JAMB UTME - Mathematics - 2008

Question 1 Rapport

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 2 Rapport

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

Détails de la réponse

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
$= - 1 \div \frac{3}{2} = - 1 \times \frac{- 2}{3} = \frac{2}{3}$

Lisez la note de cours sur Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

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Question 3 Rapport

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

128

216

215

210

Détails de la réponse

^{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

Lisez la note de cours sur Permutation And Combination (JAMB)

Permutation And Combination

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Question 4 Rapport

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 5 Rapport

If 125x = 2010 find x

2

3

4

5

Number Bases

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Question 6 Rapport

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

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Question 7 Rapport

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 8 Rapport

In how many ways can the letters of the word ACCEPTANCE be arranged?

10! / (2!2!3!)

10! / ( 2!3!)

10! / (2!2!)

10!

Permutation And Combination

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Question 9 Rapport

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 10 Rapport

A binary operation on the real set of numbers excluding -1 is such that for all m, n ∈ R, mΔn = m+n+mn. Find the identity element of the operation.

1

zero

-1/2

-1

Binary Operations

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Question 11 Rapport

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 Rapport

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Angles

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Question 13 Rapport

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 14 Rapport

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 15 Rapport

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 16 Rapport

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 17 Rapport

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 18 Rapport

The cost of kerosine per liter increase from N60 to N85. What is the percentage rate of increase?

42%

41%

40%

25%

Percentages

Fractions, Decimals, Approximations And Percentage

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Question 19 Rapport

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

16

13

12

11

Détails de la réponse

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

Lisez la note de cours sur Modular Arithmetic (WAEC)

Lisez la note de cours sur Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

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Question 20 Rapport

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}

Détails de la réponse

$\begin{array}{cc} N u m b e r & 1 & 2 & 3 & 4 & 5 & 6 \\ F r e q u e n c y & 12 & 18 & x & 30 & 2 x & 45 \end{array}$
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 21 Rapport

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 22 Rapport

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

Détails de la réponse

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

Lisez la note de cours sur Variation (JAMB)

Lisez la note de cours sur Inequalities (JAMB)

Variation

Inequalities

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Question 23 Rapport

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 24 Rapport

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

Probability

Sets

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Question 25 Rapport

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

Détails de la réponse

(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 ,

Lisez la note de cours sur Quadratic Equations (WAEC)

Quadratic Equations

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Question 26 Rapport

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 27 Rapport

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}

Détails de la réponse

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 28 Rapport

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 29 Rapport

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

-1/4

-1/2

1/4

1/2

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Question 30 Rapport

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

60o

80o

120o

160o

Détails de la réponse

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

Lisez la note de cours sur Circles (WAEC)

Circles

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Question 31 Rapport

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 32 Rapport

If sinθ = 3/5. Find Tanθ

3/4

3/5

2/5

1/4

Introductory Calculus

Trigonometry

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Question 33 Rapport

Find the area of the figure given

12.5cm2

75.0cm2

78.5cm2

84.8cm2

Détails de la réponse

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

Lisez la note de cours sur Areas (WAEC)

Areas

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Question 34 Rapport

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 35 Rapport

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 36 Rapport

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 37 Rapport

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 38 Rapport

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 39 Rapport

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Circles

Angles

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Question 40 Rapport

If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1

3x+3

3x+1

2x+5

2x+1

Algebraic Expressions

Quadratic Equations

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Question 41 Rapport

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 42 Rapport

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

zero

1

2

3

Détails de la réponse

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

Lisez la note de cours sur Integration (JAMB)

Integration

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Question 43 Rapport

If $\frac{1 + \sqrt{2}}{1 - \sqrt{2}}$ is expressed in the form of x+y√2 find the values of x and y

(-3, -2)

(-2, 3)

(3,2)

(2,-3)

Surds (radicals)

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Question 44 Rapport

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

\frac{9}{41}

\frac{5}{4}

1

\frac{9}{1}

Détails de la réponse

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