JAMB UTME - Mathematics - 2002

Pregunta 1 Informe

How many three-digit numbers can be formed from 32564 without repeating any of the digits?

120

10

20

60

Permutation And Combination

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Pregunta 2 Informe

If the 9th term of an A.P is five times the 5th term, find the relationship between a and d.

2a + 2 = 0

3a + 5d = 0

a + 3d = 0

a + 2d = 0

Solution Of Linear Equations

Sequence And Series

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Pregunta 3 Informe

Find the derivative of y = sin2(5x) with respect to x.

10 sin 5x cos 5x

5 sin5x cos 5x

2 sin 5x cos 5x

15 sin 5x cos 5x

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Pregunta 4 Informe

Find the coordinates of the mid-point of x and y intercepts of the line 2y = 4x - 8

(2, 0)

(1, -2)

(-1, -2)

(1, 2)

Coordinate Geometry

Graphs Of Linear And Quadratic Functions

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Pregunta 5 Informe

In the diagram, XZ is the diameter of the circle XYZW, with centre O and radius $ \frac{15}{2} $cm. If XY = 12cm, find the area of the triangle XYZ

45cm3

27cm3

75cm3

54cm3

Circles

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Pregunta 6 Informe

The locus of a point P which is equidistant from two given points S and T is

the perpendicular bisector of ST

the angle bisector of PS and ST

a perpendicular to ST

a line parallel to ST

Loci

Euclidean Geometry

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Pregunta 7 Informe

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = $72^\circ$, find x

36

^{\circ}

18

^{\circ}

72

^{\circ}

24

^{\circ}

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Pregunta 8 Informe

Find the range of values of x for which $ \frac{(x+2)}{4}-\frac{2x-3}{3}<4 $

x > -6

x > -3

x < 8

x < 4

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Pregunta 9 Informe

Make $r$ subject of the formula given that $\frac{x}{r+a}=\frac{a}{r}$

\frac{a^{2}}{(x - a)}

\frac{a^{2}}{(x + a)}

\frac{a}{x - a}

\frac{a}{x + a}

Introductory Calculus

Change Of Subject Of A Formula/Relation

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Pregunta 10 Informe

Find the mean of the data: 7, -3, 4, -2, 5, -9, 4, 8, -6, 12

3

4

2

1

Probability

Statistics

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Pregunta 11 Informe

In the diagram, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid

198

π c m^{3}

180

π c m^{3}

162

π c m^{3}

216

π c m^{3}

Detalles de la respuesta

V =

π r^{2} h + \frac{2}{3} π r^{3}

N.B h = r

V = $π x (3)^{2}$ x 20 = $\frac{2}{3} \times π \times (3)^{3}$

180 $π + 18 π = 198 c m^{3}$

Lee la nota de la lección en Volumes (WAEC)

Lee la nota de la lección en Euclidean Geometry (JAMB)

Volumes

Euclidean Geometry

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Pregunta 12 Informe

Solve for x in the equation x3 - 5x2 - x + 5 = 0

1, - 1, or 5

1, 1, or -5

-1, 1, or -5

1, 1, or 5

Solution Of Linear Equations

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Pregunta 13 Informe

The triangle PQR above is

an obtuse-angled triangle

a scalene triangle

an isosceles triangle

an equilateral triangle

Detalles de la respuesta

∠PQR = 180 - 128 (∠s on a straight line)
= 52

^{\circ}

∠QPR + 76 + 52 = 180(extr ∠ = sum of intr. opp ∠s)
∠QPR + 128 = 180
∠QPR = 180 - 128
= 52

^{\circ}

∴ΔPQR is an isosceles triangle

Lee la nota de la lección en Circles (WAEC)

Lee la nota de la lección en Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

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Pregunta 14 Informe

(0.21 x 0.072 x 0.00054) (0.006 x 1.68 x 0.063), correct to 4.s.f

0.01286

0.01285

0.1286

0.1285

Fractions, Decimals And Approximations

Percentages

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Pregunta 15 Informe

Using the graph find the values of $p$ and $q$ if $px + qy \ge 4$

p = 2, q = -1

p = -1, q = 2

p = 2, q = 2

p = 1, q = 2

Detalles de la respuesta

m =

\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{2 - 0}{0 - (4)} = \frac{2}{4} = \frac{1}{2}

