JAMB UTME - Mathematics - 2002

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

Bekijk antwoord

Vraag 12 Verslag

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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Vraag 13 Verslag

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

Bekijk antwoord

Vraag 14 Verslag

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)

Bekijk antwoord

Vraag 15 Verslag

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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Vraag 16 Verslag

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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Vraag 17 Verslag

Evaluate ∫sin 3x dx

(2/3) cos 3x + c

(1/3) cos 3x + c

(-1/3) cos 3x + c

(-2/3) cos 3x + c

Bekijk antwoord

Vraag 18 Verslag

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

Bekijk antwoord

Vraag 19 Verslag

Simplify (√0.7 + √70)2

84.7

70.7

217.7

168.7

Surds (radicals)

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Vraag 20 Verslag

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

Bekijk antwoord

Vraag 21 Verslag

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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Vraag 22 Verslag

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

Bekijk antwoord

Vraag 23 Verslag

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

Antwoorddetails

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.

Lees lesnotitie op Loci (WAEC)

Lees lesnotitie op Circles (WAEC)

Lees lesnotitie op Coordinate Geometry (WAEC)

Loci

Circles

Coordinate Geometry

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Vraag 24 Verslag

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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Vraag 25 Verslag

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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Vraag 26 Verslag

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°

Bekijk antwoord

Vraag 27 Verslag

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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Vraag 28 Verslag

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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Vraag 29 Verslag

Simplify 52.4 - 5.7 - 3.45 - 1.75

41.4

41.5

42.1

42.2

Fractions, Decimals And Approximations

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Vraag 30 Verslag

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

400 cm2

462 cm2

66 cm2

308 cm2

Bekijk antwoord

Vraag 31 Verslag

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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Vraag 32 Verslag

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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Vraag 33 Verslag

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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Vraag 34 Verslag

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

Bekijk antwoord

Vraag 35 Verslag

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}

Antwoorddetails

A

shaded portion

=

π R^{2} - π r^{2}

r =

\frac{2}{5}

R

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

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

Lees lesnotitie op Circles (WAEC)

Circles

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Vraag 36 Verslag

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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Vraag 37 Verslag

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}

Antwoorddetails

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 $π + 18 π = 198 c m^{3}$

Lees lesnotitie op Volumes (WAEC)

Lees lesnotitie op Euclidean Geometry (JAMB)

Volumes

Euclidean Geometry

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Vraag 38 Verslag

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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Vraag 39 Verslag

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

Bekijk antwoord

Vraag 40 Verslag

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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Vraag 41 Verslag

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

Bekijk antwoord

Vraag 42 Verslag

The triangle PQR above is

an obtuse-angled triangle

a scalene triangle

an isosceles triangle

an equilateral triangle

Antwoorddetails

∠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

Lees lesnotitie op Circles (WAEC)

Lees lesnotitie op Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

Bekijk antwoord

Vraag 43 Verslag

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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Vraag 44 Verslag

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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Vraag 45 Verslag

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

2x - (1/x2)

2x + x2

2x - x2

2x + (1/x2)

Differentiation

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Vraag 46 Verslag

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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Vraag 47 Verslag

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