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Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Solution
A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
A
36\(\pi\)cm2
B
54\(\sqrt{3}\)cm2
C
\(\sqrt{3}\)cm2
D
\(\frac{1}{x - 1}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sum of interior angle of hexagon = [2(6) - 4]90o
= 720o
sum of central angle = 360o
Each central angle = \(\frac{360}{6}\)
= 60o
Area of Hexagon = \(\frac{1}{2}\) x 6 x 6 sin 60o
\(\frac{36 \times 6\sqrt{3}}{2 \times 2}\)
= \(54 \sqrt{3}\)cm2
Source: Myschool Past Questions Archive (Record #32710)
Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Solution
If sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3, then the angle \(\theta\) is equal to
A
30o
B
45o
C
60o
D
90o
E
105o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3
Where 1 + tan\(^2\) \(\theta\) = sec\(^2\) \(\theta\)
1 + tan\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3
2 tan\(^2\) \(\theta\) = 2
tan\(^2\) \(\theta\) = 1
tan\(\theta\) = \sqrt1
where \sqrt1 = 1
tan\(\theta\) = 1
And tan 45^\circ = 1
∴ \(\theta\) = 45^\circ
Source: Myschool Past Questions Archive (Record #32712)
Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Solution
Two triangles have the same areas if
A
two sides in one triangle are equal to two sides in the other
B
three sides in one triangle are equal to three sides in the other
C
two angles in the triangle are equal to two angles in the other
D
three angles in one triangle are equal to three angles in the other
E
one side and the opposite angle in one triangle are equal to one side and the opposite angle in the other
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Two triangles have the same area if three sides in one triangle equal to three in the other.
Source: Myschool Past Questions Archive (Record #32717)
Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Solution
The locus of all points having a distance of 1 unit from each of the two fixed points a and b is
A
a line parallel to the line ab
B
a line perpendicular to the line ab through the mid-point of ab
C
a circle through a and b with centre at the mid-point of ab
D
a circle with centre at a and passes through b
E
a circle in a plane perpendicular to ab and centre at the mid-point of the line ab
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The locus of all points having a distance of 1 unit from each of the two fixed points. a and b is: a perpendicular to the (ab) through the mid-points ab
Source: Myschool Past Questions Archive (Record #32720)
Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)
A
-3
B
3
C
\(\frac{3}{5}\)
D
\(\frac{-3}{2}\)
E
1n 6 - 2 1n 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #32721)
Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Diagram
Solution
In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.
Attached Figure / Diagram
A
4cm
B
6cm
C
3cm
D
2cm
E
1cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Angles ADE and EFC are similar,
Therefore,
= \(\frac{x}{3} = \frac{4}{2}\)
= \(\frac{x}{3} = 2\)
x = 3 x 2 = 6
Source: Myschool Past Questions Archive (Record #32729)
Mathematics
UTME / JAMB 1978
Geometry and Trigonometry
Diagram
Solution
In the figure, AB is parallel to CD then x + y + z is
Attached Figure / Diagram
A
185o
B
200o
C
270o
D
360o
E
195o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x + y + z = 360^\circ (angles at a point)
Source: Myschool Past Questions Archive (Record #32730)