JAMB UTME - Mathematics - 2008

Swali 1 Ripoti

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

4

16

32

64

Maelezo ya Majibu

If logx1/264 = 3
(X 1/2)3 = 64
(X 1/2)3 = 4 3
X 1/2 = 4
X = 42
X = 16

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 2 Ripoti

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

3/8

2/3

3/4

3/2

Maelezo ya Majibu

16^{\frac{? 1}{2}} \times 4^{\frac{? 1}{2}} \times 27^{\frac{1}{3}} = \frac{1}{16^{\frac{1}{2}}} \times \frac{1}{4^{\frac{1}{2}}} \times 27^{\frac{1}{3}} = \frac{1}{\sqrt{16}} \times \frac{1}{\sqrt{4}} \times s q r t [3] 27 = \frac{1}{4} \times \frac{1}{2} \times \frac{3}{1} = \frac{3}{8}

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Number Bases

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 3 Ripoti

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

Tazama Jibu

Swali 4 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

Maelezo ya Majibu

x2 - 5x + 6 = 0
(X-2)(X-3) = 0
X-2 = 0 implies X = 2
X-3 = 0 implies X = 3
∴ x ≤ 2, x ≥ 3

Soma maelezo ya somo kwenye Progression (JAMB)

Progression

Tazama Jibu

Swali 5 Ripoti

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

-1/4

-1/2

1/4

1/2

Maelezo ya Majibu

y = x(1+x)
= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4

Tazama Jibu

Swali 6 Ripoti

Calculate the distance between points L(-1, -6) and M(-3, -5)

√5

2√3

√20

√50

Maelezo ya Majibu

L

(\begin{matrix} x_{1} & y_{1} \\ - 1 & - 6 \end{matrix})

m L

(\begin{matrix} x_{2} & y_{2} \\ - 3 & - 5 \end{matrix})

D =

\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}

D =

\sqrt{(- 3 - (- 1)^{2} + (- 5 - (- 6)^{2}}

D =

\sqrt{(- 3 + 1)^{2} + (- 5 + 6)^{2}}

D =

\sqrt{(- 2)^{2} + 1^{2}}

D =

\sqrt{4 + 1}

D =

\sqrt{5}

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Coordinate Geometry (JAMB)

Euclidean Geometry

Coordinate Geometry

Tazama Jibu

Swali 7 Ripoti

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Maelezo ya Majibu

74 + x + x = 180

2x = 180 - 74

2x = 103

x = 53

Soma maelezo ya somo kwenye Angles (WAEC)

Angles

Tazama Jibu

Swali 8 Ripoti

if X = {n2 + 1 : n = 0, 2, 3} and y = {n + 1 : n = 2, 3, 4, 5}, find x ∩ y

{1, 3}

{5,10}

Φ

(4, 6)

Maelezo ya Majibu

X = {n2 + 1 : n = 0, 2, 3}
y = {n + 1 : n = 2, 3, 4, 5}
find x ∩ y
x = (n2 + 1)(22 + 1)(32 + 1)
y = (2 + 1) (3 + 1)(5 + 1)
x = {1, 5, 10}
y = {3, 4, 6}
x ∩ y =

Φ

Soma maelezo ya somo kwenye Sets (WAEC)

Sets

Tazama Jibu

Swali 9 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 10 Ripoti

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

+/-16

+/-8

+/-4

+/-2

Maelezo ya Majibu

P ∝ 1/q
P = k/q
K = q2P
= 428
∴P = 128/q
32 = 128/q
q2 = 128/32
q2 = 4
q = √4 = +/-2

Soma maelezo ya somo kwenye Progression (JAMB)

Progression

Tazama Jibu

Swali 11 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

Maelezo ya Majibu

V = πr2h
1m = 100cm
14cm = 1400cm

∴ V = \frac{22}{7} \times \frac{100 x 100 x 1400}{1000} = 44, 000 l i t e r s

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Volumes

Inequalities

Tazama Jibu

Swali 12 Ripoti

Find the values of x and y respectively if

\[ \begin{pmatrix} 1 & 0\\ -1 & -1\\ 2 & 2 \end{pmatrix} + \begin{pmatrix} x & 1\\ -1 & 0\\ y & -2 \end{pmatrix} = \begin{pmatrix} -2 & 1\\ -2 & -1\\ -30 & 0 \end{pmatrix} \]

-3, -2

-5, -3

-2, -5

-3, -5

Maelezo ya Majibu

(\begin{matrix} 1 & 0 \\ - 1 & - 1 \\ 2 & 2 \end{matrix})

+

(\begin{matrix} x & 1 \\ - 1 & 0 \\ y & - 2 \end{matrix})

=

(\begin{matrix} - 2 & 1 \\ - 2 & - 1 \\ - 30 & 0 \end{matrix})

therefore, (x, y) = (-3, -5) respectively

Tazama Jibu

Swali 13 Ripoti

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

\frac{1}{11}

\frac{3}{11}

\frac{3}{11}

\frac{4}{11}

Maelezo ya Majibu

Obstruction
if a T is picked
p =

\frac{2}{11}

Soma maelezo ya somo kwenye Probability (WAEC)

