JAMB UTME - Mathematics - 2008

Question 1 Report

Evaluate $\int_{1}^{2} (6 x^{2} - 2 x) d x$

16

13

12

11

Answer Details

$\int_{1}^{2} (6 x^{2} - 2 x) d x = [\frac{6 x^{3}}{3} - \frac{2 x^{2}}{2}]_{1}^{2} = [2 x^{3} - x^{2}]_{1}^{2}$
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11

Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

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Question 2 Report

If X = {n2 + 1:n = 0,2,3} and Y = {n+1:n=2,3,5}, find X∩Y.

{1,3}

{5,10}

∅

{4,6}

Sets

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Question 3 Report

Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0

zero

1

2

3

Measures Of Location

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Question 4 Report

The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term.

12

4

-12

-24

Sequence And Series

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Question 5 Report

The result of rolling a fair die 150 times is as summarized in the table given.

$\begin{array}{cc} Number & 1 & 2 & 3 & 4 & 5 & 6 \\ Frequency & 12 & 18 & x & 30 & 2 x & 45 \end{array}$

What is the probability of obtaining a 5?

\frac{3}{10}

\frac{1}{5}

\frac{1}{6}

\frac{1}{10}

Answer Details

$\begin{array}{cc} N u m b e r & 1 & 2 & 3 & 4 & 5 & 6 \\ F r e q u e n c y & 12 & 18 & x & 30 & 2 x & 45 \end{array}$
12 + 18 + x + 30 + 2x + 45 = 150
3x + 105 = 150
3x = 150 - 105
3x = 45
x = $\frac{45}{3}$
x = 15
probability of 5 = $\frac{30}{150}$
= $\frac{1}{5}$

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Question 6 Report

Find the minimum value of X2 - 3x + 2 for all real values of x

-

\frac{1}{4}

-

\frac{1}{2}

\frac{1}{4}

\frac{1}{2}

Answer Details

y = X2 - 3x + 2, $\frac{d y}{d x}$ = 2x - 3
at turning pt, $\frac{d y}{d x}$ = 0
∴ 2x - 3 = 0
∴ x = $\frac{3}{2}$
$\frac{d^{2} y}{d x^{2}}$ = $\frac{d}{d x}$ ( $\frac{d}{d x}$ )
= 270
∴ ymin = 2 $\frac{3}{2}$ - 3 $\frac{3}{2}$ + 2
= $\frac{9}{4}$ - $\frac{9}{2}$ + 2
= - $\frac{1}{4}$

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Question 7 Report

Find the minimum value of the function y = x(1+x)

-1/4

-1/2

1/4

1/2

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Question 8 Report

Find the mean deviation of 2, 4, 5, and 9

1

2

5

7

Probability

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Question 9 Report

The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through

(2,5)

(5,2)

(1,0)

(0,1)

Loci

Euclidean Geometry

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Question 10 Report

Factorize complete;y (4x+3y)2 - (3x-2y)2

(x+5y)(7x+y)

(x+5y)(7x-y)

(x-5y)(7x+y)

(x-5y)(7x-y)

Algebraic Expressions

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Question 11 Report

If 2x2 - kx - 12 is divisible by x-4, Find the value of k.

4

5

6

7

Algebraic Expressions

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Question 12 Report

The solution of the quadratic inequality (x2 + x - 12) $\geq$ 0 is

x

\geq

3 or x

\geq

-4

x

\leq

3 or x

\leq

-4

x

\geq

3 or x

\leq

-4

x

\geq

-3 or x

\leq

4

Answer Details

(x2 + x - 12) $\geq$ 0 , (x - 3)(x + 4) $\geq$ 0
For the condition to hold, each of (x - 3) and (x + 4) must be of the same sign
.i.e. x - 3 $\geq$ 0 and x + 4 $\geq$ 0
or x - 3 $\leq$ 0 and x + 4 $\leq$ 0
when x $\geq$ 3, the condition is satisfied
when x $\geq$ -4, the condition is not satisfied.
when x $\leq$ 3, the condition is not satisfied
when x $\leq$ -4 , the condition is not satisfied. Thus, the solution of the inequality is x $\geq$ 3 or x $\leq$ -4 ,

