JAMB UTME - Mathematics - 2003

Question 1 Report

Evaluate $ \int_{3}^{2}(x^2-2x)\,dx $

4

2

4/3

1/3

Representation Of Data

Integration

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Question 2 Report

Simplify 1 - (7/3 x 5/4) + 2/5

-16/15

-79/60

-37/15

-151/60

Fractions, Decimals And Approximations

Number Bases

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Question 3 Report

Simplify (√98 -√50)/√32

3

1

1/2

1/4

Number Bases

Modular Arithmetic

Surds (radicals)

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Question 4 Report

The locus of a point P which moves on one side only of a straight line XY so that ∠XPY = $90^\circ$ is

a circle

a semicircle

an arc of a circle through X, Y

the perpendicular bisector of XY

Coordinate Geometry

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Question 5 Report

Three consecutive terms of a geometric progression are given as n-2, n and n=3. Find the common ratio

1/4

1/2

2/3

3/2

Sequence And Series

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Question 6 Report

A triangle has vertices P(-1,6), Q(-3, -4) and R(1, -4).Find the midpoint of PQ and QR respectively.

(0,-2) and (-1, -4)

(-1,0) and (-1,-1)

(-2,1) and (0,1)

(-2,1) and (-1,-4)

Coordinate Geometry

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Question 7 Report

Triangle OPQ is the solution of the inequalities

x - 1 < 0, y +

\geq

0, y - x

\geq

0

x + 1

\leq

0, y + x

\geq

0, y - x

\leq

0

x - 1

\geq

0, y - x

\geq

0, y + x

\geq

0

y + x

\geq

0, y - x

\leq

0

Linear Inequalities

Inequalities

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Question 8 Report

Given:

U = {Even numbers between 0 and 30}

P = {Multiples of 6 between 0 and 30}

Q = {Multiples of 4 between 0 and 30}

Find (P∪Q)c

{2, 10, 14, 22, 26}

{0, 10, 14, 22, 26}

{2,4, 14, 18, 26}

{0, 2, 6, 22, 26}

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Question 9 Report

The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24,21 and 16 is

16

21

23

24

Sets

Sequence And Series

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Question 10 Report

In the diagram, STUV is a straight line. < TSY = < UXY = 40o and < VUW = 110o. Calculate < TYW

150o

140o

130o

120o

Answer Details

< TUW = 110

^{\circ}

= 180

^{\circ}

(< s on a straight line)
< TUW = 180

^{\circ}

- 110

^{\circ}

= 70

^{\circ}

In

△

XTU, < XUT + < TXU = 180

^{\circ}

i.e. < YTS + 70

^{\circ}

= 180
< XTU = 180 - 110

^{\circ}

= 70

^{\circ}

Also < YTS + < XTU = 180 (< s on a straight line)
i.e. < YTS + < XTU - 180(< s on straight line)
i.e. < YTS + 70

^{\circ}

= 180
< YTS = 180 - 70 = 110

^{\circ}

in

△

SYT + < YST + < YTS = 180

^{\circ}

(Sum of interior < s)
SYT + 40 + 110 = 180
< SYT = 180 - 150 = 30
< SYT = < XYW (vertically opposite < s)
Also < SYX = < TYW (vertically opposite < s)
but < SYT + < XYW + < SYX + < TYW = 360
i.e. 30 + 30 + < SYX + TYW = 360
but < SYX = < TYW
60 + 2(< TYW) = 360
2(< TYW) = 360

^{\circ}

- 60
2(< TYW) = 300

^{\circ}

TYW =

\frac{300}{2}

= 150

^{\circ}

< SYT

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Question 11 Report

Triangle OPQ above is the solution of the inequalities

x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0

y + x ≤ 0, y - x ≥ 0, x -1 ≥ 0

x - 1 ≤ 0, y - x ≥ o, y + x ≥ 0

x - 1 ≤ 0, y + x ≤ 0, y - x ≤ 0

Inequalities

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Question 12 Report

Evaluate $ \log_{\sqrt{2}} 4 + \log_{\frac{1}{2}} 16 - \log_{4} 32 $

-5.5

-2.5

2.5

5.5

Logarithms

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Question 13 Report

If nP3 - 6(nC4) = 0, find the value of n

5

6

7

8

Solution Of Linear Equations

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Question 14 Report

Find the range of the value of $x$ satisfying the inequalities $5 + x \le 8$ and $13 + x \ge 7$

-3 $\leq$ x $\leq$ 3

3 $\leq$ x $\leq$ 6

-6 $\leq$ x $\leq$ 3

-6 $\leq$ x $\leq$ -3

Answer Details

5 + x $\leq$ 8 and 13 + x $\geq$ 7
5 + x $\leq$ 8
X $\leq$ 8 – 5
X $\leq$ 3
And 13 + x $\geq$ 7
X $\geq$ 7 – 15
X $\geq$ -7
Combining the two together
-6 $\leq$ x $\leq$ 3

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

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Question 15 Report

On the pie chart, there are four sectors of which three angles are $45^\circ$, $90^\circ$ and $135^\circ$. If the smallest sector represents N28.00, how much is the largest sector?

