JAMB UTME - Mathematics - 2002

Question 1 Report

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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Question 2 Report

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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Question 3 Report

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}

Answer Details

A

shaded portion

=

π R^{2} - π r^{2}

r =

\frac{2}{5}

R

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

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

Read lesson note on Circles (WAEC)

Circles

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Question 4 Report

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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Question 5 Report

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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Question 6 Report

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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Question 7 Report

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}

Answer Details

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 $π + 18 π = 198 c m^{3}$

Read lesson note on Volumes (WAEC)

Read lesson note on Euclidean Geometry (JAMB)

Volumes

Euclidean Geometry

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Question 8 Report

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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Question 9 Report

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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Question 10 Report

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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Question 11 Report

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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Question 12 Report

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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Question 13 Report

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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Question 14 Report

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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Question 15 Report

The triangle PQR above is

an obtuse-angled triangle

a scalene triangle

an isosceles triangle

an equilateral triangle

Answer Details

∠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

Read lesson note on Circles (WAEC)

Read lesson note on Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

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Question 16 Report

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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Question 17 Report

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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Question 18 Report

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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Question 19 Report

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

16/25

24/25

7/25

9/25

Trigonometry

Application Of Differentiation

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Question 20 Report

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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Question 21 Report

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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Question 22 Report

(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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Question 23 Report

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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Question 24 Report

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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Question 25 Report

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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Question 26 Report

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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Question 27 Report

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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Question 28 Report

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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Question 29 Report

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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Question 30 Report

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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Question 31 Report

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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Question 32 Report

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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Question 33 Report

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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Question 34 Report

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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Question 35 Report

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

2x - (1/x2)

2x + x2

2x - x2

2x + (1/x2)

Differentiation

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Question 36 Report

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

21/25πR2

9/25πR2

21/23πR2

5/9πR2

Circles

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Question 37 Report

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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Question 38 Report

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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Question 39 Report

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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Question 40 Report

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

Answer Details

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.

Read lesson note on Loci (WAEC)

Read lesson note on Circles (WAEC)

Read lesson note on Coordinate Geometry (WAEC)

Loci

Circles

Coordinate Geometry

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Question 41 Report

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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Question 42 Report

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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Question 43 Report

Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8.

13/6

5/2

7/6

7/3

Inequalities

Statistics

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Question 44 Report

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