Year : 
2021
Title : 
Mathematics (Core)
Exam : 
JAMB Exam

Paper 1 | Objectives

31 - 40 of 40 Questions

# Question Ans
31.

Factorize m\(^3\) - m\(^2\) + 2m - 2

A. (m2 + 1)(m - 2)

B. (m - 1)(m + 1)(m + 2)

C. (m - 2)(m + 1)(m - 1)

D. (m2 + 2)(m - 1)

Detailed Solution

Using trial expansion of each option
(m\(^2\) + 2) (m - 1)
There is an explanation video available below.
32.

The angles of a quadrilateral are 5x-30, 4x+60, 60-x and 3x+61.find the smallest of these angles​

A. 5x - 30

B. 4x + 60

C. 60 - x

D. 3x + 61

Detailed Solution

Sum of all 4 angles of a quadrilateral = 360°
(5x-30) + (3x + 61) + (60-x) + (4x+ 60) = 360°
11x + 151 = 360°
11x = 360 - 151 = 209
x = 209/11 = 19°
Each angles is :
5x - 30 = 65°
4x+ 60 = 136°
60 - x =41°
3x + 61 = 118°

Smallest of these angles is 41°
There is an explanation video available below.
33.

What is the n-th term of the sequence 2, 6, 12, 20...?

A. 4n - 2

B. 2(3n - 1)

C. n2 + n

D. n2 + 3n + 2

Detailed Solution

Given that 2, 6, 12, 20...? the nth term = n\(^2\) + n

check: n = 1, u1 = 2

n = 2, u2 = 4 + 2 = 6

n = 3, u3 = 9 + 3 = 12

∴ n = 4, u4 = 16 + 4 = 20
There is an explanation video available below.
34.

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

A. e = 1

B. e = -1

C. e = -2

D. e = 0

Detailed Solution

Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0

There is an explanation video available below.
35.

Factorize completely 81a\(^4\) - 16b\(^4\)

A. (3a + 2b)(2a - 3b)(9a2 + 4b2)

B. (3a - 2b)(2a - 3b)(4a2 - 9b2)

C. (3a - 2b)(3a + 2b)(9a2 + 4b2)

D. (6a - 2b)(8a - 3b)(4a3 - 9b2)

Detailed Solution

81a\(^4\) - 16b\(^4\) = (9a\(^2\))\(^2\) - (4b\(^2\))\(^2\)

= (9a\(^2\) + 4b\(^2\))(9a\(^2\) - 4b\(^2\))

N:B 9a\(^2\) - 4b\(^2\) = (3a - 2b)(3a + 2b)
There is an explanation video available below.
36.

Find x if log\(_9\)x = 1.5

A. 27

B. 15

C. 3.5

D. 32

Detailed Solution

If log\(_9\)x = 1.5,
9\(^{1.5}\) = x
9^\(\frac{3}{2}\) = x
(√9)\(^3\) = 3

∴ x = 27
There is an explanation video available below.
37.

List all integers satisfying the inequality in -2 < 2x-6 < 4

A. 2,3,4 and 5

B. 2,3

C. 2,5

D. 3,4

Detailed Solution

-2 < 2x - 6 AND 2x - 6 < 4
-2 + 6 <2x AND 2x < 4 + 6
4 <2x AND 2x < 10
: 2 <x AND x <5
2 < x < 5
As 3 and 4
There is an explanation video available below.
38.

X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X

A. 240°

B. 150°

C. 60°

D. 270°

Detailed Solution

Sinθ = \(\frac{6}{12}\)
Sinθ = \(\frac{1}{2}\)
θ = Sin\(^0.5\)
θ = 30°
Bearing of Z from X, (270 - 30)° = 240°
There is an explanation video available below.
39.

A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

A. 25

B. 19

C. 18

D. 17

Detailed Solution

Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
There is an explanation video available below.
40.

If (x + 2) and (x - 1) are factors of the expression \(Lx + 2kx^{2} + 24\), find the values of L and k.

A. l = -12, k = -6

B. l = -2 , k = 1

C. l = -2 , k = -1

D. l = 0, k = 1

Detailed Solution

Given (x + 2) and (x - 1), i.e. x = -2 or +1
when x = -2
L(-2) + 2k(-2)\(^2\) + 24 = 0
f(-2) = -2L + 8k = -24...(i)

And x = 1
L(1) + 2k(1) + 24 = 0

f(1):L + 2k = -24...(ii)
Subst, L = -24 - 2k in eqn (i)
-2(-24 - 2k) + 8k = -24
+48 + 4k + 8k = -24
12k = -24 - 48 = -72
k = \(frac{-72}{12}\)
k = -6
where L = -24 - 2k
L = -24 - 2(-6)
L = -24 + 12
L = -12
That is; K = -6 and L = -12




There is an explanation video available below.
31.

