idahun

Ibeere 39 Ìròyìn

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

<2, 3, 4, 5

3, 4, 5 Ìdáhùn tó tọ́

2, 3, 4

3, 4

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Inequalities (JAMB)

Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Inequalities

Areas

Wo Idahun

Ibeere 40 Ìròyìn

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 Ìdáhùn tó tọ́

N87.48

N75.52

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Ka ìwé ẹ̀kọ́ nípa Financial Arithmetic (WAEC)

Positive And Negative Integers, Rational Numbers

Areas

Financial Arithmetic

Wo Idahun

Ibeere 41 Ìròyìn

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

x + 1

x - 1

No common factor Ìdáhùn tó tọ́

(2x - 1)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 42 Ìròyìn

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

\(\frac{1 - cos x}{sin x}\) Ìdáhùn tó tọ́

1 - cos x

sin x

1 + cos x

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

Awọn alaye Idahun

Wo Idahun

Ibeere 43 Ìròyìn

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 Ìdáhùn tó tọ́

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Matrices And Determinants (JAMB)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Matrices And Determinants

Triangles And Polygons

Wo Idahun

Ibeere 44 Ìròyìn

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 Ìdáhùn tó tọ́

28:105

28:49

56:49

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Mensuration (JAMB)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Mensuration

Triangles And Polygons

Wo Idahun

Ibeere 45 Ìròyìn

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 Ìdáhùn tó tọ́

72^o

30^o

15^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 46 Ìròyìn

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

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

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

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

\(\frac{YZ}{XY}\) Ìdáhùn tó tọ́

Awọn alaye Idahun

Wo Idahun

Ibeere 47 Ìròyìn

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

(4, 16) Ìdáhùn tó tọ́

(2, 4)

(4, 1)

(1, 16)

(16, 16)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Surds (radicals)

Quadratic Equations

Wo Idahun

Ibeere 48 Ìròyìn

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 + \(\frac{2}{2}\)) Ìdáhùn tó tọ́

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 49 Ìròyìn

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 Ìdáhùn tó tọ́