JAMB UTME - Mathematics - 2004

Question 1 Report

In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm2, find the area of the trapezium PQRU

60 cm2

72 cm2

48 cm2

24 cm2

Mensuration

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Question 2 Report

The weight of 10 pupils in a class are 15 kg, 16 kg, 17 kg, 18 kg, 16 kg, 17 kg, 17 kg, 17 kg, 18 kg, and 16 kg. What is the range of this distribution?

4

3

2

1

Surds (radicals)

Measures Of Dispersion

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Question 3 Report

The shaded region in the Venn diagram above is

Pc ∪ (Q ∩ R)

Pc ∩ (Q ∪ R)

P ∩ Q

Pc ∩ (Q ∩ R)

Sets

Triangles And Polygons

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Question 4 Report

The locus of a point which is 5 cm from the line LM is a

line distance 10 cm from LM and parallel to LM

pair of line on opposite sides of LM and parallel to it, each distance 5 cm from LM

line parallel to LM and 5 cm from LM

pair of parallel lines on one side of LM and parallel to LM

Circles

Triangles And Polygons

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Question 5 Report

Simplify $ \frac{1}{\sqrt{3}+2} $ in the form $ a+b\sqrt{3} $

2 -√3

-2 - √3

2 + √3

-2 + √3

Positive And Negative Integers, Rational Numbers

Surds (radicals)

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Question 6 Report

Find P, if 4516 - P7 = 3056

627

1167

6117

1427

Solution Of Linear Equations

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Question 7 Report

Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....

2/3

1/3

3/4

1

Sequence And Series

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Question 8 Report

The graph above shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than 20 marks?

68%

28%

17%

8%

Answer Details

\begin{matrix} class-marks(x) & (freq. (f) & cum. freq. \\ 9 & 3.....3 \\ 14 & 6....3 + 6 = 9 \\ 19 & 9.....9 + 9 = 18 \\ 24 & 3.....18 + 3 = 21 \\ 29 & 2.....21 + 2 = 23 \\ 34 & 2.....23 + 2 = 25 \\ 25 \end{matrix}

% of students scoring more than 20 marks

= $\frac{7}{25}$ x 100% = 28%

Read lesson note on Percentages (WAEC)

Percentages

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Question 9 Report

Factorize completely ac - 2bc - a + 4b2

(a - 2b)(c - a - 2b)

(a - 2b)(c + a +2b)

(a - 2b)(c - a + 2b)

(a - 2b)(c + a - 2b)

Algebraic Expressions

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Question 10 Report

P, R and S lie on a circle center as shown above while Q lies outside the circle. Find ∠PSO

45o

55o

35o

40o

Circles

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Question 11 Report

I. Rectangular bars of equal width

II. The height of each rectangular bar is proportional to the frequency of the corresponding class interval.

III. Rectangular bars have common sides with no gaps in between

A histogram is described completely by

I, II and III

I and II

II and III

I and III

Answer Details

A histogram is a graphical representation of a frequency distribution of a dataset, where the data is divided into intervals or bins and the frequency of each interval is represented by the area of a rectangle or bar. To construct a histogram, we need to follow certain rules, which are described by the statements: I. Rectangular bars of equal width II. The height of each rectangular bar is proportional to the frequency of the corresponding class interval. III. Rectangular bars have common sides with no gaps in between. Therefore, a histogram is described completely by statements I, II, and III. Statement I ensures that each bar is of equal width, which is necessary to represent the intervals or bins in a consistent way. Statement II ensures that the height of each bar accurately represents the frequency of the corresponding class interval. This is important because the area of the bar represents the frequency of the interval, which is the product of the width and height of the bar. Statement III ensures that the bars are adjacent to each other without any gaps, which is necessary to accurately represent the continuity of the data. Hence, the correct answer is option (A) I, II, and III.

