JAMB UTME - Mathematics - 2008

Swali 1 Ripoti

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

-1/4

-1/2

1/4

1/2

Tazama Jibu

Swali 2 Ripoti

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

128

216

215

210

Maelezo ya Majibu

^{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

Soma maelezo ya somo kwenye Permutation And Combination (JAMB)

Permutation And Combination

Tazama Jibu

Swali 3 Ripoti

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}

Maelezo ya Majibu

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

Tazama Jibu

Swali 4 Ripoti

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)

Tazama Jibu

Swali 5 Ripoti

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}

Tazama Jibu

Swali 6 Ripoti

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

Maelezo ya Majibu

(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 ,

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 7 Ripoti

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

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Variation (JAMB)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Variation

Inequalities

Tazama Jibu

Swali 8 Ripoti

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

Tazama Jibu

Swali 9 Ripoti

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

Tazama Jibu

Swali 10 Ripoti

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

Tazama Jibu

Swali 11 Ripoti

Find the area of the figure given

12.5cm2

75.0cm2

78.5cm2

84.8cm2

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Areas (WAEC)

Areas

Tazama Jibu

Swali 12 Ripoti

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

16

13

12

11

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

Tazama Jibu

Swali 13 Ripoti

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

Tazama Jibu

Swali 14 Ripoti

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}

Maelezo ya Majibu

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

Tazama Jibu

Swali 15 Ripoti

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

Tazama Jibu

Swali 16 Ripoti

Add 11012,101112 and 1112

1110112

1101102

1010112

1010102

Number Bases

Tazama Jibu

Swali 17 Ripoti

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

zero

1

2

3

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Integration (JAMB)

Integration

Tazama Jibu

Swali 18 Ripoti

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

Tazama Jibu

Swali 19 Ripoti

If 125x = 2010 find x

2

3

4

5

Number Bases

Tazama Jibu

Swali 20 Ripoti

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

Tazama Jibu

Swali 21 Ripoti

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Angles

Tazama Jibu

Swali 22 Ripoti

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

Tazama Jibu

Swali 23 Ripoti

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

Tazama Jibu

Swali 24 Ripoti

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

Tazama Jibu

Swali 25 Ripoti

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

Tazama Jibu

Swali 26 Ripoti

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

4

16

32

64

Logarithms

Tazama Jibu

Swali 27 Ripoti

Find the area of the figure above

[π = 22/7]

12.5 cm2

75.0 cm2

78.5 cm2

84.8 cm2

Areas

Tazama Jibu

Swali 28 Ripoti

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Circles

Angles

Tazama Jibu

Swali 29 Ripoti

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

N3,000

N600

N300

N150

Financial Arithmetic

Tazama Jibu

Swali 30 Ripoti

Differentiate sin x - x cos x

x cos x

x sin x

-x cos x

-x sin x

Differentiation

Tazama Jibu

Swali 31 Ripoti

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

Tazama Jibu

Swali 32 Ripoti

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

95o

85o

78o

75o

72o

Angles

Triangles And Polygons

Tazama Jibu

Swali 33 Ripoti

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

1/11

2/11

3/11

4/11

Probability

Tazama Jibu

Swali 34 Ripoti

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

60o

80o

120o

160o

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 35 Ripoti

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

zero

1

2

3

Measures Of Location

Tazama Jibu

Swali 36 Ripoti

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

Tazama Jibu

Swali 37 Ripoti

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

Tazama Jibu

Swali 38 Ripoti

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

Tazama Jibu

Swali 39 Ripoti

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

Tazama Jibu

Swali 40 Ripoti

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

Maelezo ya Majibu

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

Soma maelezo ya somo kwenye Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

Tazama Jibu

Swali 41 Ripoti

If sinθ = 3/5. Find Tanθ

3/4

3/5

2/5

1/4

Introductory Calculus

Trigonometry

Tazama Jibu

Swali 42 Ripoti

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

Tazama Jibu

Swali 43 Ripoti

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

1

2

5

7

Probability

Tazama Jibu

Swali 44 Ripoti

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

4

5

6

7

Algebraic Expressions

Tazama Jibu

Swali 45 Ripoti

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

Tazama Jibu

Swali 46 Ripoti

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

Tazama Jibu

Swali 47 Ripoti

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

+/-16

+/-8

+/-4

+/-2

Progression

Tazama Jibu

Swali 48 Ripoti

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

\frac{9}{41}

\frac{5}{4}

1

\frac{9}{1}

Maelezo ya Majibu

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