Factorize m\(^3\) - m\(^2\) + 2m - 2

A. (m2 + 1)(m - 2)

B. (m - 1)(m + 1)(m + 2)

C. (m - 2)(m + 1)(m - 1)

D. (m2 + 2)(m - 1)

Detailed Solution

Using trial expansion of each option
(m\(^2\) + 2) (m - 1)
There is an explanation video available below.
32.

The angles of a quadrilateral are 5x-30, 4x+60, 60-x and 3x+61.find the smallest of these angles​

A. 5x - 30

B. 4x + 60

C. 60 - x

D. 3x + 61

Detailed Solution

Sum of all 4 angles of a quadrilateral = 360°
(5x-30) + (3x + 61) + (60-x) + (4x+ 60) = 360°
11x + 151 = 360°
11x = 360 - 151 = 209
x = 209/11 = 19°
Each angles is :
5x - 30 = 65°
4x+ 60 = 136°
60 - x =41°
3x + 61 = 118°

Smallest of these angles is 41°
There is an explanation video available below.
33.

What is the n-th term of the sequence 2, 6, 12, 20...?

A. 4n - 2

B. 2(3n - 1)

C. n2 + n

D. n2 + 3n + 2

Detailed Solution

Given that 2, 6, 12, 20...? the nth term = n\(^2\) + n

check: n = 1, u1 = 2

n = 2, u2 = 4 + 2 = 6

n = 3, u3 = 9 + 3 = 12

∴ n = 4, u4 = 16 + 4 = 20
There is an explanation video available below.
34.

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

A. e = 1

B. e = -1

C. e = -2

D. e = 0

Detailed Solution

Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0

There is an explanation video available below.
35.

Factorize completely 81a\(^4\) - 16b\(^4\)

A. (3a + 2b)(2a - 3b)(9a2 + 4b2)

B. (3a - 2b)(2a - 3b)(4a2 - 9b2)

C. (3a - 2b)(3a + 2b)(9a2 + 4b2)

D. (6a - 2b)(8a - 3b)(4a3 - 9b2)

Detailed Solution

81a\(^4\) - 16b\(^4\) = (9a\(^2\))\(^2\) - (4b\(^2\))\(^2\)

= (9a\(^2\) + 4b\(^2\))(9a\(^2\) - 4b\(^2\))

N:B 9a\(^2\) - 4b\(^2\) = (3a - 2b)(3a + 2b)
There is an explanation video available below.
36.

Find x if log\(_9\)x = 1.5

A. 27

B. 15

C. 3.5

D. 32

Detailed Solution

If log\(_9\)x = 1.5,
9\(^{1.5}\) = x
9^\(\frac{3}{2}\) = x
(√9)\(^3\) = 3

∴ x = 27
There is an explanation video available below.
37.

List all integers satisfying the inequality in -2 < 2x-6 < 4

A. 2,3,4 and 5

B. 2,3

C. 2,5

D. 3,4

Detailed Solution

-2 < 2x - 6 AND 2x - 6 < 4
-2 + 6 <2x AND 2x < 4 + 6
4 <2x AND 2x < 10
: 2 <x AND x <5
2 < x < 5
As 3 and 4
There is an explanation video available below.
38.

X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X

A. 240°

B. 150°

C. 60°

D. 270°

Detailed Solution

Sinθ = \(\frac{6}{12}\)
Sinθ = \(\frac{1}{2}\)
θ = Sin\(^0.5\)
θ = 30°
Bearing of Z from X, (270 - 30)° = 240°
There is an explanation video available below.
39.

A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

A. 25

B. 19

C. 18

D. 17

Detailed Solution

Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
There is an explanation video available below.
40.

If (x + 2) and (x - 1) are factors of the expression \(Lx + 2kx^{2} + 24\), find the values of L and k.

A. l = -12, k = -6

B. l = -2 , k = 1

C. l = -2 , k = -1

D. l = 0, k = 1

Detailed Solution

Given (x + 2) and (x - 1), i.e. x = -2 or +1
when x = -2
L(-2) + 2k(-2)\(^2\) + 24 = 0
f(-2) = -2L + 8k = -24...(i)

And x = 1
L(1) + 2k(1) + 24 = 0

f(1):L + 2k = -24...(ii)
Subst, L = -24 - 2k in eqn (i)
-2(-24 - 2k) + 8k = -24
+48 + 4k + 8k = -24
12k = -24 - 48 = -72
k = \(frac{-72}{12}\)
k = -6
where L = -24 - 2k
L = -24 - 2(-6)
L = -24 + 12
L = -12
That is; K = -6 and L = -12




There is an explanation video available below.