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Mathematics
WAEC / WASSCE 2009
Indices, Logarithms & Surds
Solution
If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log (\(\frac{28}{3}\))
A
2x + y - z
B
2x + z - y
C
x + y - 2x
D
x + x - y
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log (\(\frac{28}{3}) = \log (\frac{7 \times 4}{3})\)
= log 7 + log 4 - log 3
log 7 + log \(2^2\) - log 3 = log 7 + 2log2 - log 3
= z + 2x - y
= 2x + z - y
Source: WAEC / JAMB / NECO Classroom Archive (Record #36430)
Mathematics
WAEC / WASSCE 2009
Linear, Simultaneous & Quadratic Equations
Solution
Find the quadratic equation whose roots are -\(\frac{1}{2}\) and 3
A
2x2 - 2x + 3 = 0
B
2x2 - 2x - 3 = 0
C
2x2 - 5x - 3 = 0
D
3x2 - 5x - 3 = 0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x = \(\frac{-1}{2}\)
x = 3
2x = -1, x = 3; 2x + 1 = 0
x - 3 = 0
(2x + 1)(x - 3) = 0
2x2 - 6x + x - 3 = 0
2x2 - 5x - 3 = 0
Source: WAEC / JAMB / NECO Classroom Archive (Record #36476)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
The interior angles of a pentagon are (2x + 5)o, (x + 20)o, xo, (3x - 20)o and (x + 15)o. Find the value of x
A
80o
B
70o
C
65o
D
40o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(2x + 5)o + (xo + 20o) + x + (3x - 20)o + (x + 15)o = (n - 2) x 180
8n + 20 = (5 - 2) x 180
where n = 5(Pentagon)
8n + 20 = 3 x 180
8n + 20 = 540
8n = 540 - 20
8n = 520
x = 65o
Source: WAEC / JAMB / NECO Classroom Archive (Record #36451)
Mathematics
UTME / JAMB 2009
Differentiation & Applications
Solution
What value of x will make the function x(4 - x) a maximum?
A
4
B
3
C
2
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x(4 - x)
4x - x2
\(\frac{dy}{dx}\) = 4 - 2x
\(\frac{dy}{dx}\) = 0
2x = 4
x = \(\frac{4}{2}\)
= 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #29712)
Mathematics
UTME / JAMB 2009
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The histogram above represents the number of candidates that sat for Mathematics examination in a school. How many candidate scored more than 50 marks?
Attached Figure / Diagram
A
80
B
95
C
100
D
115
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} Mark & No. of Candidate\\\hline 60 & 40\\ 70 & 25\\ 80 & 15\\ 90 & 10 \\100 & 5 \\\hline & 95 \end{array}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #33142)
Mathematics
UTME / JAMB 2009
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The cumulative frequency curve above shows the distribution of the scores of 50 students in an examination. Find the 36th percentile scores?
Attached Figure / Diagram
A
18%
B
28%
C
36%
D
50%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
the 36th percentile i.e. 36% of the total frequency of 50.
\(\frac{36}{100}\) \(\times\) 50 = 18
= From the graph, 18 on the vertical axis corresponds to28 on the horizontal axis.
\(\therefore\) P\(_{36}\) = 28%
Source: WAEC / JAMB / NECO Classroom Archive (Record #33144)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify: (3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\))
A
1\(\frac{1}{4}\)
B
8\(\frac{1}{2}\)
C
35
D
47
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\)) = (7\(\frac{3 + 2}{6}) \div \frac{(5 - 4)}{6}\)
7\(\frac{5}{6} \div \frac{1}{6} = \frac{47}{6} \times \frac{6}{1}\) = 47
Source: Myschool Past Questions Archive (Record #36428)
Mathematics
WAEC / WASSCE 2009
Fractions, Decimals, Percentages & Approximations
Solution
In a particular year, the exchange rate of naira (N) varies directly with the Dollars{$}. If N1122 is equivalent to $8, find the Naira equivalent of $36
A
N8976
B
N5049
C
N140.25
D
N31.17
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
N1122 = $8; x = $36
x x $8 = N1122 x $36
\(\frac{N1122 \times $36}{$8}\) = x
x = N5049
Source: Myschool Past Questions Archive (Record #36429)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
Arrange the following numbers in descending orders of magnitude: 22three, 34five, 21six
A
21six, 22three, 34five,
B
21six, 34five, 22three
C
22three, 34five, 21six
D
34five, 21six, 22three
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
22three, 34five, 21six = (2 x 3)(2 x 3o), (3 x 51) = (4 x 50), (2 x 61) + (1 x 60)
= (6 + 2), (15 + 4), (12 + 1) = 8ten, 29ten, 13ten in descending order
29ten, 13ten, 8ten = 34five, 21six, 22three
Source: Myschool Past Questions Archive (Record #36433)
Mathematics
WAEC / WASSCE 2009
Fractions, Decimals, Percentages & Approximations
Solution
Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest
A
N3,900.00
B
N3,750.00
C
N3,600.00
D
N3,300
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
A = P + I
p + \(\frac{PRT}{100}\)
A = N3000 (1 + \(\frac{6 \times 5}{100}\))
= N3000(1 + 0.3)
A = N3000 (1.3)
= N3,900.00
Source: Myschool Past Questions Archive (Record #36434)
Mathematics
WAEC / WASSCE 2009
Fractions, Decimals, Percentages & Approximations
Solution
Express the square root of 0.000144 in the standard form
A
1.2 x 10-4
B
1.2 x 10-3
C
1.2 x 10-2
D
1.2 x 10-1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\sqrt{0.000144}\) = 0.012
= 1.2 x 10-2
Source: Myschool Past Questions Archive (Record #36435)
Mathematics
WAEC / WASSCE 2009
Sets, Logic & Venn Diagrams
Two sets are disjoint if
A
they are both empty
B
their union is an empty set
C
their intersection is an empty set
D
one of them is a subset of the other
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #36436)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
If \(\frac{3}{2x} - \frac{2}{3x} = 4\), solve for x
A
\(\frac{4}{5}\)
B
\(\frac{4}{13}\)
C
\(\frac{5}{24}\)
D
\(\frac{13}{24}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3}{2x} - \frac{2}{3x} = 4\)
\(\frac{9 - 4}{6x}\); \(\frac{5}{6x}\) = 4
5 = 24x ; x = \(\frac{5}{24}\)
Source: Myschool Past Questions Archive (Record #36437)
Mathematics
WAEC / WASSCE 2009
Indices, Logarithms & Surds
Solution
If (2x + 3)3 = 125, find the value of x
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(2x + 3 )2 = 125
2n + 3 = 3\(\sqrt{125}\)
2x + 3 = 5
2x = 5 - 3
x = \(\frac{2}{2}\)
= 1
Source: Myschool Past Questions Archive (Record #36446)
Mathematics
WAEC / WASSCE 2009
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize x2 - 2x - 3xy completely
A
(x - 2)(3x - y)
B
(x - 3y)(x - 2)
C
(x - 3y)(x - 3y)
D
(3x + y)(x - 2)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x2 - 2x - 3xy + 6y = x(x - 2) -3y(x - 2)
= (x - 3y)(x - 2)
Source: Myschool Past Questions Archive (Record #36447)