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Measures Of Location (JAMB)

Read lesson note on Measures Of Dispersion (JAMB)

Representation Of Data

Measures Of Location

Measures Of Dispersion

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Question 12 Report

What are the integer values of x which satisfy the inequality $ -1 < 3 - 2x \le 5 $?

-1. 0, 1, 2

-2, 1, 0 , -1

0, 1, 2

-1, 0, 1

Linear Inequalities

Inequalities

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Question 13 Report

A farmer planted 5000 grains of maize and harvested 5000 cobs, each bearing 500 grains. What is the ratio of the number of grains sowed to the number harvested?

1 : 250 000

1 : 25 000

1 : 500

1 : 5 000

Sine, Cosine And Tangent Of An Angle

Ratio, Proportions And Rates

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Question 14 Report

The shadow of a pole 5√3m high is 5m. Find the angle of elevation of the sun.

45o

75o

30o

60o

Trigonometry

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Question 15 Report

The sum of the interior angles of a pentagon is 6x + 6y. Find y in the terms of x

y = 90 - x

y = 150 - x

y = 60 - x

y = 120 -x

Indices

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Question 16 Report

The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum whose period is 9 sec

96 cm

324 cm

36 cm

144 cm

Variation

Probability

Algebraic Expressions

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Question 17 Report

Find the mean deviation of 1, 2, 3 and 4.

2.5

2.0

1.0

1.5

1.2

Measures Of Dispersion

Statistics

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Question 18 Report

Find the midpoint of the line joining P(-3, 5) and Q(5, -3).

(1, 1)

(2, 2)

(4, 4)

(4, -4)

Coordinate Geometry

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Question 19 Report

A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly

378 ways

462 ways

840 ways

924 ways

Representation Of Data

Variation

Sets

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Question 20 Report

Find the value of x in the figure above

15√6

20√6

3√6

5√6

Surds (radicals)

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Question 21 Report

If the operation * on the set of integers is defined by $p * Q = \sqrt{pq}$, find the value of $4 * (8 * 32)$.

8

3

16

4

View Answer

Question 22 Report

y = is inversely proportional to x and y = 4 when x = 1/2. Find x when y = 10.

2

10

1/5

1/10

Sine, Cosine And Tangent Of An Angle

Variation

Modular Arithmetic

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Question 23 Report

PQRSTV is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle PQRSTV.

56 cm

22 cm

42 cm

44 cm

Answer Details

Each interior Angle of the polygon =	(n-2)	180
	_n

=	(6-2)	180
	_6

= 4 x 30
= 120

^{\circ}

i.e ∠PQR = 120

^{\circ}

∴ RQD = 120/2 = 60

^{\circ}

also
∴ Δ QOR is equilateral Δ ∴ QO = 7cm
∴ PO = QO = RO ...... = 7cm radius of the circumference of the circle = 2πr
= 2 x 22/7 x 7/1
= 44 cm

Read lesson note on Circles (WAEC)

Circles

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Question 24 Report

If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?

90o

63o

60o

26o

0o

Trigonometry

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Question 25 Report

In how many ways can 2 students be selected from a group of 5 students in a debating competition?

25 ways

10 ways

15 ways

20 ways

16 ways

Permutation And Combination

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Question 26 Report

The shaded region in the Venn diagram above is

P $^{\circ}$ $\cap$ (Q $\cap$ R)

P $\cap$ Q

P $^{\circ}$ $\cup$ (Q $\cap$ R)

P $^{\circ}$ $\cup$ (Q $\cup$ R)

View Answer

Question 27 Report

Find the value of α2 + β2 if α + β = 2 and the distance between points (1, α) and (β, 1)is 3 units

14

3

5

11

Number Bases

Algebraic Expressions

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Question 28 Report

Given that 3√42x = 16, find the value of x

4

6

3

2

Surds (radicals)

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Question 29 Report

Some white balls put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white balls from the baskets is 3/7, how many white balls were introduced?

