JAMB UTME - Mathematics - 2008

Ibeere 1 Ìròyìn

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

4

5

6

7

Algebraic Expressions

Wo Idahun

Ibeere 2 Ìròyìn

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

Wo Idahun

Ibeere 3 Ìròyìn

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

Wo Idahun

Ibeere 4 Ìròyìn

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

Wo Idahun

Ibeere 5 Ìròyìn

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

zero

1

2

3

Measures Of Location

Wo Idahun

Ibeere 6 Ìròyìn

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

\frac{9}{41}

\frac{5}{4}

1

\frac{9}{1}

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Sine, Cosine And Tangent Of An Angle (WAEC)

Ka ìwé ẹ̀kọ́ nípa Trigonometry (JAMB)

Sine, Cosine And Tangent Of An Angle

Trigonometry

Wo Idahun

Ibeere 7 Ìròyìn

Add 11012,101112 and 1112

1110112

1101102

1010112

1010102

Number Bases

Wo Idahun

Ibeere 8 Ìròyìn

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

Wo Idahun

Ibeere 9 Ìròyìn

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

Wo Idahun

Ibeere 10 Ìròyìn

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

Wo Idahun

Ibeere 11 Ìròyìn

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

Wo Idahun

Ibeere 12 Ìròyìn

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

Wo Idahun

Ibeere 13 Ìròyìn

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

Wo Idahun

Ibeere 14 Ìròyìn

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

Wo Idahun

Ibeere 15 Ìròyìn

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

Wo Idahun

Ibeere 16 Ìròyìn

Differentiate sin x - x cos x

x cos x

x sin x

-x cos x

-x sin x

Differentiation

Wo Idahun

Ibeere 17 Ìròyìn

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

60o

80o

120o

160o

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 18 Ìròyìn

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

Wo Idahun

Ibeere 19 Ìròyìn

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

Wo Idahun

Ibeere 20 Ìròyìn

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

+/-16

+/-8

+/-4

+/-2

Progression

Wo Idahun

Ibeere 21 Ìròyìn

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Circles

Angles

Wo Idahun

Ibeere 22 Ìròyìn

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

4

16

32

64

Logarithms

Wo Idahun

Ibeere 23 Ìròyìn

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

Wo Idahun

Ibeere 24 Ìròyìn

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

Wo Idahun

Ibeere 25 Ìròyìn

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

128

216

215

210

Awọn alaye Idahun

^{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

Ka ìwé ẹ̀kọ́ nípa Permutation And Combination (JAMB)

Permutation And Combination

Wo Idahun

Ibeere 26 Ìròyìn

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

1/11

2/11

3/11

4/11

Probability

Wo Idahun

Ibeere 27 Ìròyìn

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

Wo Idahun

Ibeere 28 Ìròyìn

If sinθ = 3/5. Find Tanθ

3/4

3/5

2/5

1/4

Introductory Calculus

Trigonometry

Wo Idahun

Ibeere 29 Ìròyìn

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

16

13

12

11

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

Wo Idahun

Ibeere 30 Ìròyìn

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}

Wo Idahun

Ibeere 31 Ìròyìn

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

Wo Idahun

Ibeere 32 Ìròyìn

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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Variation (JAMB)

Ka ìwé ẹ̀kọ́ nípa Inequalities (JAMB)

Variation

Inequalities

Wo Idahun

Ibeere 33 Ìròyìn

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

Wo Idahun

Ibeere 34 Ìròyìn

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

1

2

5

7

Probability

Wo Idahun

Ibeere 35 Ìròyìn

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Angles

Wo Idahun

Ibeere 36 Ìròyìn

Find the area of the figure above

[π = 22/7]

12.5 cm2

75.0 cm2

78.5 cm2

84.8 cm2

Areas

Wo Idahun

Ibeere 37 Ìròyìn

Find the area of the figure given

12.5cm2

75.0cm2

78.5cm2

84.8cm2

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Areas

Wo Idahun

Ibeere 38 Ìròyìn

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

Wo Idahun

Ibeere 39 Ìròyìn

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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

Wo Idahun

Ibeere 40 Ìròyìn

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

zero

1

2

3

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Integration

Wo Idahun

Ibeere 41 Ìròyìn

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

Awọn alaye Idahun

(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 ,

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 42 Ìròyìn

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

95o

85o

78o

75o

72o

Angles

Triangles And Polygons

Wo Idahun

Ibeere 43 Ìròyìn

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}

Awọn alaye Idahun

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

Wo Idahun

Ibeere 44 Ìròyìn

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}

Awọn alaye Idahun

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
= - $\frac{1}{4}$

Wo Idahun

Ibeere 45 Ìròyìn

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

Wo Idahun

Ibeere 46 Ìròyìn

If 125x = 2010 find x

2

3

4

5

Number Bases

Wo Idahun

Ibeere 47 Ìròyìn

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