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} \geq m$

$\frac{y - 0}{x + 4} \geq \frac{1}{2}$

2y $\geq$ x + 4, -x + 2y $\geq$ 4 = px + qy $\geq$ 4

p = -1, q = 2

Lee la nota de la lección en Solution Of Linear Equations (WAEC)

Lee la nota de la lección en Algebraic Expressions (WAEC)

Lee la nota de la lección en Graphs Of Linear And Quadratic Functions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

Graphs Of Linear And Quadratic Functions

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Pregunta 16 Informe

A chord of a circle subtends an angle of 12o degrees at the centre of a circle of diameter 4√3 cm. Calculate the area of the major sector.

4π cm2

32 π cm2

16 π cm2

8 π cm2

Circles

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Pregunta 17 Informe

A solid hemisphere has a radius of 7 cm. Find the total surface area.

400 cm2

462 cm2

66 cm2

308 cm2

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Pregunta 18 Informe

In the diagram are two concentric circles of radii r and R respectively with centre O. If $r = \frac{2}{5}R$, express the area of the shaded portion in terms of $\pi$ and R

\frac{5}{9} π R^{2}

\frac{21}{25} π R^{2}

\frac{21}{23} π R^{2}

\frac{9}{25} π R^{2}

Detalles de la respuesta

A

shaded portion

=

π R^{2} - π r^{2}

r =

\frac{2}{5}

R

A $shaded portion$ = $π R^{2} - π (\frac{2}{3} R)^{2} = π R^{2} - \frac{4 π R^{2}}{25}$

= $π R^{2} (1 - \frac{2}{3}) = \frac{21}{25} π R^{2}$

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Circles

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Pregunta 19 Informe

If dy/dx = 2x - 3 and y = 3 when x = 0, find y in terms of x.

2x2 - 3x

x2 - 3x

x2 - 3x - 3

x2 - 3x + 3

Differentiation

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Pregunta 20 Informe

The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is

11/3

10/3

5/2

3/2

Sequence And Series

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Pregunta 21 Informe

In the diagram above, a cylinder is summounted by a hemisphere bowl. Calculate the volume of the solid.

180 πcm3

162 πcm3

216 πcm3

198 πcm3

Volumes

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Pregunta 22 Informe

Simplify $ \frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right) $

\frac{4}{5}

\frac{7}{10}

\frac{6}{6}

\frac{21}{6}

Fractions, Decimals And Approximations

Number Bases

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Pregunta 23 Informe

A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?

2π

5π

π

4π

Circles

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Pregunta 24 Informe

The probability of a student passing any examination is 2/3. If the students takes three examination, what is the probability that he will not pass any of them

2/3

4/9

8/27

1/27

Probability

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Pregunta 25 Informe

The range of the data: k+2, k-3, k+4, k-2, k, k-5, k+3, k-1, and k+6 is

10

11

6

8

Sets

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Pregunta 26 Informe

If tan θ = 4/3, calculate sin2θ - cos2θ.

16/25

24/25

7/25

9/25

Trigonometry

Application Of Differentiation

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Pregunta 27 Informe

The slope of the tangent to the curve $y = 2x^2 - 2x + 5$ at the point $(1, 6)$ is

4

1

6

5

3

Introductory Calculus

Trigonometry

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Pregunta 28 Informe

The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

12

20

40

10

Mensuration

Triangles And Polygons

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Pregunta 29 Informe

The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?

