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Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
Given that x = 2 and y = -\(\frac{1}{4}\), evaluate \(\frac{x^2y - 2xy}{5}\)
A
zero
B
\(\frac{1}{5}\)
C
1
D
2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given; x = 2; y = \(\frac{-1}{4}\)
= \(\frac{x^2y - 2xy}{5}\)
= \(\frac{2^2(\frac{-1}{4}) - 2(2)(\frac{-1}{4})}{5}\)
= \(\frac{4(\frac{-1}{4}) + 4(\frac{-1}{4})}{5}\)
= \(\frac{1 + 1}{5}\)
= \(\frac{0}{5}\)
= 0
Source: Myschool Past Questions Archive (Record #36341)
Mathematics
WAEC / WASSCE 2008
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize 5y2 + 2ay - 3a2
A
(a - y)(5y - 3a)
B
(y - a)(5y - 3a)
C
(y - a)(5y + 3a)
D
(y + a)(5y - 3a)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
5y2 + 2ay - 3a2 = 5y2 + 5ay - 3a2
= 5y(y + a) - 3a(y + a)
= (y + a)(5y - 3a)
Source: Myschool Past Questions Archive (Record #36343)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x?
A
3
B
6
C
9
D
12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
4y - 9 > y + 3x; 4y - y > 3x + 9
3y > 3(x + 3); y = > \(\frac{3(x + 3)}{3}\)
y > x + 3; y - 3 > x
y is greater than x by 3
Source: Myschool Past Questions Archive (Record #36353)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r
A
\(\frac{9}{25} pr^2\)
B
\(\frac{9}{25} p^2r\)
C
\(\frac{25}{9} p^2r\)
D
\(\frac{25}{9} pr^2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
p = \(\frac{3}{5} \sqrt{\frac{q}{r}}; \frac{5p}{3} = \sqrt{\frac{q}{r}}\)
= (\(\frac{5}{3}p\))2
= \(\frac{q}{r}\)
= \(\frac{25p^2}{9} = \frac{q}{r}\)
q = \(\frac{25}{9} p^2 r\)
Source: Myschool Past Questions Archive (Record #36354)
Mathematics
WAEC / WASSCE 2008
Linear, Simultaneous & Quadratic Equations
Solution
Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)
A
\(\frac{x + 4}{2x + 3}\)
B
\(\frac{x + 4}{2x - 3}\)
C
\(\frac{x - 4}{2x + 3}\)
D
\(\frac{x - 4}{2x - 3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{2x^2 - 5x - 12}{4x^2 - 9}\) = \(\frac{2x^2 - 8x + 3x - 12}{(2x)^2 - 3^2}\)
= \(\frac{2x(x - 4) + 3(x - 4)}{(2x - 3)(2x + 3)} - \frac{(x - 4) + (2x + 3)}{(2x - 3) (2x + 3)}\)
= \(\frac{x - 4}{2x - 3}\)
Source: Myschool Past Questions Archive (Record #36355)
Mathematics
WAEC / WASSCE 2008
Fractions, Decimals, Percentages & Approximations
Solution
PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)]
A
4.19cm2
B
8.38cm2
C
10.5cm2
D
20.9cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given q2 = 25 - r2.....(1)
from pythagora's theorem
P2 = q2 + r2.......(2)
put (1) into (2)
p2 = 25 - p2 + x2
p2 = 25
p = \(\sqrt{25}\)
= 5
Source: Myschool Past Questions Archive (Record #36358)
Mathematics
WAEC / WASSCE 2008
Mensuration (Areas, Perimeters & Volumes)
Solution
If the volume of a cube is 343cm3, find the length of its side
A
3cm
B
6cm
C
7cm
D
96cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of a cube = (side)3
= (side)3
(side)3 = 343
side = 3\(\sqrt{343}\)
side = 7cm
Source: Myschool Past Questions Archive (Record #36359)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
The angles of a quadrilateral are (x + 10)o, 2yo, 90o and (100 - y)o, Find y in terms of x
A
y = 160 + x
B
y = 100 + x
C
y = 160 - x
D
y = x - 100
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sum of the angles in a quadrilateral = 360o
(x + 10o) + 2y + 90o + 100 - y = 360o
x + y + 200 = 360o
y = 360 - 200 - x
y = 160 - x
Source: Myschool Past Questions Archive (Record #36361)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
If xo is obtuse, which of the following is true?
A
x . 90
B
180 < x < 270
C
x < 90
D
90 < x < 180
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
obtuse angle \(\to\) 90o o
Source: Myschool Past Questions Archive (Record #36362)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form
A
2\(\sqrt{2}\)
B
\(\frac{1}{2} \sqrt{2}\)
C
\(\sqrt{2}\)
D
2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
tan x = 1; x = tan-1(10 = 45o
sin x + cos x
= sin 45o + cos 45o
= \(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} + \sqrt{2}}{2}\)
= \(\frac{2\sqrt{2}}{2}\)
= \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #36363)
Mathematics
WAEC / WASSCE 2008
Trigonometry, Elevation & Bearings
Solution
If cos (x + 25)o = sin 45o, find the value of x
A
20
B
30
C
45
D
60
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
cos(x + 25o) = sin 45o
using cos \(\theta\) = sin(90 - \(\theta\))
cos(x + 25o) = cos(90 - 45)
cos(x + 25o) = cos 45
x + 25 = 45
x = 45 - 25
x = 20o
Source: Myschool Past Questions Archive (Record #36364)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)
A
5(106)
B
2(106)
C
5(105)
D
2(105)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(2^n\) = 128
\(2^n = 2^7\)
n = 7
(2\(^{n - 1}\))(5\(^{n - 2}\)), then, put n = 7
= (2\(^{7 - 1}\))(5\(^{7 - 2}\))
= (\(2^6\))(\(2^5\))
= \(2^1 \times 2^5 \times 2^5\)
= 2 x (\(2 \times 5)^5\)
= 2(\(10^5\))
Source: Myschool Past Questions Archive (Record #36366)
Mathematics
WAEC / WASSCE 2008
Variations
If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>?
A
x varies directly as y
B
x varies inversely as y
C
x is partly constant and partly varies as y
D
x vries jointly as 45 and directly as y
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 #36367)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2} \log 2\)
C
\(\frac{3}{2}\)
D
\(\log 2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #36368)
Mathematics
WAEC / WASSCE 2008
Linear, Simultaneous & Quadratic Equations
Solution
A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M
A
15
B
12
C
10
D
9
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Average speed = \(\frac{Distance}{Time}\)
\(\frac{400km}{hr} = \frac{60km}{Time}\)
Time = \(\frac{60km}{400 km/hr}\)
= \(\frac{60hr}{400}\)
M = \(\frac{60hr}{400} \times \frac{60min}{1hr}\)
= 9 minutes
Source: Myschool Past Questions Archive (Record #36381)