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Chemistry
WAEC / WASSCE 1992
Particulate Nature of Matter, Laws & Formulae
Solution
What is the number of oxygen atoms in 32g of the gas? (O = 16, L = 6.0 X 10\(^{23}\) mol\(^{-1}\))
A
3.2 X 10 23
B
6.0 X 1023
C
1.2 X 1024
D
1.6 X 1024
E
2.0 X 1024
medium Difficulty
Verified Correct Answer: Option B
Chemical Principles & Mechanism
Oxygen is Diatomic
: 1 mole of oxygen contains 2 ATOMS
→ 2 X 16g = 32g
32g of the gas = 6.0 X 10\(^{23}\) mol\(^{-1}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #36225)
Chemistry
WAEC / WASSCE 1992
Kinetic Theory of Matter & Gas Laws
Solution
If the volume of a given mass of gas at 298 K and pressure of 205.2 x 10\(^3\) Nm\(^{-2}\) is 2.12dm\(^3\), what is volume of the gas at s.t.p? (Standard pressure = 101.3 x 10\(^3\) Nm\(^{-2}\), Standard temperature = 273K)
A
39.3dm 3
B
22.4dm3
C
4.93dm3
D
3.93dm3
E
0.393dm3
medium Difficulty
Verified Correct Answer: Option D
Chemical Principles & Mechanism
V\(_1\) = 2.12dm\(^3\), V\(_2\) = ?
P\(_1\) = 205.2 x 10\(^3\) Nm\(^{-2}\), P\(_2\) = 101.3 x 10\(^3\) Nm\(^{-2}\)
T\(_1\) = 293K, T\(_2\) = 273K
Using \(\frac{P_1 * V_1}{T_1}\) = \(\frac{P_2 * V_2}{T_2}\)
: V\(_2\) = \(\frac{P_1 * V_1 * T_2}{P_2 * T_1}\)
→ \(\frac{205.2 x 10^3 * 2.12 * 273}{101.3 x 10^3 * 293}\)
= 4.0dm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #36182)
Chemistry
WAEC / WASSCE 1992
Chemical Energetics & Thermochemistry
Solution
Study carefully the reaction represented by the equation below. 2H2O 2(l) → O 2(g) + 2H2O(l). Which of the following will not reaction increase the reaction rate?
A
Heating the hydrogen peroxide
B
Adding a pinch of MnO2 to the reactant
C
increasing the concentration of the H2O2
D
Adding water to the reactant
E
Exposing the reactant to sunlight
medium Difficulty
Verified Correct Answer: Option D
Chemical Principles & Mechanism
Reaction of decomposition of hydrogen peroxide is very slow in moderate temperatures without the presence of a catalyst.
It can be sped up by increasing the temperature, which triggers the reaction of thermal decomposition.
Source: WAEC / JAMB / NECO Classroom Archive (Record #36178)
Mathematics
WAEC / WASSCE 1992
Sets, Logic & Venn Diagrams
Solution
Let U = {1, 2, 3, 4}, P = {2, 3} and Q = {2, 4}. What is (P∩Q)'?
A
(1, 2, 3)
B
(1, 3, 4)
C
(2, 3)
D
(1, 3)
E
(1, 4)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
U = {1,2,3,4}; P = {2,3}; Q = {2,4}; P∩Q = {2}
(P∩Q)' = {1,3,4}
Source: Myschool Past Questions Archive (Record #23139)
Mathematics
WAEC / WASSCE 1992
Inequalities & Linear Programming
Diagram
If x varies over the set of real numbers, which of the following is illustrated in the diagram above?
Attached Figure / Diagram
A
-3
B
-3≤x<2
C
-3
D
-3≤x≤2
E
x≥2
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 #23141)
Mathematics
WAEC / WASSCE 1992
Number Bases & Modular Arithmetic
Solution
Convert 77 to a number in base two
A
1001 101
B
111001
C
100110
D
10101
E
10011
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} 2 & 77 \\ \hline 2 & 38 R1 \\ 2 & 19 R0 \\ 2 & 9 R1 \\ 2 & 4 R1 \\ 2 & 2 R0 \\ 2 & 1 R0 \\ & 0 R1\end{array}\)
77ten = 1001101two
Source: Myschool Past Questions Archive (Record #23142)
Mathematics
WAEC / WASSCE 1992
Fractions, Decimals, Percentages & Approximations
Solution
A bricklayer measured the length of a wall and obtained 4.10m. If the actual length of the wall is 4.25m, find his percentage error.
A
3 9/17%
B
3 27/41%
C
15%
D
35 5/17%
E
36 24/41%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Error = 4.25 - 4.10 = 0.15
% error = \(\frac{0.15}{4.25} \times 100%\)
= \(\frac{15}{\frac{17}{4}} = \frac{15 \times 4}{17}\)
= \(3\frac{9}{17} %\)
Source: Myschool Past Questions Archive (Record #23143)
Mathematics
WAEC / WASSCE 1992
Sequences & Series (AP & GP)
Solution
The nth term of a sequence is given by 3.2\(^{n-2}\). Write down the first three terms of the sequence.