15 days

12 days

5 days

9 days

Variation

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Pregunta 30 Informe

If y = x2 - (1/x). find dy/dx

2x - (1/x2)

2x + x2

2x - x2

2x + (1/x2)

Differentiation

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Pregunta 31 Informe

In the diagram PQ is parallel to RS. What is the value of $ \alpha + \beta + \gamma $

180

^{\circ}

90

^{\circ}

360

^{\circ}

200

^{\circ}

Angles And Intercepts On Parallel Lines

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Pregunta 32 Informe

Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7

y = 3

x = 3

x = 4

y = 4

Detalles de la respuesta

To find the set of points which are equidistant from the parallel lines x=1 and x=7, we can begin by finding the midpoint of the segment connecting the two parallel lines. The midpoint of the segment joining the two parallel lines is ((1+7)/2, 0) = (4,0). Now, let (x,y) be any point that is equidistant from the two parallel lines. Then, the distance from (x,y) to the line x=1 is |x-1|, and the distance from (x,y) to the line x=7 is |x-7|. Since the point (x,y) is equidistant from the two lines, we have: |x-1| = |x-7| Solving for x, we get: x-1 = -(x-7) or x-1 = x-7 Solving each equation for x, we get: x = 4 or x = -6 Since the distance from (x,y) to x=1 is the same as the distance from (x,y) to x=7, it follows that the set of points that are equidistant from the two parallel lines is the vertical line passing through the midpoint of the segment joining the two parallel lines, namely, the line x=4. Therefore, the equation of the set of points which are equidistant from the parallel lines x=1 and x=7 is x = 4. Thus, the correct option is x = 4.

Lee la nota de la lección en Loci (WAEC)

Lee la nota de la lección en Circles (WAEC)

Lee la nota de la lección en Coordinate Geometry (WAEC)

Loci

Circles

Coordinate Geometry

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Pregunta 33 Informe

Find the maximum value of y in the equation y = 1 - 2x - 3x2

5/4

5/3

3/4

4/3

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Quadratic Equations

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Pregunta 34 Informe

A hunter 1.6 m tall, views a bird on top of a tree at an angle of 45 degrees. if the distance between the hunter and the tree is 10.4 m, find the height of the tree.

9.0 m

12. 0 m

8.8 m

10.4 m

Coordinate Geometry

Number Bases

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Pregunta 35 Informe

The inverse function f(x) = 3x + 4 is

(x-4)/3

(x-5)/5

(x+3)/4

(x+4)/3

Logarithms

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Pregunta 36 Informe

The ninary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2 * (3 * 4).

59

19

67

38

Binary Operations

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Pregunta 37 Informe

The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set.

105

100

95

110

Integration

Euclidean Geometry

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Pregunta 38 Informe

The acres for rice, pineapple, cassava, cocoa, and palm oil in a certain district are given respectively as 2, 5, 3, 11, and 9. What is the angle sector for cassava in a pie chart?

108°

180°

36°

60°

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Pregunta 39 Informe

Find the value of a if the line 2y - ax + 4 = 0 is perpendicular to the line y + (x/4) - 7 = 0

-4

4

8

-8

Algebraic Expressions

Application Of Differentiation

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Pregunta 40 Informe

The venn diagram above shows the numbers of students offering music and history in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?

0.38

0.13

0.50

0.25

Sets

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Pregunta 41 Informe

A bucket is 12 cm in diameter at the top, 8 cm in diameterat the bottom and 4 cm deep. Calculate its volume.

304π/3 cm3

144π cm3

128π cm3

72π cm3

Volumes

Areas

Angles

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Pregunta 42 Informe

Evaluate ∫sin 3x dx

(2/3) cos 3x + c

(1/3) cos 3x + c

(-1/3) cos 3x + c

(-2/3) cos 3x + c

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Pregunta 43 Informe

Without using tables, evaluate (343)1/3 x (

0.14)-1 x (25)-1/2

10

12

8

7

Number Bases

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Pregunta 44 Informe

Simplify (√0.7 + √70)2

84.7

70.7

217.7

168.7

Surds (radicals)

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Pregunta 45 Informe

In a school, 220 students offer Biology or Mathematics or both, 125 offer Biology and 110 Mathematics. How many offer Biology but not Mathematics?

95

80

125

110

120

Sets

Surds (radicals)

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Pregunta 46 Informe

In the diagram above, $XZ$ is the diameter of the circle $XZW$, with center $O$ and radius $15/2$ cm. If $XY = 12$ cm, find the area of the triangle $XYZ$

54 cm2

45 cm2

27 cm2

75 cm2

Circles

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Pregunta 47 Informe

A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy?

60

50

45

36

Fractions, Decimals And Approximations

Ratio, Proportions And Rates

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Pregunta 48 Informe

In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of π and R