Probability

Tazama Jibu

Swali 14 Ripoti

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

N3,000

N600

N300

N150

Maelezo ya Majibu

I = \frac{P \times T \times R}{100} = \frac{7500 \times 8 \times 5}{100} = N 3000

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Financial Arithmetic

Tazama Jibu

Swali 15 Ripoti

\[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x\, dx \]

7

1

2

3

Maelezo ya Majibu

\int_{- \frac{π}{2}}^{\frac{π}{2}}

cosx

[s i n x]_{\frac{π}{2}}^{\frac{π}{2}}

= sin

\frac{π}{2}

- (-sin

\frac{π}{2}

)
= sin

\frac{π}{2}

+ sin

\frac{π}{2}

= 2 sin

\frac{π}{2}

= 2 sin 1.5714
= 2(0.2704)
= 0.5
= 1

Soma maelezo ya somo kwenye Integration (JAMB)

Integration

Tazama Jibu

Swali 16 Ripoti

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

Number	1	2	3	4	5	6
Frequency	12	18	$x$	30	$2x$	45

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 17 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 18 Ripoti

A binary operation on the set of real numbers excluding -1 is such that sor all $m, n \in R$, $m \Delta n = m + n + mn$. Find the identity element of the operation.

1

0

-

\frac{1}{2}

-1

Maelezo ya Majibu

m

Δ

n = m + n + mn
m

Δ

e = e

Δ

m = m
m

Δ

e = m
m + e + me = m
e + me = m - m
e + me = 0
e(1 + m) = 0
e =

\frac{0}{1 + m}

= 0

Soma maelezo ya somo kwenye Binary Operations (JAMB)

Binary Operations

Tazama Jibu

Swali 19 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)

Maelezo ya Majibu

X = \frac{6 + 2}{2} = \frac{10}{2} = 5 Y = \frac{2 + 2}{2} = \frac{4}{2} = 2 ∴ X, Y = (5, 2)

Soma maelezo ya somo kwenye Loci (JAMB)

Soma maelezo ya somo kwenye Loci (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

Tazama Jibu

Swali 20 Ripoti

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

zero

1

2

3

Maelezo ya Majibu

4, 4, 1, 0, 4, 4, 2, 0
Arrange in ascending order:
0, 0, 1, 1, 2, 4, 4, 4, 4
Position of median = N+1 / 2 = 9+1 / 2 = 5th
Median = 2

Soma maelezo ya somo kwenye Measures Of Location (JAMB)

Measures Of Location

Tazama Jibu

Swali 21 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)

Maelezo ya Majibu

\frac{1 + \sqrt{2}}{1 - \sqrt{2}} \times \frac{1 + \sqrt{2}}{1 + \sqrt{2}} = \frac{1 + (1 + \sqrt{2}) + \sqrt{2} (1 + \sqrt{2})}{1^{2} - (\sqrt{2})^{2}} = \frac{(1 + \sqrt{2} + \sqrt{2} + 2)}{1 - 2} = \frac{3 + 2 \sqrt{2}}{- 1} = - 3 - 2 \sqrt{2} ∴ X a n d Y = - 3 a n d - 2

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Surds (radicals)

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

Maelezo ya Majibu

x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1
Range = 3x+2 - (x-3)
= 3x+2 - x - 3
= 2x + 5

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 23 Ripoti

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

\frac{10!}{2! 2! 3!}

\frac{10!}{2! 3!}

\frac{10!}{2! 2!}

\frac{10!}{3! 2! 2!}

Maelezo ya Majibu

Acceptance

\frac{10!}{3! 2! 2!}

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Soma maelezo ya somo kwenye Permutation And Combination (JAMB)

Soma maelezo ya somo kwenye Probability (JAMB)

Representation Of Data

Permutation And Combination

Probability

Tazama Jibu

Swali 24 Ripoti

If $ \log X^{\frac{1}{2}} $ 64 = 3, find the value of x.

4

16

32

64

Maelezo ya Majibu

l o g X^{\frac{1}{2}}

64 = 3, find the value of X
recall that X = 10p
log10X = P
64 =

X^{\frac{1}{2}}

43 =

X^{\frac{1}{2}}

4^{3 \times \frac{1}{2}}

=

X^{\frac{1}{2} \times \frac{1}{3}}

4 =

X^{\frac{1}{2}}

(4)2 =

X^{\frac{1}{2} \times 2}

x = 16

Tazama Jibu

Swali 25 Ripoti

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

1

2

5

7

Maelezo ya Majibu

X = 20/4
= 5
mean deviation = 8/4 = 2

Soma maelezo ya somo kwenye Probability (WAEC)

Probability

Tazama Jibu

Swali 26 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

Maelezo ya Majibu

mΔn = m+n+mn
Let e be the identity element
∴mΔe = eΔm = m
m+e+me = m
e+me = m-m
e+me = 0
e(1+m) = 0
e = 0 / (1+m)
e = 0

Soma maelezo ya somo kwenye Binary Operations (JAMB)

Binary Operations

Tazama Jibu

Swali 27 Ripoti

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

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 28 Ripoti

The solution of the quadratic inequality $x^2 + x - 12 \ge 0$ 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 29 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 30 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 31 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!