N96.00

N84.00

N48.00

N42.00

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Question 16 Report

In a class of 40 students, 32 offer mathematics, 24 offer Physics, and 4 offer neither Mathematics nor Physics. How many offer both Mat
ematics and Physics?

20

16

8

4

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Question 17 Report

The sum of the first n terms of an arithmetic progresssion is 252. If the first term is -16 and the last term is 72, find the number of terms in the series

6

7

8

9

Sequence And Series

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Question 18 Report

The histogram above shows the ages of the victims of a pollution. How many people were involved in the pollution?

15

18

20

21

Euclidean Geometry

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Question 19 Report

The length a person can jump is inversely proportional to his weight. If a 20 kg person can jump 1.5 m, find the constant of proportionality

60

30

20

15

Logical Reasoning

Ratio, Proportions And Rates

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Question 20 Report

An arc of a circle subtends an angle of $30^\circ$ on the circumference of a circle of radius 21cm. Find the length of the arc.

11cm

22cm

44cm

66cm

Answer Details

θ = 30 x 2(∠ at center twice ∠ at θ)
∴ θ = 60

^{\circ}

Length of arc =

\frac{θ}{360} \times 2 π r = \frac{60}{360} \times 2 \times \frac{22}{7} \times \frac{21}{1} = 22 c m

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Question 21 Report

A trapezium has two parallel sides of length 5cm and 9cm. If the area is 21cm2, find the distance between the parallel sides

3 cm

4 cm

6 cm

7 cm

Areas

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Question 22 Report

In the diagram above, PQ is parallel to RS. What is the value of ? + ? + ??

360

^{\circ}

200

^{\circ}

180

^{\circ}

90

^{\circ}

Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Question 23 Report

XYZ is a circle enter o and a radius 7cm. Find the area of the shaded region. θ = 45 x 2 = 90

84cm2

77cm2

38cm2

14cm2

Circles

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Question 24 Report

If y = 3 sin(-4x), dy/dx is

12x cos (4x)

-12x cos (-4x)

-12 cos (-4x)

12 sin (-4x)

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Question 25 Report

x varies directly as the product of u and v and inversely as their sum. If x = 3 when u = 3 and v = 1, what is the value of x if u = 3 and v = 3?

3

4

6

9

Variation

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Question 26 Report

The sum of four numbers is 12145. What is the average expressed in base five?

114

141

401

411

Number Bases

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Question 27 Report

Simplify 2134 x 234

103114

103214

122314

132114

Number Bases

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Question 28 Report

Find the slope of the curve y = 2x2n+ 5x - 3 at (1, 4).

4

6

7

9

Introductory Calculus

Integration

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Question 29 Report

The graph of the function y = x2 + 4 and a straight line PQ are drawn to solve the equation x2 - 3x + 2 = 0. What is the equation of PQ?

y = 3x - 2

y = 3x + 2

y = 3x - 4

y = 3x + 4

Graphs Of Linear And Quadratic Functions

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Question 30 Report

A cinema halll contains a certain number of people. If 25/2% are children, 95/2% are men and 84 are women, find the number of men in the hall.

63

84

113

133

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Question 31 Report

The result of tossing a fair die 120 times is summarized above. Find the value of x

19

20

21

22

Probability

Transformation In The Cartesian Plane

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Question 32 Report

An aeroplane flies due north from airport P to Q and then flies due east R. If Q is equidistant from P and R, find the bearing of P and R

90

^{\circ}

135

^{\circ}

225

^{\circ}

270

^{\circ}

Answer Details

Since PQ = QR, Δ PQR is a right angle isosceles triangle

∴ ∠PQR = 45

^{\circ}

=> The bearing of P from R = 180 + 45
= 225

^{\circ}

Read lesson note on Bearings (WAEC)

Read lesson note on Circles (WAEC)

Bearings

Circles

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Question 33 Report

A bag contains 5 blacks balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and red balls are picked?

15/28

13/28

5/14

3/14