JAMB UTME - Mathematics - 2008

Frage 1 Bericht

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)

Antwortdetails

(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)

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 2 Bericht

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

3/8

2/3

3/4

3/2

Antwortdetails

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}

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Simple Operations On Algebraic Expressions (WAEC)

Number Bases

Simple Operations On Algebraic Expressions

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Frage 3 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

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Frage 4 Bericht

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

7

1

2

3

Antwortdetails

\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

Lies die Unterrichtsnotiz zu Integration (JAMB)

Integration

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Frage 5 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Binary Operations (JAMB)

Binary Operations

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Frage 6 Bericht

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

4

16

32

64

Antwortdetails

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

Antwort anzeigen

Frage 7 Bericht

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

1

2

5

7

Antwortdetails

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

Lies die Unterrichtsnotiz zu Probability (WAEC)

Probability

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Frage 8 Bericht

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}

Antwortdetails

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}

Antwort anzeigen

Frage 9 Bericht

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

4

5

6

7

Antwortdetails

2x2 - kx - 12 is divisible by x-4
implies x is a factor ∴ x = 4
f(4) implies 2(4)2 - k(4) - 12 = 0
32 - 4k - 12 = 0
-4k + 20 = 0
-4k = -20
k = 5

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 10 Bericht

Solve the quadratic inequalities x2 - 5x + 6 ≥0

x ≤ 2, x ≥ 3

x ≤ 3, x ≥ 2

x ≤ -2, x ≥ -3

x ≤-3, x ≥ 2

Antwortdetails

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

Lies die Unterrichtsnotiz zu Progression (JAMB)

Progression

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Frage 11 Bericht

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

Antwortdetails

(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 ,

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Quadratic Equations

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Frage 12 Bericht

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

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Frage 13 Bericht

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

\frac{1}{11}

\frac{3}{11}

\frac{3}{11}

\frac{4}{11}

Antwortdetails

Obstruction
if a T is picked
p =

\frac{2}{11}

Lies die Unterrichtsnotiz zu Probability (WAEC)

Probability

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Frage 14 Bericht

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

4

16

32

64

Antwortdetails

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

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Logarithms

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Frage 15 Bericht

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

N3,000

N600

N300

N150

Antwortdetails

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

Lies die Unterrichtsnotiz zu Financial Arithmetic (WAEC)

Financial Arithmetic

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Frage 16 Bericht

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

zero

1

2

3

Antwortdetails

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

Lies die Unterrichtsnotiz zu Measures Of Location (JAMB)

Measures Of Location

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Frage 17 Bericht

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

16

13

12

11

Antwortdetails

\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

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

Antwort anzeigen

Frage 18 Bericht

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)

Antwortdetails

\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

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Surds (radicals)

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Frage 19 Bericht

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

60o

80o

120o

160o

Antwortdetails

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

Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 20 Bericht

Find the area of the figure given

12.5cm2

75.0cm2

78.5cm2

84.8cm2

Antwortdetails

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

Lies die Unterrichtsnotiz zu Areas (WAEC)

Areas

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Frage 21 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Bearings (WAEC)

Lies die Unterrichtsnotiz zu Coordinate Geometry (WAEC)

Bearings

Coordinate Geometry

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Frage 22 Bericht

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}

Antwortdetails

\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}

Antwort anzeigen

Frage 23 Bericht

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)

Antwortdetails

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

Lies die Unterrichtsnotiz zu Sets (WAEC)

Sets

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Frage 24 Bericht

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

+/-16

+/-8

+/-4

+/-2

Antwortdetails

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

Lies die Unterrichtsnotiz zu Progression (JAMB)

Progression

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Frage 25 Bericht

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

Antwortdetails

M e a n = \frac{t + 2 t - 1 + t - 2 + 2 t - 14 t + 2 t + 2}{6} M e a n = \frac{12 t - 2}{6} = \frac{2 (6 t - 1)}{6} = \frac{6 t - 1}{3} = \frac{6 t}{3} - \frac{1}{3} = 2 t - \frac{1}{3}

Lies die Unterrichtsnotiz zu Representation Of Data (JAMB)

Representation Of Data

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Frage 26 Bericht

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

-

\frac{1}{8}

\frac{3}{8}

\frac{5}{8}

\frac{1}{4}

Antwortdetails

-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}

Antwort anzeigen

Frage 27 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Probability (WAEC)

Lies die Unterrichtsnotiz zu Sets (WAEC)

Probability

Sets

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Frage 28 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Matrices And Determinants (JAMB)

Lies die Unterrichtsnotiz zu Binary Operations (JAMB)

Matrices And Determinants

Binary Operations

Antwort anzeigen

Frage 29 Bericht

Evaluate $ \frac{\left(\frac{3}{8} \div \frac{1}{2} + \frac{1}{2}\right)}{\left(\frac{1}{8} \times \frac{2}{3} + \frac{1}{3}\right)} $

