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Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
Solve: 6(x - 4) + 3(x + 7) = 3
A
3/2
B
2/3
C
1/2
D
1/3
E
o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
6(x - 4) + 3(x + 7) = 3
6x - 24 + 3x + 21 = 3
9x - 3 = 3
9x = 6
x = \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #22875)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
If 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?
A
1
B
3
C
7
D
10
E
17
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2x + y = 7 = i
3x - 2y = 3 = ii
i x 2 + ii = 4x + 2y = 14
\(\frac {3x - 2y = 3}{7x = 17}\)
x = \(\frac {17}{7}\) = 7x = 17 x 1/7 x 7
17 - 10 = 7
Source: Myschool Past Questions Archive (Record #22876)
Mathematics
WAEC / WASSCE 1991
Mensuration (Areas, Perimeters & Volumes)
Solution
A cylinder of base radius 4cm is open at one end . If the ratio of the area of its base to that of its curved surface is 1:4, calculate the height of the cylinder
A
1cm
B
2cm
C
4cm
D
8cm
E
16cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
r= 4cm; base area = \(\pi\)r2; Curve S.A = 2\(\pi\)rh
\(\frac{base area}{curved area}\) = 1/4; \(\pi\)/2\(\pi\)rh
=h = \(\frac{4 x 4cm}{2}\)
h= 8cm
Source: Myschool Past Questions Archive (Record #22877)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Solution
A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum (p.a) and the wife earns N4,000 (P.a), find the sum of their annual contribution to the fund
A
N1045
B
N605
C
N545
D
N490
E
N440
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Husband contributions = \(\frac{7}{100}\) x N5,500 = N385
Wife contribution = \(\frac{4}{100}\) x N4,000 = N160
Sum of their Annual contribution = N385 + N160 = N545
Source: Myschool Past Questions Archive (Record #22878)
Mathematics
WAEC / WASSCE 1991
Linear, Simultaneous & Quadratic Equations
Solution
A car is travelling at an average speed of 80km/hr. Its speed in meters per second (m/s) is
A
13.3m/s
B
22.2m/s
C
133.3m/s
D
222.2m/s
E
1333.3m/s
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
80km/h = \(\frac{80}{60}\) x \(\frac{1000}{60}\) = 3 x 3= \(\frac{40 x 5}{9}\)
= \(\frac{200m/s}{9}\) = 22.22m/s
Source: Myschool Past Questions Archive (Record #22879)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Solution
Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.
A
41.2%
B
18.3%
C
5.3%
D
1.7%
E
1.4%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Error =12.75 - 7.50 = 5.25
Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%
Source: Myschool Past Questions Archive (Record #22880)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
In the diagram above, PXR and PYO are two semi-circles with diameters 14cm and 7cm respectively. Find the area of the enclosed region, PXROY correct to the nearest whole number
Attached Figure / Diagram
A
96cm2
B
116cm2
C
154cm2
D
192cm2
E
385cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Area of the bigger semi circle PRO = \(\frac{\pir^2}{2}\)
= \(\frac{22}{7}\) x \(\frac{49}{2}\) = 77cm\(^2\)
2nd Area of the smaller circle DYO = \(\frac{22}{7}\) x \(\frac{3.5^2}{2}\) = 19.25cm\(^2\)
Total Area = 77 + 19.25 = 96.25 ≈ 96.00cm\(^2\)
Source: Myschool Past Questions Archive (Record #22911)
Mathematics
WAEC / WASSCE 1991
Coordinate Geometry
Diagram
Solution
Find the coordinates of point B
Attached Figure / Diagram
A
(0,11/2)
B
(O,2)
C
(2,0)
D
(11/2, 2)
E
(11/2, 0)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
B occurs at the point y = 0.
When y = 0, we have
4x + 3(0) = 6
4x = 6
x = 1\(\frac{1}{2}\)
B = \((1\frac{1}{2}, 0)\)
Source: Myschool Past Questions Archive (Record #22915)
Mathematics
WAEC / WASSCE 1991
Sequences & Series (AP & GP)
Solution
The first term a of an A.P is equal to twice the
common difference d. Find, in terms of d, the 5th
term of the A.P.
A
4d
B
5d
C
6d
D
a + 5d
E
2a + 4d
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Tn = a + (n - 1)d; AP; a = 2d; Tn = 2d + (n - 1)d
T5 = 2d + (5 - 1)d = 2d + 4d = 6d
Source: Myschool Past Questions Archive (Record #22916)
Mathematics
WAEC / WASSCE 1991
Sequences & Series (AP & GP)
Solution
The common ratio of a G.P. is 2. If the 5th term is
greater than the 1st term by 45, find the 5th term,
A
3
B
6
C
45
D
48
E
90
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
a = 1st term ; ar\(^4\) = 5th term
∴ ar\(^4\) = a(2)\(^4\) = 16a; 16a = 45 + a, a = 3;
3(2)\(^4\) = 48
Source: Myschool Past Questions Archive (Record #22917)
Mathematics
WAEC / WASSCE 1991
Trigonometry, Elevation & Bearings
Solution
Two towns, P and Q, are on (4oN 40oW) and (4oN
20oE) respectively. What is the distance between
them, along their line of latitude? (Give your
answer in teems of π and R, the radius of the earth).
A
2πR cos4o
B
πR sin40o
C
πR/2 cos4o
D
πR/3 cos4o
E
πR/6 cos4o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Angular distance = 40o + 20o = 60o
using θ/360 x 2πr for distance between p and Q
= 60/360 x 2πRcos4o = 1/3πRcos4o
Source: Myschool Past Questions Archive (Record #22918)
Mathematics
WAEC / WASSCE 1991
Trigonometry, Elevation & Bearings
Diagram
Solution
the graph above is a sketch of
Attached Figure / Diagram
A
y = sin 2x
B
y=sinx
C
y=cos2x
D
y=2sinx
E
y = 2cos x
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
by using trial and error Y = sinx since \(\pi\) in radian = 180º
Source: Myschool Past Questions Archive (Record #22920)
Mathematics
WAEC / WASSCE 1991
Inequalities & Linear Programming
Solution
Given that sin \(\theta\) = -0.9063, where O \(\leq\) \(\theta\) \(\leq\) 270^\circ, find \(\theta\).
A
65o
B
115o
C
145o
D
245o
E
265o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sin\(\theta\) = -0.9063; \(\theta\) = sin-1(0.9063)
\(\theta\) = -64.99 = -65^\circ
\(\theta\) = 180^\circ - (-65);
180 + 65 = 245^\circ
Source: Myschool Past Questions Archive (Record #22921)
Mathematics
WAEC / WASSCE 1991
Trigonometry, Elevation & Bearings
Solution
From the top of a cliff, the angle of depression of
a boat on the sea is 60o, if the top of the cliff is
25m above the sea level, calculate the horizontal
distance from the bottom of the cliff to the boat.
A
50√3m
B
25√3m
C
25√3m/3
D
25m/3
E
√3m/25
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x/25 = tan 30o
x = 25/√3 = 25√3/3
Source: Myschool Past Questions Archive (Record #22923)
Mathematics
WAEC / WASSCE 1991
Trigonometry, Elevation & Bearings
Solution
The angle of elevation of the top of a tree 39m
away from a point on the ground is 30o. Find the height of the tree
A
39√3m
B
13√3m
C
13/\(\sqrt{3}\)m
D
13/3\(\sqrt{3}\)m
E
\(\sqrt{3}\)/13m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x/25 = tan 30o
x = 39 x 1/√3 = 13√3m
Source: Myschool Past Questions Archive (Record #22924)