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Mathematics
WAEC / WASSCE 1988
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
A water tank is made with a right-angled trapezium - shaped vertical cross-section so that when it is placed on sloping ground the top of the tank is level. The dimension are given in the diagram above
By what number will you multiply your answer in 22 above to determine the capacity of the tank in liters?
Attached Figure / Diagram
A
1/10
B
1
C
10
D
100
E
1000
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
The shape is a prism so volume of the tank = base area x height = \(\frac{1}{2}\)( a + b) x height = \(\frac{1}{2}\)(4 + 7) x 4 x 6 = 132cm\(^3\)
But 1000cm\(^3\) = 1litres
132cm\(^3\) =
Source: Myschool Past Questions Archive (Record #22085)
Mathematics
WAEC / WASSCE 1988
Indices, Logarithms & Surds
Solution
Evaluate log106 + log1045 - log1027 without using logarithm tables
A
o
B
1
C
1.1738
D
1.3802
E
10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log106 + log1045 - log1027
log10 \(\frac{6 \times 45}{27}\)
= log102 x 5
log1010 = 1
Source: Myschool Past Questions Archive (Record #22092)
Mathematics
WAEC / WASSCE 1988
Sequences & Series (AP & GP)
Solution
Find the product xy if, x, 3/2, 6/7, y are in G.P
A
24/49
B
4/7
C
9/7
D
7/4
E
21/8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In GP, when you are given three consecutive terms, say f, g, h, then
\(f \times h = g^2\)
Given: \(x, \frac{3}{2}, \frac{6}{7}, y\), then
\(\frac{6x}{7} = (\frac{3}{2})^2 \implies \frac{6x}{7} = \frac{9}{4} ... (i)\)
Also, \(\frac{3y}{2} = (\frac{6}{7})^2 \implies \frac{3y}{2} = \frac{36}{49} ... (ii)\)
From \(\frac{6x}{7} = \frac{9}{4} \implies x = \frac{9 \times 7}{6 \times 4}\)
\(x = \frac{21}{8}\)
Also, \(\frac{3y}{2} = \frac{36}{49} \implies y = \frac{2 \times 36}{3 \times 49}\)
= \(\frac{24}{49}\)
\(xy = \frac{21}{8} \times \frac{24}{49} = \frac{9}{7}\)
Source: Myschool Past Questions Archive (Record #22101)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, O is the center of the circle, BOC is a diameter and angle ADC is 37o
What is ACB?
Attached Figure / Diagram
A
147o
B
127o
C
65o
D
53o
E
37o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From the figure \(< ABC = < ADC = 37^\circ\) (angles on the same segment)
\(< BCA = 90^\circ\) (angle in semi-circle)
\(\therefore\) In \(\Delta ABC\), \(< ACB = 180^\circ - (37^\circ + 90^\circ)\)
= 53^\circ
Source: Myschool Past Questions Archive (Record #22148)
Mathematics
WAEC / WASSCE 1988
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize 5y\(^2\) + 2ay - 3a\(^2\)
A
(5y - a) (y + 3a)
B
(5y + a) (y - 3a)
C
5y2 + a (2y - 3a)
D
(y - a) (5y + 3a)
E
(y + a) (5y - 3a)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
5y 2 + 5ay - 3ay - 3a 2
5y(y + a) - 3a(y + a)
(y + a) (5y - 3a)
Source: Myschool Past Questions Archive (Record #22160)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Diagram
Which of the following is a correct method for constructing an angle of 60o at Q?
Attached Figure / Diagram
A
I only
B
II only
C
III only
D
I and II only
E
II and III only
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 #22161)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
IN the diagram above, LK/PQ, reflex angle KLM = 241^\circ and ∠QPM = 89^\circ. What is the value of ∠LMP?
Attached Figure / Diagram
A
30o
B
61o
C
89o
D
119o
E
150o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Produce ML to R.
From the figure < LRM = 89^\circ (corresponding angles)
In triangle LRM, < LMR = 180^\circ - (61^\circ + 89^\circ)
= 30^\circ
Source: Myschool Past Questions Archive (Record #22165)
Mathematics
WAEC / WASSCE 1988
Mensuration (Areas, Perimeters & Volumes)
Solution
Abidjan is 4o west of Accra and on the same circle of latitude. If the radius of this circle of latitude is 6370km, how far is Abidjan west of Accra, correct to the nearest kilometer? [Take π = 22/7]
A
222km
B
445km
C
890km
D
5005km
E
10010km
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
θ/360* 2πr = Rcos4o
4/360* 40041/1= 445km
Source: Myschool Past Questions Archive (Record #22182)
Mathematics
UTME / JAMB 1988
Inequalities & Linear Programming
Solution
Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.
A
4≤X≤5
B
5≤X≤8
C
5≤X≤10
D
8≤X≤10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Number of oranges = X; Costing N5X.
Number of mangoes = 2X; Costing N8X.
\(\therefore 65 \leq 5X + 8X \leq 130\)
\(5 \leq X \leq 10\)
Source: Myschool Past Questions Archive (Record #21)
Chemistry
WAEC / WASSCE 1988
Reaction Rates & Chemical Equilibrium
Equilibrium is said to be attained in reversible reaction when
A
all the reactants have been used up
B
all the products have been formed
C
there is no further change in temperature
D
the rates of the forward and backward reactions are equal
E
the rate of formation of the products decreases with time
medium Difficulty
Verified Correct Answer: Option D
Chemical Principles & Mechanism
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #36020)
Chemistry
WAEC / WASSCE 1988
Organic Chemistry II: Functional Groups, Polymers & Biomolecules
An acid present in proteins is
A
lactic acid
B
amino acid
C
propanoic acid
D
palmitic acid
E
stearic acid
medium Difficulty
Verified Correct Answer: Option B
Chemical Principles & Mechanism
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #36021)
Chemistry
WAEC / WASSCE 1988
Metals, Transition Elements & Extraction
The following are uses of sulphur except
A
manufacture of tetraoxosulphate (VI) acid
B
prevention of the growth of fungi
C
vulcanization rubber
D
manufacture of dyes
E
coating of steel to prevent rusting
medium Difficulty
Verified Correct Answer: Option E
Chemical Principles & Mechanism
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #36022)
Chemistry
WAEC / WASSCE 1988
Acids, Bases, pH & Salts
The reaction represented by the equation NaOH(aq) + HCI(aq) → NaCI(aq) + H2O(/)
A
is a double decomposition
B
is a neutralization
C
is reversible
D
is usually catalysed
E
attains equilibrium after a few seconds
medium Difficulty
Verified Correct Answer: Option B
Chemical Principles & Mechanism
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #36023)
Chemistry
WAEC / WASSCE 1988
Organic Chemistry I: Hydrocarbons & Crude Oil
Which of the following compound is aromatic?
A
Benzene
B
Cyclobutane
C
Cyclopentane
D
Hexane
E
Ethene
medium Difficulty
Verified Correct Answer: Option A
Chemical Principles & Mechanism
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #36024)
Chemistry
WAEC / WASSCE 1988
Reaction Rates & Chemical Equilibrium
Which of the following does not affect the rate of a chemical reaction?
A
Addition or presence of a catalyst
B
Size of the reacting particles
C
The enthalpy change for the reaction
D
Concentration of the reactants
E
Temperatureat which the reaction is carried out
medium Difficulty
Verified Correct Answer: Option C
Chemical Principles & Mechanism
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #36025)