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Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
In the diagram PQ is a diameter of circle PMQN center O, if ∠PQM = 63o, find ∠MNQ
Attached Figure / Diagram
A
58.5o
B
44o
C
35o
D
31.5o
E
27o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
In the given diagram,
< PMQ = 90º (< in a semi-circle)
Source: Myschool Past Questions Archive (Record #26357)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ∠POQ = 50o. Use the diagram to answer question below. (take π = 3.142)
Calculate correct to one decimal place, the length of arc PQ.
Attached Figure / Diagram
A
175.0cm
B
157.1cm
C
37.7cm
D
11.0cm
E
3.1cm
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #26358)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector
A
\(1\frac{3}{5}cm^2\)
B
2cm2
C
8cm2
D
10cm2
E
20cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26361)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
The diagram above is a rectangle. If the perimeter is 36m, find the area of the rectangle
Attached Figure / Diagram
A
\(64m^2\)
B
\(65m^2\)
C
\(84m^2\)
D
\(124m^2\)
E
\(275m^2\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #26364)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Solution
In \(\triangle PQR\). T is a point on QR such that \(\angle QPT = 39^o and \angle PTR = 83^o. Calculate \angle PQT\)
A
\(34^o\)
B
\(44^o\)
C
\(45^o\)
D
\(97^o\)
E
\(107^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In △ PQR, < PQT + 39º = 83º (sum of opposite interior
Source: Myschool Past Questions Archive (Record #26365)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
Find the angle x in the diagram above
Attached Figure / Diagram
A
310o
B
230o
C
190o
D
130o
E
100o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The given shape is a pentagon(5-sided polygon) = 540º
540º - ( 105º + 105º + 50º + 50º) = yº
yº = 230º
But yº + xº = 360º (
Source: Myschool Past Questions Archive (Record #26367)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
P varies inversely as Q. The table above shows the value of Q for some selected values of P
What is the missing value of Q in the table?
Attached Figure / Diagram
A
4
B
9
C
15
D
16
E
144
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
K = 6 x 24 = 144 from the first column
P = \(\frac{\text{K}}{\text{Q}}\)
when P = 9, Q = ?
Q = \(\frac{144}{9}\) = 16
Source: Myschool Past Questions Archive (Record #26371)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Three of the angles of a hexagon are each Xo. The others are each 3Xo. Find X
A
30o
B
40o
C
60o
D
80o
E
120o
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 #26372)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Solution
Evaluate \(3.0\times 10^1 - 2.8\times 10^{-1}\)leaving the answer in standard form
A
\(2\times 10^{-1}\)
B
\(2\times 10^{2}\)
C
\(2.972 \times 10^{1}\)
D
\(2.972 \times 10^{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3.0\times 10^1 - 2.8\times 10^{-1}\) = 30 - 0.28 = 29.72 = 2.972 x 10\(^1\)
Source: Myschool Past Questions Archive (Record #26376)
Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
Solution
A man is paid r naira per hour for normal work and double rate for overtime. if he does a 35-hour week which includes q hours of overtime, what is his weekly earning in naira?
A
r(35 + q)
B
q(35r - q)
C
q(35 + r)
D
r(35 + 2q)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The cost of normal work = 35r
The cost of overtime = q x 2r = 2qr
The man's total weekly earning = 35r + 2qr
= r(35 + 2q)
Source: Myschool Past Questions Archive (Record #30650)
Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
The locus of all points at a distance 8cm from a point N passes through points T and S. If S is equidistant from T and N, find the area of triangle STN.
A
4\(\sqrt{3cm^2}\)
B
16\(\sqrt{3cm^2}\)
C
32cm2
D
64cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #30722)
Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
Solution
If the distance between the points (x, 3) and (-x, 2) is 5. Find x
A
6.0
B
2.5
C
\(\sqrt{6}\)
D
\(\sqrt{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
d2 = (y - y)2 + (x - x)2
5 = 4x2 + 1 = 25= 4x2 + 1
= 4x2 = 25 - 1= 24
x2 = \(\frac{24}{4}\)
x = \(\sqrt{6}\)
Source: Myschool Past Questions Archive (Record #30724)
Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
Solution
From the top of a vertical mast 150m high., two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are 60o and 45o respectively. Find the distance between the huts
A
150(1 + \(\sqrt{3}\))m
B
50(3 + \(\sqrt{3}\))m
C
150 \(\sqrt{3}\)m
D
\(\frac{50}{\sqrt{3}}\)m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Tan60º = \(\frac{150}{y}\)
\(\sqrt{3}\) = \(\frac{150}{y}\)
y = \(\frac{150\sqrt3}{3}\)
y = 50\(\sqrt3\)
Tan45º = \(\frac{150}{z}\)
1 = \(\frac{150}{z}\)
z = 150
But x = z + y
x = 150 + 50\(\sqrt3\)
x = 50(3 +\(\sqrt{3}\))m
Source: Myschool Past Questions Archive (Record #30734)
Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
Solution
Differentiate \(\frac{x}{cosx}\) with respect to x
A
1 + x sec x tan x
B
1 + sec2 x
C
cos x + x tan x
D
x sec x tan x + secx
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
let y = \(\frac{x}{cosx}\) = x sec x ( since \(\frac{1}{cosx}\) = sec x )
let u = x, v = sec x
\(\frac{dy}{dx}\) = U\(\frac{dy}{dx}\) + V\(\frac{du}{dx}\)
\(\frac{dy}{dx}\) = x [secx tanx] + secx
Therefore, \(\frac{dy}{dx}\)\(\frac{x}{cosx}\) = x secx tanx + secx
Source: Myschool Past Questions Archive (Record #30738)
Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
Solution
Find the positive value of x if the standard deviation of the numbers 1, x + 1, 2x + 1 is \(\sqrt6\)
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
mean (x̄) = \(\frac{1 + x + 1 + 2x + 1}{3}\)
= \(\frac{3x + 3}{3}\)
= 1 + x
\(\begin{array}{c|c} X & (X -X) & (X -X)^2\\ \hline 1 & -x & x^2 \\ x + 1 & 0 & 0\\2x + 1 & x & x^2\\ \hline & & 2x^2\end{array}\)
S.D = \(\sqrt{\frac{\sum(x - x)^2}{n}}\) = \(\sqrt{(6)}\) ( given )
\(\sqrt{(6)}\) = \(\sqrt{\frac{2x^2}{3}}\)
cancel square roots and cross multiply
\(2x^2\) = 18
divide both sides by 2
\(x^2\) = 9
∴ x = \(\pm\) \(\sqrt{9}\)
= \(\pm\)3
Source: Myschool Past Questions Archive (Record #30751)