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 13 Report

Find the range of values of x which satisfy the inequalities 4x - 7 $\leq$ 3x and 3x - 4 $\leq$ 4x

-4

\leq

x

\leq

7

-7

\leq

x

\leq

4

x

\geq

-7

\leq

x

\leq

6

Answer Details

4X - 7 $\leq$ 3X and 3X - 4 $\leq$ 4X
4X - 3X $\leq$ 7 and 3X - 4X $\leq$ 4
X $\leq$ 7 and -X $\leq$ 4 = X $\geq$ -4
Range -4 $\leq$ x $\leq$ 7

Read lesson note on Variation (JAMB)

Read lesson note on Inequalities (JAMB)

Variation

Inequalities

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Question 14 Report

Evaluate $\int_{\frac{- π}{2}}^{\frac{π}{2}} c o s x d x$

zero

1

2

3

Answer Details

$\int_{\frac{- π}{2}}^{\frac{π}{2}} c o s x d x = [s i n x]_{\frac{- π}{2}}^{\frac{π}{2}} = s i n \frac{π}{2} - s i n \frac{- π}{2}$
= sin90 – sin-90
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2

Read lesson note on Integration (JAMB)

Integration

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Question 15 Report

If sinθ = 3/5. Find Tanθ

3/4

3/5

2/5

1/4

Introductory Calculus

Trigonometry

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Question 16 Report

Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters

[π = 22/7]

44,000 liters

4,400 liters

440 liters

44 liters

Volumes

Inequalities

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Question 17 Report

Evaluate $\frac{(\frac{3}{8} \div \frac{1}{2} + \frac{1}{2})}{(\frac{1}{8} \times \frac{2}{3} + \frac{1}{3})}$

1/4

1/3

1/2

1

Solution Of Linear Equations

Positive And Negative Integers, Rational Numbers

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Question 18 Report

If p = varies inversely as the square of q and p=8 when q=4, find when p=32

+/-16

+/-8

+/-4

+/-2

Progression

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Question 19 Report

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Angles

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Question 20 Report

The result of rolling a fair die 150 times is ass summarized in the table above. What is the probability of obtaining a 5

3/10

1/5

1/6

1/10

Probability

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Question 21 Report

The bar chart above shows the number of times the word a, and , in, it, the , to appear in a paragraph in a book. What is the ratio of the least frequent word?

1/4

1/3

2/3

3/4

Representation Of Data

Integration

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Question 22 Report

calculate the simple interest on N6,500 for 8 years at 5% per annum.

N3,000

N600

N300

N150

Financial Arithmetic

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Question 23 Report

Find the area of the figure given

12.5cm2

75.0cm2

78.5cm2

84.8cm2

Answer Details

Area of semicircle + Area of rectangle

A = $\frac{1}{2} π r^{2}$ + LB

A = $\frac{1}{2} \times \frac{22}{77} \times (\frac{5}{2})^{2} + (15 \times 5)$

= $\frac{1}{2} \times \frac{22}{7} \times \frac{25}{4} + 75$

A = $\frac{275}{28} + \frac{75}{1}$

$\frac{275 + 2100}{28} = \frac{2375}{28}$

A = 84.8cm2

Read lesson note on Areas (WAEC)

Areas

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Question 24 Report

A binary operation * is defined on the set of positive integers is such x*y = 2x-3y+2 for all positive integers x and y. The binary operation is

commutative and close on the set of positive integers

neither commutative nor closed on the set of ppositive integers

commutative but not closed on the set of positive integers

not cummutative but closed on the set of positive integers

Matrices And Determinants

Binary Operations

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Question 25 Report

If tan $θ$ = $\frac{5}{4}$ find sin2 $θ$ - cos2 $θ$

\frac{9}{41}

\frac{5}{4}

1

\frac{9}{1}

Answer Details

(tan $θ$ = $\frac{o p p}{a d j}$ )
|AB|2 = 52 + 42 $\to$ |AB|2 = 41
$\to$ AB = $\sqrt{41}$ sin2 $θ$ - cos2 $θ$
$\to$ $\frac{5^{2}}{\sqrt{41}}$ - ( ${\frac{4}{\sqrt{41}}}^{2}$ ) = $\frac{25}{41}$ - $\frac{16}{41}$
= ( $\frac{9}{41}$ )

