JAMB UTME - Mathematics - 2008

Ibeere 1 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Progression (JAMB)

Progression

Wo Idahun

Ibeere 2 Ìròyìn

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

4

16

32

64

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 3 Ìròyìn

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)

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Sets (WAEC)

Sets

Wo Idahun

Ibeere 4 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 5 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Matrices And Determinants (JAMB)

Ka ìwé ẹ̀kọ́ nípa Binary Operations (JAMB)

Matrices And Determinants

Binary Operations

Wo Idahun

Ibeere 6 Ìròyìn

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

4

5

6

7

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 7 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 8 Ìròyìn

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

zero

1

2

3

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Measures Of Location (JAMB)

Measures Of Location

Wo Idahun

Ibeere 9 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Binary Operations (JAMB)

Binary Operations

Wo Idahun

Ibeere 10 Ìròyìn

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

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 11 Ìròyìn

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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Bearings (WAEC)

Ka ìwé ẹ̀kọ́ nípa Coordinate Geometry (WAEC)

Bearings

Coordinate Geometry

Wo Idahun

Ibeere 12 Ìròyìn

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

\frac{1}{11}

\frac{3}{11}

\frac{3}{11}

\frac{4}{11}

Awọn alaye Idahun

Obstruction
if a T is picked
p =

\frac{2}{11}

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Probability

Wo Idahun

Ibeere 13 Ìròyìn

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)

Awọn alaye Idahun

\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

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Surds (radicals)

Wo Idahun

Ibeere 14 Ìròyìn

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

1

2

5

7

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Probability

Wo Idahun

Ibeere 15 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)

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Loci (JAMB)

Ka ìwé ẹ̀kọ́ nípa Loci (WAEC)

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Loci

Euclidean Geometry

Wo Idahun

Ibeere 16 Ìròyìn

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

Awọn alaye Idahun

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}

Ka ìwé ẹ̀kọ́ nípa Change Of Subject Of A Formula/Relation (WAEC)

Ka ìwé ẹ̀kọ́ nípa Simple Operations On Algebraic Expressions (WAEC)

Change Of Subject Of A Formula/Relation

Simple Operations On Algebraic Expressions

Wo Idahun

Ibeere 17 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

Awọn alaye Idahun

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}

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Representation Of Data

Wo Idahun

Ibeere 18 Ìròyìn

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

Wo Idahun

Ibeere 19 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

Awọn alaye Idahun

(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

Wo Idahun

Ibeere 20 Ìròyìn

Add 11012,101112 and 1112

1110112

1101102

1010112

1010102

Awọn alaye Idahun

11012 + 101112 + 1112 = 101011

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Number Bases

Wo Idahun

Ibeere 21 Ìròyìn

In the diagram < OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Awọn alaye Idahun

74 + x + x = 180

2x = 180 - 74

2x = 103

x = 53

Ka ìwé ẹ̀kọ́ nípa Angles (WAEC)

Angles

Wo Idahun

Ibeere 22 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Volumes (WAEC)

Ka ìwé ẹ̀kọ́ nípa Inequalities (JAMB)

Volumes

Inequalities

Wo Idahun

Ibeere 23 Ìròyìn

In the diagram above ∠OPQ is

90

^{\circ}

53

^{\circ}

36

^{\circ}

26

^{\circ}

Awọn alaye Idahun

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

^{\circ}

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Ka ìwé ẹ̀kọ́ nípa Angles (WAEC)

Circles

Angles

Wo Idahun

Ibeere 24 Ìròyìn

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

4

16

32

64

Awọn alaye Idahun

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

Wo Idahun

Ibeere 25 Ìròyìn

Express 1223456 to 3 significant figures

123000

124000

125000

126000

Fractions, Decimals And Approximations

Wo Idahun

Ibeere 26 Ìròyìn

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

Awọn alaye Idahun

(\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

Wo Idahun

Ibeere 27 Ìròyìn

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

N3,000

N600

N300

N150

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Financial Arithmetic (WAEC)

Financial Arithmetic

Wo Idahun

Ibeere 28 Ìròyìn

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

-

\frac{1}{8}

\frac{3}{8}

\frac{5}{8}

\frac{1}{4}

Awọn alaye Idahun

-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}

Wo Idahun

Ibeere 29 Ìròyìn

Find the area of the figure above

[π = 22/7]

12.5 cm2

75.0 cm2

78.5 cm2

84.8 cm2

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Areas

Wo Idahun

Ibeere 30 Ìròyìn

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

-1/4

-1/2

1/4

1/2

Awọn alaye Idahun

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

Wo Idahun

Ibeere 31 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Representation Of Data

Integration

Wo Idahun

Ibeere 32 Ìròyìn

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!}

Awọn alaye Idahun

Acceptance

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

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Ka ìwé ẹ̀kọ́ nípa Permutation And Combination (JAMB)

Ka ìwé ẹ̀kọ́ nípa Probability (JAMB)

Representation Of Data

Permutation And Combination

Probability

Wo Idahun

Ibeere 33 Ìròyìn

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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Binary Operations (JAMB)

Binary Operations

Wo Idahun

Ibeere 34 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Ka ìwé ẹ̀kọ́ nípa Sets (WAEC)

Probability

Sets

Wo Idahun

Ibeere 35 Ìròyìn

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

7

1

2

3

Awọn alaye Idahun

\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

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Integration

Wo Idahun

Ibeere 36 Ìròyìn

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

+/-16

+/-8

+/-4

+/-2

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Progression (JAMB)

Progression

Wo Idahun

Ibeere 37 Ìròyìn

If 125x = 2010 find x

2

3

4

5

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Number Bases

Wo Idahun

Ibeere 38 Ìròyìn

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

3/8

2/3

3/4

3/2

Awọn alaye Idahun

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}

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Simple Operations On Algebraic Expressions (WAEC)

Number Bases

Simple Operations On Algebraic Expressions

Wo Idahun

Ibeere 39 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 40 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)

Awọn alaye Idahun

(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)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 41 Ìròyìn

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

Awọn alaye Idahun

\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

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Solution Of Linear Equations

Positive And Negative Integers, Rational Numbers

Wo Idahun

Ibeere 42 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 43 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

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Wo Idahun

Ibeere 44 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 45 Ìròyìn

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

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 46 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 47 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!

Awọn alaye Idahun

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

Ka ìwé ẹ̀kọ́ nípa Permutation And Combination (JAMB)

Permutation And Combination

Wo Idahun

Ibeere 48 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}

Awọn alaye Idahun

X = {1,5,10}
Y = {3,4,6}
X∩Y = ∅

Ka ìwé ẹ̀kọ́ nípa Sets (JAMB)

Sets

Wo Idahun

Ibeere 49 Ìròyìn

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

√5

2√3

√20

√50

Awọn alaye Idahun

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}

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Ka ìwé ẹ̀kọ́ nípa Coordinate Geometry (JAMB)

Euclidean Geometry

Coordinate Geometry

Wo Idahun

Ibeere 50 Ìròyìn

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}

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






Tẹ mọ́ & Dì mú láti fà yíká.
Tẹ ibi lati pa

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