Maelezo ya Majibu

ACCEPTANCE = 10 Letters
A = 2 letters
C = 3 letters
E = 2 letters
Can be arranged in 10! / (2!3!2!) ways

Soma maelezo ya somo kwenye Permutation And Combination (JAMB)

Permutation And Combination

Tazama Jibu

Swali 32 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

Maelezo ya Majibu

Ratio of least to most = 3:12
= 3/12
= 1/4

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Soma maelezo ya somo kwenye Integration (JAMB)

Representation Of Data

Integration

Tazama Jibu

Swali 33 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 34 Ripoti

A student sitting on a tower 68 metres high observes his principal's car at the angle of depression of 20o. How far is the car from the bottom of the tower to the nearest metre?

184m

185m

186m

187m

Maelezo ya Majibu

Tan 20o =

\frac{68 m}{x}

x tan 20o = 68
x =

\frac{68}{t a n 20}

=

\frac{68}{0.364}

x = 186.8
= 187m

Soma maelezo ya somo kwenye Bearings (WAEC)

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Bearings

Coordinate Geometry

Tazama Jibu

Swali 35 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

Maelezo ya Majibu

X * Y = 2X - 3Y + 2
2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer

Soma maelezo ya somo kwenye Matrices And Determinants (JAMB)

Soma maelezo ya somo kwenye Binary Operations (JAMB)

Matrices And Determinants

Binary Operations

Tazama Jibu

Swali 36 Ripoti

On a pie chart, there are six sectors of which four angles are 30o, 45o, 60o, 90o and the remaining two angles are in the ratio 2 : 1. Find the smaller angles of the remaining two angles

15o

30o

45o

60o

Tazama Jibu

Swali 37 Ripoti

If 125x = 2010 find x

2

3

4

5

Maelezo ya Majibu

125x = 20
1xX2 + 2xX1 + 5xX0 = 20
X2 + 2X + 5 = 20
X2 + 2X - 15 = 0
(X + 5)( X - 3) = 0
X + 5 implies X = -5
X - 3 implies X = 3
But X cannot be negative
∴X = 3

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 38 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)

Maelezo ya Majibu

(4x+3y)2 - (3x-2y)2
(4x+3y+3x-2y)(4x+3y-(3x-2y))
(4x+3y+3x-2y)(4x+3y-3x+2y)
(x+5y)(7x+y)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 39 Ripoti

\[ \begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix} + \begin{pmatrix} p & q \\ r & s \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}. \] What is the value of r?

-

\frac{1}{8}

\frac{3}{8}

\frac{5}{8}

\frac{1}{4}

Maelezo ya Majibu

-2p + r = 1.......(i)
2p + 3r = 0.......(ii)
r - 1 + 2p ........(iii)
2p + 3(1 + 2p) = 0
2p + 3(1 + 2p) = 0
2p + 3 + 6p = 0
3 - 8p = 0

\to

8p = 3
p =

\frac{3}{8}

6 = 1 - 2

\frac{3}{8}

= 1 -

\frac{6}{8}

\frac{8 - 6}{8}

=

\frac{2}{8}

=

\frac{1}{4}

Tazama Jibu

Swali 40 Ripoti

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}

Maelezo ya Majibu

X = {1,5,10}
Y = {3,4,6}
X∩Y = ∅

Soma maelezo ya somo kwenye Sets (JAMB)

Sets

Tazama Jibu

Swali 41 Ripoti

Add 11012,101112 and 1112

1110112

1101102

1010112

1010102

Maelezo ya Majibu

11012 + 101112 + 1112 = 101011

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 42 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

Maelezo ya Majibu

(x – 3) ∝ y2
X-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2(6)2
X-3 = 1/2 x 30/1
X-3 = 18
X = 21

Tazama Jibu

Swali 43 Ripoti

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

\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

Maelezo ya Majibu

L = \frac{4}{3} M \sqrt{P Q} = \frac{3}{4 M} \times L = \sqrt{P Q} = {(\frac{3 L}{4 M})}^{2} = (\sqrt{P Q})^{2} = \frac{9 L^{2}}{16 M^{2}} = P Q = Q = \frac{9 L^{2}}{16 M^{2} P}

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Change Of Subject Of A Formula/Relation

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 44 Ripoti

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Maelezo ya Majibu

a = a(base ∠s of Iss Δ)
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53

^{\circ}

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Circles

Angles

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

Maelezo ya Majibu

n(M) only = 30-10 = 20
n(E) only = 20-10 = 10
n(M∩E) = 10
∴M∪E = 20+10+10
= 40

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Sets (WAEC)

Probability

Sets

Tazama Jibu

Swali 46 Ripoti