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Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
calculate the surface area of a sphere of radius 7cm [Take \pi = 22/7]
A
86cm2
B
154cm2
C
616cm2
D
1434cm2
E
4312cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Surface area of a sphere = \(4\pi r^2\)
= \(4 \times \frac{22}{7} \times 7 \times 7\)
= \(616 cm^2\)
Source: Myschool Past Questions Archive (Record #22665)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
If the radius of the parallel of latitude 30^\circN is equal to the radius of the parallel of latitude \theta^\circS, what is the value of \theta?
A
75o
B
60o
C
45o
D
30o
E
0o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\theta_{1} = \theta_{2} = 30^\circ\)
Source: Myschool Past Questions Archive (Record #22667)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
A cylindrical container closed at both ends, has a radius of 7cm and height 5cm [Take \pi = 22/7]
Find the total surface area of the container
A
35cm2
B
154cm2
C
220cm2
D
528cm2
E
770cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
TSA of a cylinder = \(2\pi r^2 + 2\pi rh\)
= \(2\pi r (r + h)\)
= \(2 \times \frac{22}{7} \times 7 (7 + 5)\)
= \(44 \times 12\)
= \(528 cm^2\)
Source: Myschool Past Questions Archive (Record #22668)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
A cylindrical container closed at both ends, has a radius of 7cm and height 5cm [Take \pi = 22/7]. What is the volume of the container?
A
35cm3
B
154cm3
C
220cm3
D
528cm3
E
770cm3
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Volume = \(\pi r^2 h\)
= \(\frac{22}{7} \times 7^2 \times 5\)
= \(770 cm^3\)
Source: Myschool Past Questions Archive (Record #22670)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Diagram
Solution
In the diagram above, |PQ| = |PR| = |RS| and ∠RPS = 32^\circ. Find the value of ∠QPR
Attached Figure / Diagram
A
72o
B
64o
C
52o
D
32o
E
26o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the figure, < PSR = 32^\circ (base angles of an isos. triangle)
\(\therefore\) < PRS = 180^\circ - (32^\circ + 32^\circ) = 116^\circ (sum of angles in a triangle)
< QRP = 180^\circ - 116^\circ = 64^\circ (angle on a straight line)
< PQR = 64^\circ (base angles of an isos. triangle)
< QPR = 180^\circ - (64^\circ + 64^\circ) = 52^\circ
Source: Myschool Past Questions Archive (Record #22672)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Diagram
Solution
In the diagram above, WXYZ is a rhombus and ∠WYX = 20^\circ. What is the value of ∠XZY
Attached Figure / Diagram
A
20o
B
30o
C
45o
D
60o
E
70o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Diagonals bisect at 90^\circ; < YXZ = 90^\circ - 20^\circ = 70^\circ
But ZY = XY (sides of a rhombus)
\(\therefore\) < XYZ = 70^\circ (base angle of an isos. triangle)
Source: Myschool Past Questions Archive (Record #22674)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Diagram
Solution
Which triangle is equal in area to \DeltaVWZ
Attached Figure / Diagram
A
ΔVXZ
B
ΔVYZ
C
ΔXYV
D
ΔWYV
E
ΔWYZ
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of \(\Delta\) VYZ = Area of \(\Delta\) VWZ (same base and within same parallel)
Source: Myschool Past Questions Archive (Record #22678)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Diagram
Solution
In the diagram above, PQRS s a cyclic quadrilateral, ∠PSR = 86o and ∠QPR = 38o. Calculate PRQ
Attached Figure / Diagram
A
58o
B
53o
C
48o
D
43o
E
38o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
PQR = 180o - 86o = 94o
∴PRQ = 180o - 94o - 36o = 48o
Source: Myschool Past Questions Archive (Record #22683)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Diagram
Solution
The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chart
How much money did he invest in agriculture?
Attached Figure / Diagram
A
N1,200.00
B
N1,440.00
C
N2,000.00
D
N2,910.00
E
N4,000.00
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Agric project = \(\frac{120}{360} \times N12,000.00\)
= \(N4,000.00\)
Source: Myschool Past Questions Archive (Record #22698)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
The H.C.F. of a2bx + ab2x and a2b - b2 is
A
b
B
a + b
C
b(a \(\div\) b)
D
abx(a2 - b2)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a2bx + ab2x; a2b - b2
abx(a + b); b(a2 - b2)
b(a + b)(a + b)
∴ H.C.F. = (a + b)
Source: Myschool Past Questions Archive (Record #31430)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
Simplify 3log\(_6\)9 + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
A
5
B
7776
C
log631
D
(7776)6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3 log\(_6\)9 + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
= log\(_6\)9\(^3\) + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
log\(_6\)729 + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
log\(_6\)[\(\frac{(729 \times 12 \times 64)}{72}\)] = log\(_6\)7776
= log\(_6\)6\(^5\) = 5log\(_6\)6 = 5
N.B: log\(_6\)6 = 1
Source: Myschool Past Questions Archive (Record #31441)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
Simplify (\(\frac{1}{x^{-1}} \div \frac{1}{y^{-1}}\))-1
A
\(\frac{y}{x}\)
B
xy
C
\(\frac{x}{y}\)
D
(xy)-1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Simplify (\(\frac{1}{x^{-1}} \div \frac{1}{y^{-1}}\))-1 = (\(\frac{1}{x^{-1}} \div \frac{1}{y^{-1}}\))-1
= \((x \div y)^{-1}\) = \(\frac{(x^{-1})}{y^{-1}}\)
= \(\frac{y}{x}\)
Source: Myschool Past Questions Archive (Record #31445)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
If a = 2, b = -2 and c = -\(\frac{1}{2}\), evaluate (ab2 - bc2)(a2c - abc)
A
2
B
-28
C
-30
D
-34
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(ab2 - bc2)(a2c - abc)
[2(2)2 - (- 2x\(\frac{1}{2}\))] [22(-\(\frac{1}{2}\)) - 2(-2)(-\(\frac{1}{2}\))]
[8 = \(\frac{1}{2}\)][-2 - 2] = \(\frac{17}{2}\) x 42
= -34
Source: Myschool Past Questions Archive (Record #31447)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
If f(x - 4) = x2 + 2x + 3, Find, f(2)
A
6
B
11
C
27
D
51
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
f(x - 4) = x2 + 2x + 3
To find f(2) = f(x - 4)
= f(2)
x - 4 = 2
x = 6
f(2) = 62 + 2(6) + 3
= 36 + 12 + 3
= 51
Source: Myschool Past Questions Archive (Record #31452)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
If a2 + b2 = 16 and 2ab = 7.Find all the possible values of (a - b)
A
3, -3
B
2, -2
C
1, -1
D
3, -1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
a2 + b2 = 16 and 2ab = 7
To find all possible values = (a - b)2 + b2 - 2ab
Substituting the given values = (a - b)2
= 16 - 7
= 9
(a - b) = \(\pm\)9
= \(\pm\)3
OR a - b = 3, -3
Source: Myschool Past Questions Archive (Record #31454)