JAMB UTME - Mathematics - 2008

Pregunta 1 Informe

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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Pregunta 2 Informe

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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Pregunta 3 Informe

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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Pregunta 4 Informe

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

4

16

32

64

Logarithms

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Pregunta 5 Informe

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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Pregunta 6 Informe

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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Pregunta 7 Informe

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Angles

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Pregunta 8 Informe

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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Pregunta 9 Informe

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

\frac{9}{41}

\frac{5}{4}

1

\frac{9}{1}

Detalles de la respuesta

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

Lee la nota de la lección en Sine, Cosine And Tangent Of An Angle (WAEC)

Lee la nota de la lección en Trigonometry (JAMB)

Sine, Cosine And Tangent Of An Angle

Trigonometry

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Pregunta 10 Informe

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

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Pregunta 11 Informe

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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Pregunta 12 Informe

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Circles

Angles

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Pregunta 13 Informe

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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Pregunta 14 Informe

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

Detalles de la respuesta

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

Lee la nota de la lección en Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

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Pregunta 15 Informe

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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Pregunta 16 Informe

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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Pregunta 17 Informe

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

Detalles de la respuesta

(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 ,

Lee la nota de la lección en Quadratic Equations (WAEC)

Quadratic Equations

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Pregunta 18 Informe

Find the area of the figure given

12.5cm2

75.0cm2

78.5cm2

84.8cm2

Detalles de la respuesta

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

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Areas

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Pregunta 19 Informe

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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Pregunta 20 Informe

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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Pregunta 21 Informe

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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Pregunta 22 Informe

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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Pregunta 23 Informe

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

zero

1

2

3

Detalles de la respuesta

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

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Integration

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Pregunta 24 Informe

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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Pregunta 25 Informe

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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Pregunta 26 Informe

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

Detalles de la respuesta

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

Lee la nota de la lección en Variation (JAMB)

Lee la nota de la lección en Inequalities (JAMB)

Variation

Inequalities

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Pregunta 27 Informe

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

128

216

215

210

Detalles de la respuesta

^{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

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Permutation And Combination

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Pregunta 28 Informe

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

-1/4

-1/2

1/4

1/2

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Pregunta 29 Informe

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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Pregunta 30 Informe

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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Pregunta 31 Informe

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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Pregunta 32 Informe

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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Pregunta 33 Informe

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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Pregunta 34 Informe

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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Pregunta 35 Informe

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

1

2

5

7

Probability

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Pregunta 36 Informe

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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Pregunta 37 Informe

Differentiate sin x - x cos x

x cos x

x sin x

-x cos x

-x sin x

Differentiation

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Pregunta 38 Informe

If 125x = 2010 find x

2

3

4

5

Number Bases

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Pregunta 39 Informe

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

4

5

6

7

Algebraic Expressions

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Pregunta 40 Informe

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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Pregunta 41 Informe

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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Pregunta 42 Informe

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}

Detalles de la respuesta

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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Pregunta 43 Informe

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

16

13

12

11

Detalles de la respuesta

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

Lee la nota de la lección en Modular Arithmetic (WAEC)

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Modular Arithmetic

Quadratic Equations

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Pregunta 44 Informe

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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Pregunta 45 Informe

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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Pregunta 46 Informe

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}

Detalles de la respuesta

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