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Physics
UTME / JAMB 1988
Equilibrium of Forces, Moments & Flotation
Diagram
Solution
the fig above shows three different ways of hanging a heavy picture from a hook. the tension in the string will be?
Attached Figure / Diagram
A
Greatest in X
B
Greatest in Y
C
Greatest in Z
D
Same in each one
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
Gravity is always directed in a vertical fashion at X (i.e. 90 degrees which is where tension will be minimum).
The more horizontally aligned the cable is, the more it will pull horizontally. This increased horizontal pull will increase the tension in the cable.
Source: WAEC / JAMB / NECO Classroom Archive (Record #41668)
Physics
WAEC / WASSCE 1988
Magnetism, Electromagnetism & AC Circuits
Solution
What is the effect of using split-rings in a simple d.c motor?
A
The direction of rotation of the coil is reversed
B
The current in the coil flows in the same direction
C
The current in the coil becomes alternating
D
The direction of the force on the coil is reversed
E
The contact with the voltage is cut-off
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Split ring is used for reversing the direction of current in the coil. For the continuous rotation of the coil in the same direction, the current in the coil must be reversed.
Source: WAEC / JAMB / NECO Classroom Archive (Record #23840)
Chemistry
UTME / JAMB 1988
Particulate Nature of Matter, Laws & Formulae
Solution
2.25g of a sample of an oxide of copper on reduction gave 2.0g of copper. 2.50g of another oxide of copper on reduction also gave 2.0g of copper. These results are in accordance with the law of?
A
constant composition
B
conservation of matter
C
multiple proportions
D
definite proportions
medium Difficulty
Verified Correct Answer: Option C
Chemical Principles & Mechanism
law of multiple proportions, statement that when two elements combine with each other to form more than one compound, the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.
Source: WAEC / JAMB / NECO Classroom Archive (Record #14226)
Chemistry
UTME / JAMB 1988
Organic Chemistry II: Functional Groups, Polymers & Biomolecules
Solution
Alkanoates are formed by the reaction of alkanoic acid with?
A
Alkyl halides
B
alkanols
C
ethers
D
sodium
medium Difficulty
Verified Correct Answer: Option B
Chemical Principles & Mechanism
Alkanoate: Any salt or ester formed from the reaction of an alkanoic acid and alkanol.
Source: WAEC / JAMB / NECO Classroom Archive (Record #14219)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Diagram
Which of the regions P, Q, R, S and T satisfies the following 0 < y < 1, y < x + 2, x < 0
Attached Figure / Diagram
A
P
B
Q
C
R
D
S
E
T
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 #22185)
Mathematics
WAEC / WASSCE 1988
Mensuration (Areas, Perimeters & Volumes)
Solution
A cone is made from a sector of circle of radius 14cm and angle of 90o. What is the area of the curved surface of the cone? (Take x = 22/7)
A
22cm2
B
38.5cm2
C
77cm2
D
154cm2
E
308cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Length of arc = θ/360 * 2πr
=> r = 90/360 * 14/4 = 3.5
slant height t = 14cm
curved surface area of cone = πrl
=> 3.142 x 3.5 x 14 = 153.95
Source: Myschool Past Questions Archive (Record #22192)
Mathematics
WAEC / WASSCE 1988
Mensuration (Areas, Perimeters & Volumes)
Solution
A rope of length 18m is used to form a sector of a circle of radius 3.5m on a school playing field. What is the size of the angle of the sector, correct to the nearest degree?
A
33o
B
40o
C
90o
D
180o
E
270o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Circumference = 2\pir
2 x 22/7 x 3.5 ≅ 22m
22m = 360o
11m = 360/22 x 11 = 180o
Source: Myschool Past Questions Archive (Record #22199)
Mathematics
WAEC / WASSCE 1988
Trigonometry, Elevation & Bearings
Diagram
Solution
In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?
