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Chemistry
UTME / JAMB 1991
Atomic Structure, Orbitals & Nuclear Chemistry
Solution
The electronic configuration of an elements is 1s22s22p63s23p3. How many unpaired electrons are there in the element?
A
5
B
4
C
3
D
2
medium Difficulty
Verified Correct Answer: Option C
Chemical Principles & Mechanism
The atomic number of phosphorus is 15 and the 3p sublevel has three unpaired electrons.
Source: WAEC / JAMB / NECO Classroom Archive (Record #12998)
Chemistry
UTME / JAMB 1991
Water, Solutions & Solubility
Solution
The solubility of copper (II) tetraoxosulphate (Iv) is 75g in 100g of water at 100°C and 25g in 100g of water at 30°C. What mass of the salt would crystallize, if 50g of copper (II) tetraoxosulphate (VI) solution saturated at 100°C were cooled to 30°C ?
A
57.5
B
42.2
C
28.6
D
14.3
medium Difficulty
Verified Correct Answer: Option D
Chemical Principles & Mechanism
solute + solvent = solution
at 100oC; 75g + 100g = 175g
at30oC; \(\frac{25g}{50g}\) + 100g = 125g
From 100oC - 30oC; 175g CuSO4 ppt 50g
From 100oC - 30oC; 50g CuSO4 ppt \(\frac{50 \times 50}{175}\) = 14.3
Source: WAEC / JAMB / NECO Classroom Archive (Record #13030)
Chemistry
WAEC / WASSCE 1991
Stoichiometry, Mole Concept & Volumetric Analysis
Solution
2NaNO3 → 2NaNO2 + O2. From the equation above, what is the volume of oxygen produced at s.t.p. when 8.5g of 2NaNO3 is heated until no further gas is evolved? (2NaNO3 = 85, molar volume of gases at s.t.p. = 22.4dm3)
A
1.12dm3
B
2.24dm3
C
4.48dm3
D
11.2dm3
E
22.4dm3
medium Difficulty
Verified Correct Answer: Option A
Chemical Principles & Mechanism
85g of 2NaNO\(_3\) will liberated 22.4dm\(_3\)
8.5g = xdm\(_3\)
cross multiply: x = [8.5 * 22.4] / 85
x = 2.24dm\(_3\)
: 8.5g of 2NaNO\(_3\) = 2.24dm\(_3\)
where 2moles of NaNO\(_3\) liberates 1mole of O\(_2\)
2.24dm\(_3\) of NaNO\(_3\) liberates 1.12dm\(_3\) of O\(_2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #36138)
Chemistry
UTME / JAMB 1991
Chemical Energetics & Thermochemistry
Solution
1.1 g of CaCI2 dissolved in 50 cm3 of water caused a rise in temperature of 3.4°C. The heat of reaction, ∆H for CaCI2 in kj per mole is?
(Ca = 40, CI = 35.5, specific heat of water is 4.18 jk-1)
A
-71.1
B
-4.18
C
+71.1
D
+111.0
medium Difficulty
Verified Correct Answer: Option A
Chemical Principles & Mechanism
Q = mct = (50 x 4.18 x 3.4) / (1000)
= 0.71606 kj
1.1 g of \(CaCl_2\) contains
(1.1) / (111) = 0.01 moles of \(CaCl_2\)
If 0.01 liberates 0.7106 quantity of heat.
1 will liberate (0.7106 x 1) / (0.01)
Exothermic = 71.06 = -71.1
Source: WAEC / JAMB / NECO Classroom Archive (Record #13077)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Solution
Express 0.0462 in standard form
A
0.462 x 10-1
B
0.462 x 10-2
C
4.62 x 10-1
D
4.62 x 10-2
E
4.62 x 103
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4.62 x 10-2
Source: Myschool Past Questions Archive (Record #22864)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Solution
The population of a village is 5846. Express this number to three significant figures
A
5850
B
5846
C
5840
D
585
E
584
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
5846 \(\approxeq\) 5850 (to 3 s.f.)
Source: Myschool Past Questions Archive (Record #22865)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Simplify: log6 + log2 - log12
A
-4
B
-1
C
0
D
1
E
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log 6 + log 2 - log 12
= \(\log (\frac{6 \times 2}{12})\)
= \(\log 1\)
= 0
Source: Myschool Past Questions Archive (Record #22866)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Find the number whose logarithm to base 10 is 2.6025
A
400.4
B
0.4004
C
0.04004
D
0.004004
E
0.0004004
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
For the log to be 2.6025, there must be three digits before the decimal point.
