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Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, PQ is the tangent to the circle RST at T.|ST| = ST and ∠RTQ = 68o. Find ∠PTS
Attached Figure / Diagram
A
68o
B
62o
C
61o
D
56o
E
34o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
∠TSR = 68o ∴ STR = 180-68/2 = 56o
PTS= 180-(68+56) = 56o
Source: Myschool Past Questions Archive (Record #23573)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram above shows a circle PQRS in which ∠PRQ = 54o and ∠SPQ = 97o. Find ∠PQS
Attached Figure / Diagram
A
61o
B
51o
C
43o
D
39o
E
29o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
PSQ = 54o ∴PQS = 180o - (97 + 54)o = 29o
Source: Myschool Past Questions Archive (Record #23574)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74º. Find ∠QPS
Attached Figure / Diagram
A
32o
B
37o
C
48o
D
53o
E
74o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Join PR.
< PQR = 180º - 74º = 106º
Source: Myschool Past Questions Archive (Record #23575)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
A ladder 6m long leans against a vertical wall so that it makes an angle of 60o with the wall. Calculate the distance of the foot of the ladder from the wall
A
3m
B
6m
C
2√3m
D
3√3m
E
6√3m
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 #23576)
Mathematics
WAEC / WASSCE 1994
Trigonometry, Elevation & Bearings
The bearing of Q from P is 122o, what is the bearing of P from Q?
A
212o
B
238o
C
248o
D
292o
E
302o
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 #23577)
Mathematics
WAEC / WASSCE 1994
Trigonometry, Elevation & Bearings
cos 57o has the same value as
A
sin 213o
B
-cos 303o
C
sin 147o
D
cos 123o
E
cos237o
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 #23578)
Mathematics
WAEC / WASSCE 1994
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The median of the distribution is
Attached Figure / Diagram
A
9.5kg
B
11kg
C
67kg
D
65.5kg
E
68kg
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{67 + 68}{2} = 67.5 = 68kg\)
Source: Myschool Past Questions Archive (Record #23579)
Mathematics
WAEC / WASSCE 1994
Fractions, Decimals, Percentages & Approximations
Diagram
The percentage of the students with mass less than 69kg is
Attached Figure / Diagram
A
56%
B
62.5%
C
68%
D
70%
E
87.5%
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 #23580)
Mathematics
WAEC / WASSCE 1994
Statistics (Data Representation, Central Tendency & Dispersion)
The mean heights of the three groups of students consisting of 20, 16 and 14 students are 1.67m, 1.50m and 1.40m respectively. Find the mean height of the students
A
1.52m
B
1.53m
C
1.54m
D
1.55m
E
1.56m
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 #23581)
Mathematics
WAEC / WASSCE 1994
Permutations, Combinations & Probability
Solution
Two cards are drawn one after the other with replacement from a well-shuffled ordinary deck of 52 cards containing four Aces. Find the probability that they are both Aces
A
1/221
B
1/169
C
1/52
D
1/26
E
1/13
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
1st card prob = 4/52 2nd card prob = 4/52
prob.both are aces = (4/52) x (4/52) = 1/169
Source: Myschool Past Questions Archive (Record #23582)
Mathematics
WAEC / WASSCE 1994
Permutations, Combinations & Probability
Solution
Find the probability that a number selected from the number 30 to 50 inclusive is a prime
A
1/4
B
5/21
C
2/7
D
3/10
E
1/3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
30 (31) 32 33 34 35 36 (37) 38 39 40 (41) 42 (43) 44 45 46 (47) 48 49 50
prob = 5/21
Source: Myschool Past Questions Archive (Record #23583)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Solution
The length of an exercise book is given as 20cm correct to the nearest centimeter. In which of the following ranges of possible measurement does the actual length lie?
A
19.5 - 20.4cm
B
19.1 - 20.9cm
C
19.9 - 20.1cm
D
19.95 - 20.05cm
E
19 - 21cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In mathematics, numbers ranging from 0.5 - 0.9 are approximated to 1, while 0.1 - 0.4 are taken down to 0.
Source: Myschool Past Questions Archive (Record #23584)
Mathematics
UTME / JAMB 1994
Indices, Logarithms & Surds
Solution
Solve for x if \(25^{x} + 3(5^{x}) = 4\)
A
1 or -4
B
0
C
1
D
-4 or 0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(25^{x} + 3(5^{x}) = 4\)
Let \(5^{x}\) = y.
\((5^{2})^{x} + 3(5^{x}) - 4 = 0\)
\(y^{2} + 3y - 4 = 0\)
\(y^{2} - y + 4y - 4 = 0\)
\(y(y - 1) + 4(y - 1) = 0\)
\((y + 4)(y - 1) = 0\)
\(y = -4 ; y = 1\)
y = -4 is not possible.
y = 1 \(\implies\) x = 0.
Source: Myschool Past Questions Archive (Record #30952)
Mathematics
UTME / JAMB 1994
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number
A
29
B
26
C
25
D
24
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let the sum of the 12 numbers be x and the 13th number be y.
\(\frac{x}{12} = 3 \implies x = 36\)
\(\frac{36 + y}{13} = 5 \implies 36 + y = 65\)
\(y = 65 - 36 = 29\)
Source: Myschool Past Questions Archive (Record #30953)
Mathematics
UTME / JAMB 1994
Plane Geometry, Polygons & Circle Theorems
Solution
Evaluate \(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)
A
\(\frac{28}{39}\)
B
\(\frac{13}{39}\)
C
\(\frac{39}{28}\)
D
\(\frac{84}{13}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)
\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} - \frac{10}{10} + \frac{3}{4})]\)
= \(\frac{1}{3} \div [\frac{5}{7}(\frac{-1}{10} + \frac{3}{4})]\)
= \(\frac{1}{3} \div [\frac{5}{7}(\frac{-2 + 15}{20})]\)
= \(\frac{1}{3} \div [\frac{5}{7} \times \frac{13}{20}]\)
\(\frac{1}{3} + [\frac{13}{28}]\) = \(\frac{1}{3} \times \frac{28}{13}\)
= \(\frac{28}{39}\)
Source: Myschool Past Questions Archive (Record #30957)