Year : 
2008
Title : 
Mathematics (Core)
Exam : 
JAMB Exam

Paper 1 | Objectives

21 - 30 of 49 Questions

# Question Ans
21.

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.

A. 1

B. zero

C. -1/2

D. -1

Detailed Solution

There is an explanation video available below.
22.

Open photo

A. 100o

B. 80o

C. 50o

D. 30o

Detailed Solution

Exterior angle = sum of two interior opposite angles
y = 50° (vert. opp ∠s are equal)
X = y + 30
X = 50 + 30
X = 80°
There is an explanation video available below.
23.

Find the exterior angle of a 12 sided regular polygon

A. 12o

B. 24o

C. 25o

D. 30o

Detailed Solution

Exterior angle = 360 / n
= 360 / 12
= 30o
There is an explanation video available below.
24.

In the diagram above ∠OPQ is?

A. 90o

B. 53o

C. 36o

D. 26o

Detailed Solution

a = a(base ∠s of Iss Δ)
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53o
There is an explanation video available below.
25.

Find the area of the figure above
[π = 22/7]

A. 12.5 cm2

B. 75.0 cm2

C. 78.5 cm2

D. 84.8 cm2

Detailed Solution

Area of the figure = Area of rect + area of semi circle
\(=L \times h + \frac{1}{2}\pi r^2\\
5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times \left(\frac{5}{2}\right)^2\\
=75+\frac{(22\times 25)}{2\times7}\\
=75 + 9\frac{23}{28}\\
=84.8cm\)
There is an explanation video available below.
26.

Find the angle subtended at the center of a circle by a chord which is equal in length to the radius of the circle.

A. 30o

B. 45o

C. 60o

D. 90o

Detailed Solution

If a length of a chord is equal to the length of a radius in the same circle, the triangle formed y the chord and the radii is an equilateral triangle
∴each angle = 60o
There is an explanation video available below.
27.

Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters
[π = 22/7]

A. 44,000 liters

B. 4,400 liters

C. 440 liters

D. 44 liters

Detailed Solution

V = πr2h
1m = 100cm
14cm = 1400cm
\(∴V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\
= 44, 000 liters\)
There is an explanation video available below.
28.

The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through?

A. (2,5)

B. (5,2)

C. (1,0)

D. (0,1)

Detailed Solution

\(X = \frac{6+2}{2}=\frac{10}{2}=5\\
Y = \frac{2+2}{2}=\frac{4}{2}=2\\
∴X,Y = (5,2)\)
There is an explanation video available below.
29.

Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

A. 3/2

B. 2/3

C. -2/3

D. -3/2

Detailed Solution

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
\(=-1 \div \frac{3}{2}\\
=-1 \times \frac{-2}{3}=\frac{2}{3}\)
There is an explanation video available below.
30.

If sinθ = 3/5. Find Tanθ

A. 3/4

B. 3/5

C. 2/5

D. 1/4

Detailed Solution

sinθ = 3/5
x2 = 52 - 32
There is an explanation video available below.
21.

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.

A. 1

B. zero

C. -1/2

D. -1

Detailed Solution

There is an explanation video available below.
22.

Open photo

A. 100o

B. 80o

C. 50o

D. 30o

Detailed Solution

Exterior angle = sum of two interior opposite angles
y = 50° (vert. opp ∠s are equal)
X = y + 30
X = 50 + 30
X = 80°
There is an explanation video available below.
23.

Find the exterior angle of a 12 sided regular polygon

A. 12o

B. 24o

C. 25o

D. 30o

Detailed Solution

Exterior angle = 360 / n
= 360 / 12
= 30o
There is an explanation video available below.
24.

In the diagram above ∠OPQ is?

A. 90o

B. 53o

C. 36o

D. 26o

Detailed Solution

a = a(base ∠s of Iss Δ)
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53o
There is an explanation video available below.
25.

Find the area of the figure above
[π = 22/7]

A. 12.5 cm2

B. 75.0 cm2

C. 78.5 cm2

D. 84.8 cm2

Detailed Solution

Area of the figure = Area of rect + area of semi circle
\(=L \times h + \frac{1}{2}\pi r^2\\
5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times \left(\frac{5}{2}\right)^2\\
=75+\frac{(22\times 25)}{2\times7}\\
=75 + 9\frac{23}{28}\\
=84.8cm\)
There is an explanation video available below.
26.

Find the angle subtended at the center of a circle by a chord which is equal in length to the radius of the circle.

A. 30o

B. 45o

C. 60o

D. 90o

Detailed Solution

If a length of a chord is equal to the length of a radius in the same circle, the triangle formed y the chord and the radii is an equilateral triangle
∴each angle = 60o
There is an explanation video available below.
27.

Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters
[π = 22/7]

A. 44,000 liters

B. 4,400 liters

C. 440 liters

D. 44 liters

Detailed Solution

V = πr2h
1m = 100cm
14cm = 1400cm
\(∴V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\
= 44, 000 liters\)
There is an explanation video available below.
28.

The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through?

A. (2,5)

B. (5,2)

C. (1,0)

D. (0,1)

Detailed Solution

\(X = \frac{6+2}{2}=\frac{10}{2}=5\\
Y = \frac{2+2}{2}=\frac{4}{2}=2\\
∴X,Y = (5,2)\)
There is an explanation video available below.
29.

Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

A. 3/2

B. 2/3

C. -2/3

D. -3/2

Detailed Solution

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
\(=-1 \div \frac{3}{2}\\
=-1 \times \frac{-2}{3}=\frac{2}{3}\)
There is an explanation video available below.
30.

If sinθ = 3/5. Find Tanθ

A. 3/4

B. 3/5

C. 2/5

D. 1/4

Detailed Solution

sinθ = 3/5
x2 = 52 - 32
There is an explanation video available below.