Source: Myschool Past Questions Archive (Record #22867)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Simplify: \((\frac{1}{4})^{-1\frac{1}{2}}\)
A
1/8
B
1/4
C
2
D
4
E
8
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\((\frac{1}{4})^{-1\frac{1}{2}}\)
= \((\frac{1}{4})^{-\frac{3}{2}}\)
= \((\sqrt{\frac{1}{4}})^{-3}\)
= \((\frac{1}{2})^{-3}\)
= \(2^3\)
= 8
Source: Myschool Past Questions Archive (Record #22868)
Mathematics
WAEC / WASSCE 1991
Algebraic Expressions, Polynomials & Factorisation
Solution
For what value of y is the expression \(\frac{y + 2}{y^{2} - 3y - 10}\) undefined?
A
y = 0
B
y = 2
C
y = 3
D
y = 5
E
y = 10
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{y + 2}{y^2 - 3y - 10}\)
\(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\)
\(y(y - 5) + 2(y - 5) = 0\)
\((y - 5)(y + 2) = 0\)
\(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\)
\(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.
Source: Myschool Past Questions Archive (Record #22869)
Mathematics
WAEC / WASSCE 1991
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize 3a\(^2\) - 11a + 6
A
(3a - 2)(a - 3)
B
(2a -2)(a - 3)
C
(3a - 2)(a + 3)
D
(3a + 2)(a - 3)
E
(2a-3)(a + 2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3a\(^2\) - 11a + 6
3a\(^2\) - 9a - 2a + 6
3a(a - 3) - 2(a - 3)
= (3a - 2)(a - 3)
Source: Myschool Past Questions Archive (Record #22870)
Mathematics
WAEC / WASSCE 1991
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation: 3a + 10 = a\(^2\)
A
a = 5 or a = 2
B
a = -5 or a = 2
C
a = 10 or a = 0
D
a = 5 or a = 0
E
a = 5 or a = -2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
3a + 10 = a\(^2\)
a\(^2\) - 3a - 10 = 0
a\(^2\) - 5a + 2a - 10 = 0
a(a - 5) + 2(a - 5) = 0
(a - 5)(a + 2) = 0
a = 5 or a = -2.
Source: Myschool Past Questions Archive (Record #22871)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\)
A
\(\frac{2y - 5x}{4}\)
B
\(\frac{9(2x - 5x)}{x^2y^2}\)
C
\(\frac{5x - 2y}{2}\)
D
\(\frac{c^2y^2}{18y - 45x}\)
E
\(\frac{4}{2y - 5x}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\)
= \((\frac{6y - 15x}{2xy}) \div \frac{6}{xy}\)
= \(\frac{6y - 15x}{2xy} \times \frac{xy}{6}\)
= \(\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}\)
= \(\frac{2y - 5x}{4}\)
Source: Myschool Past Questions Archive (Record #22872)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Simplify: \(\frac{1}{4}(2^n - 2^{n + 2}\))
A
\(2^{n - 2} - 2^n\)
B
\(2^{n-2}(1-2^n\))
C
\(2^n + 2^{2 + n}\)
D
\(2^{2n}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{1}{4}(2^n - 2^{n + 2}\)) = \(\frac{1}{4}(2^n - 2^n \times2^2\))
\(\frac{1}{4} \times2^n(1 - 2^2\)) = \(2^{-2}\times2^n(1 - 2^2\))
\(2^{n - 2}(2^0 - 2^2\)) = \(2^{n - 2} - 2^n\)
Source: Myschool Past Questions Archive (Record #22873)
Mathematics
WAEC / WASSCE 1991
Linear, Simultaneous & Quadratic Equations
Solution
Find the equation whose roots are -2/3 and -1/4
A
12x2 + 11x + 2 = 0
B
12x2 - 11x + 2 = 0
C
x2 - 11/12x + 2 = 0
D
12x2 - 11x - 2 = 0
E
x2 - 11/12x - 2 = 0
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)
Source: Myschool Past Questions Archive (Record #22874)