Read lesson note on Sine, Cosine And Tangent Of An Angle (WAEC)

Read lesson note on Trigonometry (JAMB)

Sine, Cosine And Tangent Of An Angle

Trigonometry

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Question 26 Report

Make Q the subject of formula when $L = \frac{4}{3} M \sqrt{P Q}$

\frac{9 L^{2}}{16 M^{2}} P

\frac{3 L}{4 M \sqrt{P}}

\frac{\sqrt{3 L}}{4 M P}

\frac{3 L^{2}}{16 M^{2}} P

Change Of Subject Of A Formula/Relation

Simple Operations On Algebraic Expressions

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Question 27 Report

Find the area of the figure above

[π = 22/7]

12.5 cm2

75.0 cm2

78.5 cm2

84.8 cm2

Areas

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Question 28 Report

Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

3/2

2/3

-2/3

-3/2

Answer Details

3X + 2Y + 1 = 0
2Y = -3X - 1
$\frac{- 3}{2} X - \frac{1}{2}$
Gradient of 3X + 2Y +1 = 0 is -3/2
Gradient of a line perpendicular to 3X + 2Y + 1 = 0
$= - 1 \div \frac{3}{2} = - 1 \times \frac{- 2}{3} = \frac{2}{3}$

Read lesson note on Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

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Question 29 Report

Differentiate sin x - x cos x

x cos x

x sin x

-x cos x

-x sin x

Differentiation

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Question 30 Report

Solve the quadratic inequalities x2 - 5x + 6 ≥0

x ≤ 2, x ≥ 3

x ≤ 3, x ≥ 2

x ≤ -2, x ≥ -3

x ≤-3, x ≥ 2

Progression

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Question 31 Report

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

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Question 32 Report

What is the mean of the data t, 2t-1, t-2, 2t-1, 4t and 2t+2?

2t

2t-1

2/3t+1

2t-1/3

Representation Of Data

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Question 33 Report

Find the derivative of $y = \frac{x^{7} - x^{5}}{x^{4}}$

x(x2-1)

3x(x2-1)

3x2-1

7x6-5x4

Trigonometry

Differentiation

Application Of Differentiation

Quadratic Equations

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Question 34 Report

If 125x = 2010 find x

2

3

4

5

Number Bases

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Question 35 Report

If logx1/264 = 3, find the value of x

4

16

32

64

Logarithms

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Question 36 Report

Which of the following angles is an exterior angle of a regular polygon?

95o

85o

78o

75o

72o

Angles

Triangles And Polygons

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Question 37 Report

Find the number of ways of selecting 6 out of 10 subjects for an examination

128

216

215

210

Answer Details

^{10} C_{6} = \frac{10!}{(10 - 6)! 6!} = \frac{10!}{4! 6!} = \frac{10 \times 9 \times 8 \times 7 \times 6!}{4 \times 3 \times 2 \times 1 \times 6!} = 2

Read lesson note on Permutation And Combination (JAMB)

Permutation And Combination

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Question 38 Report

If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6.

30

21

16

12

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Question 39 Report

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Circles

Angles

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Question 40 Report

In the diagram, find the size of the angle marked ao

60o

80o

120o

160o

Answer Details

2 x s = 280o(Angle at centre = 2 x < at circum)

S = $\frac{280^{o}}{2}$

= 140

< O = 360 - 280 = 80o

60 + 80 + 140 + a = 360o

(< in a quad); 280 = a = 360

a = 360 - 280

a = 80o

Read lesson note on Circles (WAEC)

Circles

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Question 41 Report

simplify $16^{\frac{- 1}{2}} \times 4^{\frac{- 1}{2}} \times 27^{\frac{1}{3}}$

3/8

2/3

3/4

3/2

Number Bases

Simple Operations On Algebraic Expressions

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Question 42 Report

The bar chart shows the number of times the word a, and, in, it, he, to appear in a paragraph in a book. What is the ratio of the least frequent word?

\frac{1}{4}

\frac{1}{3}

\frac{2}{3}

\frac{3}{4}

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Question 43 Report

The probability of picking a letter T fr4om the word OBSTRUCTION is

1/11

2/11

3/11

4/11

Probability

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Question 44 Report

A book seller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books, How many customers has he altogether.

30

40

50

60