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Mathematics
WAEC / WASSCE 2006
Algebraic Expressions, Polynomials & Factorisation
Solution
Given that y = 1 - \(\frac{2x}{4x - 3}\), find the value of x for which y is undefined
A
3
B
\(\frac{3}{4}\)
C
\(\frac{-3}{4}\)
D
-3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
for undefined expression, the denomination is zero 4x - 3 = 0
4x = 3; x = \(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #36160)
Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is
A
a straight line joining A and P
B
the perpendicular bisector of AP
C
a circle with centre A
D
the triangle with centre P
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 #36161)
Mathematics
WAEC / WASSCE 2006
Permutations, Combinations & Probability
Solution
A fair coin is tossed three times. Find the probability of getting two heads and one tail.
A
\(\frac{1}{2}\)
B
\(\frac{3}{8}\)
C
\(\frac{1}{4}\)
D
\(\frac{1}{8}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Pr(head) = \(\frac{1}{2}\), Pr(tail) = \(\frac{1}{2}\):Pr(2 heads)
= \(\frac{1}{2}\) x \(\frac{1}{2}\) = \(\frac{1}{4}\)
Pr(2 heads and tail) 3 times
= (\(\frac{1}{4}\) x \(\frac{1}{2}\)) x 3
= \(\frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #36162)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
If 30% of y is equal to x, what in terms of x, is 30% of 3y?
A
\(\frac{x}{9}\)
B
\(\frac{x}{3}\)
C
x
D
3x
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If 30% of y = x, then 30% of 3y = 3x
Source: Myschool Past Questions Archive (Record #36163)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
A baker used 40% of a 50kg bag of flour. If \(\frac{1}{8}\) of the amount used was for the cake, how many kilogram of flour was used for the cake?
A
2\(\frac{1}{2}\)
B
6\(\frac{1}{2}\)
C
15\(\frac{3}{8}\)
D
17\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{40}{100} \times 50\)kg = 20kg
\(\frac{1}{8}\) of 20kg for cake; \(\frac{1}{8}\) x \(\frac{20}{1}\)
= 2\(\frac{1}{2}\)kg
Source: Myschool Past Questions Archive (Record #36164)
Mathematics
WAEC / WASSCE 2006
Trigonometry, Elevation & Bearings
Solution
If tan y = 0.404, where y is acute, find cos 2y
A
0.035
B
0.719
C
0.808
D
0.927
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
tan y = 0.404; y = tan-1 0.0404(tables);y = 22o
cos 2y = cos 2(22o); cos 44o
= 0.719
Source: Myschool Past Questions Archive (Record #36165)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
The ratio of boys to girls in a class is 5:3. Find the probability of selecting at random, a girl from the class
A
\(\frac{1}{8}\)
B
\(\frac{1}{3}\)
C
\(\frac{3}{8}\)
D
\(\frac{3}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
ratio of boys to girls = 5:3
total = 5 + 3 = 8
Pr(girl) = \(\frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #36166)
Mathematics
WAEC / WASSCE 2006
Indices, Logarithms & Surds
Solution
\(\begin{array}{c|c} x & 1 & 4 & p \\ \hline y & 0.5 & 1 & 2.5\end{array}\). The table above satisfies the relation y = k\(\sqrt{x}\), where k is a positive constant. Find the value of K.
A
0.5
B
1
C
1.5
D
2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
y = k\(\sqrt{x}\) when y = 1, x = 4
k = \(\frac{y}{\sqrt{x}}\)
= \(\frac{1}{\sqrt{4}}\)
= \(\frac{1}{2}\)
= 0.5
Source: Myschool Past Questions Archive (Record #36167)
Mathematics
WAEC / WASSCE 2006
Indices, Logarithms & Surds
Solution
\(\begin{array}{c|c} x & 1 & 4 & p \\ \hline y & 0.5 & 1 & 2.5\end{array}\). The table below satisfies the relation y = k\(\sqrt{x}\), where k is a positive constant. Find the value of P,
A
2
B
4
C
10
D
25
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From y = \(\frac{1}{2} \sqrt{x}\)
when y = 2.5 or \(\frac{5}{2}\), x = P
\(\frac{5}{2} \times \frac{1}{2} \sqrt{P}\)
\(\sqrt{P} = \frac{10}{2} = 5\)
P = \(5^2\)
= 25
Source: Myschool Past Questions Archive (Record #36168)
Mathematics
WAEC / WASSCE 2006
Linear, Simultaneous & Quadratic Equations
Solution
What must be added to x2 - 3x to make it a perfect square?
A
\(\frac{9}{4}\)
B
\(\frac{9}{2}\)
C
6
D
9
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x2 - 3x + k(perfect square)
k = (-\(\frac{3}{2}\))2 ; k = \(\frac{9}{4}\)
Source: Myschool Past Questions Archive (Record #36169)
Mathematics
WAEC / WASSCE 2006
Linear, Simultaneous & Quadratic Equations
Solution
Given that (2x - 1)(x + 5) = 2x2 - mx - 5, what is the value of m
A
11
B
5
C
-9
D
-10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(2x - 1)(x + 5) = 2x2 - mx - 5
2x2 + 10x - x - 5
= 2x2 + 9x - 5 = 2x2 - mx - 5
comparing the co-efficient of x
-m = 9
m = -9
Source: Myschool Past Questions Archive (Record #36170)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
What is the place value of 9 in the number 3.0492?
A
\(\frac{9}{10000}\)
B
\(\frac{9}{1000}\)
C
\(\frac{9}{100}\)
D
\(\frac{9}{10}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Place value of 9 in 3.0492
= 0.009
= \(\frac{9}{1000}\)
Source: Myschool Past Questions Archive (Record #36171)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
If the simple interest on a sum of money invested at 3% per annum for 2\(\frac{1}{2}\) years is N123, find the principal.
A
N676.50
B
N820
C
N1,640
D
N4,920
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
I = N123; R = 3%' T = 2\(\frac{1}{2}\) yrs; P = \(\frac{100 \times 1}{RT}\)
P = \(\frac{100 \times 123}{3 \times 2.5}\)
principal(P) = N1640
Source: Myschool Past Questions Archive (Record #36172)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?
A
N16,200
B
N1,4,200
C
12,000
D
8000.
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
D = P(I - \(\frac{R}{100}\))n where P = N20,000; R = 10%, n = 2
D = 20,000(I - \(\frac{10}{100}\))2
= 20000(0.9)2
20,000 x 0.81 = N16,200
Source: Myschool Past Questions Archive (Record #36176)
Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
Solution
If 2x + y = 10, and y \(\neq\) 0, which of the following is not a possible value of x?
A
4
B
5
C
8
D
10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The value for which the equation is impossible
2x = 10 (if y = 0)
x = 5
Source: Myschool Past Questions Archive (Record #36177)