Attached Figure / Diagram
A
135o
B
105o
C
90o
D
75o
E
60o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\Delta RPS\) = Isosceles triangle
\(\therefore < RPS = \frac{180^\circ - 90^\circ}{2}\) = 45^\circ
In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\) = 30^\circ
\(\therefore < QPS = 30^\circ + 45^\circ = 75^\circ\)
Source: Myschool Past Questions Archive (Record #22208)
Mathematics
WAEC / WASSCE 1988
Mensuration (Areas, Perimeters & Volumes)
Solution
Cotonou and Niamey are on the same line of longitude and Niamey is 7o north of Cotonou. If the radius of the earth is 6400km, how far is Niamey north of Cotonou along the line of longitude, correct to the nearest kilometer? [Take π = 22/7]
A
391km
B
503km
C
782km
D
1006km
E
2012km
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
θ/360 * 2πR
= 7/360 * 2 * 22/7 * 6400 = 782km
Source: Myschool Past Questions Archive (Record #22226)
Mathematics
WAEC / WASSCE 1988
Sets, Logic & Venn Diagrams
Solution
If Q = (all perfect squares less than 30) and P = (all odd numbers from 1 to 10). Find Q ∩ P.
A
(1, 4, 9, 16, 25)
B
(1, 3, 4, 5, 7, 9, 16, 25)
C
(1, 3, 5, 7, 9)
D
(1, 9)
E
Φ
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Q = {1, 4, 9, 16, 25} P = { 1, 3, 5, 7, 9}
Q ∩ P = { 1, 9}
Source: Myschool Past Questions Archive (Record #22227)
Mathematics
WAEC / WASSCE 1988
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. How many candidates scored at most 30%?
Attached Figure / Diagram
A
15,000
B
20,000
C
25,000
D
35,000
E
60,000
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Those who scored at most 30% = ( 5 + 10 + 20)thousand = 35000
Source: Myschool Past Questions Archive (Record #22229)
Mathematics
WAEC / WASSCE 1988
Permutations, Combinations & Probability
Solution
The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname
What is the probability that the surname of a child picked at random from the class begins with either O or A?
A
5/8
B
7/8
C
9/16
D
14/25
E
39/40
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No. of possible outcome = 40
No. of expected outcome = 16 + 9 = 25
Probability = 25/40 = 5/8
Source: Myschool Past Questions Archive (Record #22230)
Mathematics
WAEC / WASSCE 1988
Permutations, Combinations & Probability
Solution
The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname
If more than one surname begins with a letter besides A and O, how may surnames begin with that letter
A
2
B
3
C
4
D
5
E
6
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
14 of the letters of the alphabet do not appear as the first letter of surname
∴ the no. of letters that appeared = 26-14 = 12 alphabets
15 surnames begin with 10 letters beside O and A
∴ 6 surnames begin with a letter
Source: Myschool Past Questions Archive (Record #22231)
Mathematics
UTME / JAMB 1988
Indices, Logarithms & Surds
Solution
If \(1P03{_4} = 115_{10}\) find P
A
o
B
1
C
2
D
3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(1 x 4^3 + P x 4^2 + 0 x 4 + 3 = 115_{10}\)
16p + 67 = 115 p = \(\frac{48}{16}\)
= 3
Source: Myschool Past Questions Archive (Record #30761)
Mathematics
UTME / JAMB 1988
Plane Geometry, Polygons & Circle Theorems
Solution
If \(\frac{1}{p}\) = \(\frac{a^2 + 2ab + b^2}{a - b}\) and \(\frac{1}{q}\) = \(\frac{a + b}{a^2 - 2ab + b^2}\) Find \(\frac{p}{q}\)
A
\(\frac{a + b}{a - b}\)
B
\(\frac{1}{a^2 - b^2}\)
C
\(\frac{a - b}{a + b}\)
D
a2 - b2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{p} = \frac{a^{2} + 2ab + b^{2}}{a - b}\)
\(\frac{1}{q} = \frac{a + b}{a^{2} - 2ab + b^{2}}\)
\(\frac{1}{p} = \frac{(a + b)^{2}}{a - b}\)
\(\frac{1}{q} = \frac{a + b}{(a - b)^{2}}\)
\(\therefore p = \frac{a - b}{(a + b)^{2}}\)
\(\frac{p}{q} = p \times \frac{1}{q} = \frac{a - b}{(a + b)^{2}} \times \frac{a + b}{(a - b)^{2}}\)
= \(\frac{1}{(a + b)(a - b)}\)
= \(\frac{1}{a^{2} - b^{2}}\)
Source: Myschool Past Questions Archive (Record #31627)