12

21

28

32

Probability

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Question 30 Report

Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3

-4

4

1

-1

Solution Of Linear Equations

Modular Arithmetic

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Question 31 Report

An unbiased die is rolled 100 times and the outcome is tabulated above.

What is the probability of obtaining a 5?

1/5

1/2

1/6

1/4

Probability

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Question 32 Report

A container has 30 gold medals, 22 silver medals and 18 bronze medals. If one medals is selected at the random from the container, what is the probability that it is not a gold medal?

9/35

11/35

4/7

3/7

Probability

Surds (radicals)

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Question 33 Report

Evaluate $ \frac{\frac{1}{10}\times\frac{2}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{3}{5}}-\frac{1}{4}}} $

\frac{7}{12}

\frac{19}{35}

\frac{2}{25}

\frac{19}{60}

View Answer

Question 34 Report

Find the derivatives of the function y = 2x2(2x - 1) at the point x = -1

18

16

-4

-6

Differentiation

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Question 35 Report

In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ∠NKM = 55o and ∠KML = 40o. Find ∠LKM.

35o

40o

45o

50o

55o

View Answer

Question 36 Report

Three teachers shared a packet of chalk. The first teacher got 2/5 of the chalk and the second teacher received 2/15 of the remainder. What fraction the the third teacher receive?

8/15

11/25

12/25

13/25

View Answer

Question 37 Report

The nth term of two sequences are Qn = 3 . 2n - 2 and Um = 3 . 22m - 3. Find the product of Q2 and U2.

18

12

6

3

Sequence And Series

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Question 38 Report

Given that the first and forth terms of G.P are 6 and 162 respectively, find the sum of the first three terms of the progression

27

8

78

48

Sequence And Series

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Question 39 Report

The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested

6000 tonnes

1500 tonnes

1200 tonnes

9000 tonnes

Answer Details

Sectorial angle of beans = 360 - (150 + 90 + 60)
= 360 -300
= 60

^{\circ}

if 150

^{\circ}

represents 3000 tonnes
1

^{\circ}

3000/150
60

^{\circ}

will represents (3000/150) * (60/1)
= 1200 tonnes

Read lesson note on Sets (JAMB)

Sets

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Question 40 Report

Determine the locus of a point inside a square PQRS which is eqidistant from PQ and QR

The diagonal QS

the perpendicular bisector of PQ

The diagonal PR

side SR

Loci

Coordinate Geometry

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Question 41 Report

If y = 3 cos(x/3), find dy/dx when x = (3π/2)

1

13

2

-1

Introductory Calculus

Differentiation

Application Of Differentiation

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Question 42 Report

Evaluate $ \int_{1}^{3}(X^2 - 1)\,dx $

\frac{2}{3}

- \frac{2}{3}

- 6 \frac{2}{3}

6 \frac{2}{3}

Integration

Trigonometry

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Question 43 Report

What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?

8π

16π

2π

4π

Integration

Differentiation

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Question 44 Report

If 6logx2 - 3logx3 = 3log50.2, find x.

8/3

4/3

3/4

3/8

Positive And Negative Integers, Rational Numbers

Logarithms

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Question 45 Report

An arc of length 22cm subtends an angle of θ at the center of the circle. What is the value of θ if the radius of the circle is 15cm?[Take π = 22/7]

70o

84o

96o

156o

168o

Circles

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Question 46 Report

Find the derivatives of (2 + 3x)(1 - x) with respect to x

6

-3

1 - 6x

6x - 1

Differentiation

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Question 47 Report

The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group

9

7

42

15

Integration

Euclidean Geometry

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Question 48 Report

The shaded area in the diagram above is represented by

{(x,y) : y - 3x < -6}

{(x,y) : y + 3x < 6}

{(x,y) : y + 3x < -6}

{(x,y) : y - 3x < 6}

Linear Inequalities

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JAMB UTME - Mathematics - 2004

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