1/4

1/3

1/2

1

Antwortdetails

\frac{(\frac{3}{8} \div \frac{1}{2} + \frac{1}{2})}{(\frac{1}{8} \times \frac{2}{3} + \frac{1}{3})} = \frac{(\frac{3}{8} \times \frac{2}{1} + \frac{1}{2})}{(\frac{1}{8} \times \frac{2}{3} + \frac{1}{3})} = \frac{(\frac{3}{4} - \frac{1}{3})}{(\frac{1}{12} + \frac{1}{3})} = (\frac{9 - 4}{12}) \div (\frac{1 + 4}{12}) = (\frac{5}{12}) \div (\frac{5}{12}) = \frac{5}{12} \times \frac{12}{5} = 1

Lies die Unterrichtsnotiz zu Solution Of Linear Equations (WAEC)

Lies die Unterrichtsnotiz zu Positive And Negative Integers, Rational Numbers (WAEC)

Solution Of Linear Equations

Positive And Negative Integers, Rational Numbers

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Frage 30 Bericht

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

Antwort anzeigen

Frage 31 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Binary Operations (JAMB)

Binary Operations

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Frage 32 Bericht

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

10! / (2!2!3!)

10! / ( 2!3!)

10! / (2!2!)

10!

Antwortdetails

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

Lies die Unterrichtsnotiz zu Permutation And Combination (JAMB)

Permutation And Combination

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Frage 33 Bericht

Find the area of the figure above

[π = 22/7]

12.5 cm2

75.0 cm2

78.5 cm2

84.8 cm2

Antwortdetails

Area of the figure = Area of rect + area of semi circle

= L \times h + \frac{1}{2} π r^{2} 5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times {(\frac{5}{2})}^{2} = 75 + \frac{(22 \times 25)}{2 \times 7} = 75 + 9 \frac{23}{28} = 84.8 c m

Lies die Unterrichtsnotiz zu Areas (WAEC)

Areas

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Frage 34 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Volumes (WAEC)

Lies die Unterrichtsnotiz zu Inequalities (JAMB)

Volumes

Inequalities

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Frage 35 Bericht

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!}

Antwortdetails

Acceptance

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

Lies die Unterrichtsnotiz zu Representation Of Data (JAMB)

Lies die Unterrichtsnotiz zu Permutation And Combination (JAMB)

Lies die Unterrichtsnotiz zu Probability (JAMB)

Representation Of Data

Permutation And Combination

Probability

Antwort anzeigen

Frage 36 Bericht

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

Antwortdetails

(\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

Antwort anzeigen

Frage 37 Bericht

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}

Antwortdetails

X = {1,5,10}
Y = {3,4,6}
X∩Y = ∅

Lies die Unterrichtsnotiz zu Sets (JAMB)

Sets

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Frage 38 Bericht

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)

Antwortdetails

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

Lies die Unterrichtsnotiz zu Loci (JAMB)

Lies die Unterrichtsnotiz zu Loci (WAEC)

Lies die Unterrichtsnotiz zu Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

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Frage 39 Bericht

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

Antwortdetails

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}

Lies die Unterrichtsnotiz zu Change Of Subject Of A Formula/Relation (WAEC)

Lies die Unterrichtsnotiz zu Simple Operations On Algebraic Expressions (WAEC)

Change Of Subject Of A Formula/Relation

Simple Operations On Algebraic Expressions

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Frage 40 Bericht

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Antwortdetails

74 + x + x = 180

2x = 180 - 74

2x = 103

x = 53

Lies die Unterrichtsnotiz zu Angles (WAEC)

Angles

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Frage 41 Bericht

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

Antwortdetails

(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

Antwort anzeigen

Frage 42 Bericht

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

128

216

215

210

Antwortdetails

^{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

Lies die Unterrichtsnotiz zu Permutation And Combination (JAMB)

Permutation And Combination

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Frage 43 Bericht

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

√5

2√3

√20

√50

Antwortdetails

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}

Lies die Unterrichtsnotiz zu Euclidean Geometry (JAMB)

Lies die Unterrichtsnotiz zu Coordinate Geometry (JAMB)

Euclidean Geometry

Coordinate Geometry

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Frage 44 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Variation (JAMB)

Lies die Unterrichtsnotiz zu Inequalities (JAMB)

Variation

Inequalities

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Frage 45 Bericht

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Antwortdetails

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

^{\circ}

Lies die Unterrichtsnotiz zu Circles (WAEC)

Lies die Unterrichtsnotiz zu Angles (WAEC)

Circles

Angles

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Frage 46 Bericht

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

-1/4

-1/2

1/4

1/2

Antwortdetails

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

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Frage 47 Bericht

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

Antwortdetails

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

Lies die Unterrichtsnotiz zu Representation Of Data (JAMB)

Lies die Unterrichtsnotiz zu Integration (JAMB)

Representation Of Data

Integration

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Frage 48 Bericht

Add 11012,101112 and 1112

1110112

1101102

1010112

1010102

Antwortdetails

11012 + 101112 + 1112 = 101011

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Number Bases

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Frage 49 Bericht

If 125x = 2010 find x

2

3

4

5

Antwortdetails

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

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Number Bases

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Frage 50 Bericht

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

Antwortdetails

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}

Lies die Unterrichtsnotiz zu Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

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Number	1	2	3	4	5	6
Frequency	12	18	\(x\)	30	\(2x\)	45