A
2/3, 0, 6
B
3/2, 3, 6,
C
2/3, 3, 8/3
D
2/3, 3/4, 6
E
2/3, 3, 1/3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(T_n = 3. 2^{n - 2} \\
T_{1} = 3. 2^{1 - 2} = 3. 2^{-1} \\
T_1 = \frac{3}{2} \)
\(T_2 = 3. 2^{2 - 2} \\
T_2 = 3. 2^0 = 3\)
\(T_3 = 3. 2^{3 - 2} = 3. 2^1 \\
T_3 = 6\)
The first 3 terms of the sequence are \(\frac{3}{2}\), 3 and 6.
Source: Myschool Past Questions Archive (Record #23144)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify: \((\frac{16}{81})^{\frac{1}{4}}\)
A
8/27
B
1/3
C
4/9
D
2/3
E
-4/3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((\frac{16}{81})^{\frac{1}{4}}\)
= \(((\frac{2}{3})^{4})^{\frac{1}{4}}\)
= \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #23145)
Mathematics
WAEC / WASSCE 1992
Indices, Logarithms & Surds
Solution
Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
A
0.2
B
2
C
100
D
409
E
490
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
= \(\log_{10} (\frac{25 \times 32}{8})\)
= \(\log_{10} 100 \)
= 2
Source: Myschool Past Questions Archive (Record #23146)
Mathematics
WAEC / WASSCE 1992
Linear, Simultaneous & Quadratic Equations
Solution
Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2.
A
3x2-3x+2=0
B
3x2+3x-2=0
C
2x2+3x-2=0
D
2x2-3x+2=0
E
2x2-3x-2=0
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
If x = \(-\frac{1}{2}\) and 2; then
\(x + \frac{1}{2} = 0\) and \(x - 2 = 0\)
\(\implies (x + \frac{1}{2})(x - 2) = 0\)
\(x^2 - 2x + \frac{1}{2}x - 1 = 0\)
\(x^2 - \frac{3}{2}x - 1 = 0\)
\(2x^2 - 3x - 2 = 0\)
Source: Myschool Past Questions Archive (Record #23148)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Solution
Write as a single fraction \(\frac{1}{1 - x} + \frac{2}{1 + x}\)
A
\(\frac{x + 3}{1 - x^2}\)
B
\(\frac{3 - x}{(1 - x)^2}\)
C
\(\frac{3 - x}{1 + x^2}\)
D
\(\frac{3 - x}{(1 + x)^2}\)
E
\(\frac{3 - x}{1 - x^2}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{1}{1 - x} + \frac{2}{1 + x}\)
= \(\frac{(1 + x) + 2(1 - x)}{(1 - x)(1 + x)}\)
= \(\frac{1 + x + 2 - 2x}{1 - x^2}\)
= \(\frac{3 - x}{1 - x^2}\)
Source: Myschool Past Questions Archive (Record #23149)
Mathematics
WAEC / WASSCE 1992
Linear, Simultaneous & Quadratic Equations
Solution
What must be added to the expression x\(^2\) - 18x to make it a perfect square?
A
3
B
9
C
36
D
72
E
81
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
x\(^2\) - 18x to be a perfect square.
\((\frac{b}{2})^2\) is added to ax\(^2\) + bx + c in order to make it a perfect square.
\(x^2 - 18x + (\frac{-18}{2})^2\)
= \(x^2 - 18x + 81\)
Source: Myschool Past Questions Archive (Record #23150)
Mathematics
WAEC / WASSCE 1992
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation \(\frac{m}{3} + \frac{1}{2} = \frac{3}{4} + \frac{m}{4}\)
A
-3
B
-2
C
2
D
3
E
4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{m}{3} + \frac{1}{2} = \frac{3}{4} + \frac{m}{4}\)
\(\frac{m}{3} - \frac{m}{4} = \frac{3}{4} - \frac{1}{2}\)
\(\frac{m}{12} = \frac{1}{4}\)
\(4m = 12 \implies m = 3\)
Source: Myschool Past Questions Archive (Record #23151)
Mathematics
WAEC / WASSCE 1992
Mensuration (Areas, Perimeters & Volumes)
Solution
The angle of a sector of a circle of radius 8cm is 240^\circ. This sector is bent to form a cone. Find the radius of the base of the cone.
A
16/3cm
B
15/3cm
C
16/5cm
D
8/3cm
E
16/10cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
L = \theta/360 x 2\piR = 240/360 x 2 x 22/7 x 8/1 ... (1)
This must be equal to the circumference of the circle which is 2\pir = 44R/7 .... (2)
equate (1) and (2)
r = 16/3 = 5\(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #23152)