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Mathematics
WAEC / WASSCE 2007
Trigonometry, Elevation & Bearings
Solution
Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the :
(a) distance of Z from Y ;
(b) bearing of Z from Y.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) < ZXY = 225^\circ - 135^\circ
= 90^\circ.
\(\therefore /ZY/ = 80^{2} + 60^{2}\)
= \(6400 + 3600 = 10000\)
\(/ZY/ = \sqrt{10000}\)
= 100 km.
(b) From \(\Delta\) XYZ,
\(\tan \theta = \frac{opp}{adj}\)
\(\tan \theta = \frac{80}{60} = 1.333\)
\(\theta = \tan^{-1} (1.333)\)
\(\theta = 53.13^\circ\)
Bearing of Z from Y = \(360^\circ - (45^\circ + 53.13^\circ)\)
= \(360^\circ - 98.13^\circ\)
= \(261.87^\circ \approxeq 262^\circ\) (3 significant figures)
Source: WAEC / JAMB / NECO Classroom Archive (Record #52971)
Mathematics
WAEC / WASSCE 2007
Binary Operations, Matrices & Determinants
Solution
Evaluate \((111_{two})^2\) and leave your answer in base 2
A
\(111001_{two}\)
B
\(110001_{two}\)
C
\(101001_{two}\)
D
\(10010_{two}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\((111_{two})^{2}=(111_{two})(111_{two})\\
=1 \times 2^{2}+1\times2^{1}+1\times 2^{0}=4+2+1=7_{_{ten}}\\
(111_{two})^{2}=7\times 7=49\\
\begin{matrix}
2 & 49\\
2 & 24\hspace{1mm}R\hspace{1mm}1\\
2 & 12\hspace{1mm}R\hspace{1mm}0\\
2 & 6\hspace{1mm}R\hspace{1mm}0\\
2 & 3\hspace{1mm}R\hspace{1mm}0\\
2 & 1\hspace{1mm}R\hspace{1mm}1\\
& 0\hspace{1mm}R\hspace{1mm}1\hspace{1mm}\uparrow
\end{matrix} \\
=110001_{2}\)
Source: Myschool Past Questions Archive (Record #26717)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Find the LCM of \(2^{3}\times 3\times 5^{2}, 2\times 3^{2}\times 5 \hspace{1mm}and \hspace{1mm}2^{2}\times 3^{2}\times 5\)
A
\(2^{2}\times 3^{3}\times 5^{2}\)
B
\(2^{3}\times 3^{23}\times 5\)
C
\(2^{2}\times 3^{2}\times 5^{2}\)
D
\(2^{3}\times 3^{3}\times 5^{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26718)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Simplify \((0.3\times 10^{5})\div (0.4\times 10^{7})\)leaving your answer in standard form
A
\(7.5\times 10^{-4}\)
B
\(7.5\times 10^{-3}\)
C
\(7.5\times 10^{-2}\)
D
\(7.5\times 10^{-1}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\((0.3\times 10^{5})\div (0.4\times 10^{7})\\
\frac{3}{10}\times 10^{5}\div \frac{4}{10}\times 10^{7}=3\times 10^{4}\div 4\times 10^{6}\\
\frac{3\times 10^{4}}{4\times 10^{7}}=\frac{3}{4}\times 10^{-2}=0.75\times 10^{-2}\\
7.5\times 10^{-3}\)
Source: Myschool Past Questions Archive (Record #26719)
Mathematics
WAEC / WASSCE 2007
Variations
Solution
If \(p\propto \frac{1}{q}\), which of the following is true?
A
\(\propto p^{2}\)
B
\(p\propto \frac{1}{q^{2}}\)
C
\(q\propto \sqrt{p}\)
D
\(q\propto \frac{1}{p}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(p\propto \frac{1}{q} = q \propto \frac{1}{p}\)
Source: Myschool Past Questions Archive (Record #26720)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Simplify \(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\)leaving your answer in surd form
A
\(29\sqrt{5}\)
B
\(14\sqrt{15}\)
C
\(12\sqrt{15}\)
D
\(11\sqrt{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\)
3\(\sqrt{5\times 9}-12\sqrt{5}+16\sqrt{4\times 5}\)
3\(\times 3\sqrt{5}-12\sqrt{5}+16\times 2\sqrt{5}\)
9\(\sqrt{5}-12\sqrt{5}+32\sqrt{5}\)
29\(\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #26721)
Mathematics
WAEC / WASSCE 2007
Inequalities & Linear Programming
Which of the following is true for the set \(P = \{-3.2\leq x< 5\}\) where x is an integer
A
least value of x is -3.2
B
least value of x is -3
C
greatest value of x is 4.9
D
greatest value of x is 5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #26722)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify\(\frac{3x^{3}}{(3x)^{3}}\)
A
1
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
\(\frac{1}{27}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3x^{3}}{(3x)^{3}}\\
\frac{3x^{3}}{3x\times 3x\times 3x}=\frac{3\times x\times x\times x}{3\times 3\times 3\times x\times x\times x}=\frac{1}{9}\)
Source: Myschool Past Questions Archive (Record #26723)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
N140,000 is shared between ABU, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode's share?
A
N80,000
B
N40,000
C
N20,000
D
N10,000
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(Abu = 2x\\
Kayode = x\\
Uche = \frac{x}{2}\\
2x+x+\frac{x}{2}=140,000\\
\frac{7x}{2}=140,000\\
7x = 280,000\\
x=\frac{280,000}{7}\\
x=40,000\)Kayode receives N40,000
Source: Myschool Past Questions Archive (Record #26724)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
I am x years old and my brother is 3 years older. How old was my brother last year
A
(x - 4) years
B
(x + 2) years
C
(3x - 1) years
D
(3x + 1) years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If I am x years old, then my brother will be (x + 3)years old
then last year my brother was (x + 3) - 1 = (x + 2)years old
Source: Myschool Past Questions Archive (Record #26725)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
For what value of x is the expression \(\frac{2x-1}{x+3}\)not defined?
A
3
B
2
C
1/2
D
-3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x + 3 = 0 => x = -3
Source: Myschool Past Questions Archive (Record #26726)
Mathematics
WAEC / WASSCE 2007
Linear, Simultaneous & Quadratic Equations
Solution
If x =3, y = 2 and z = 4 what is the value of \(3x^{2}-2y+z\)
A
17
B
27
C
35
D
71
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3x\(^2\) - 2 y + z
= 3(3)\(^{2}\) - 2(2) + 4
= 27 - 4 +4 =27
Source: Myschool Past Questions Archive (Record #26727)
Mathematics
WAEC / WASSCE 2007
Linear, Simultaneous & Quadratic Equations
Solution
Solve the simultaneous equation: x+y=2 and 3x-2y=1
A
x=2 and y=1
B
x=1 and y=1
C
x=1 and y=2
D
x=-1 and y=1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x + y = 2 --- eqn I
3x - 2y = 1 --- eqn II
Multiply eqn I by 2
2x + 2y = 4 --- eqn III
add eqn II to eqn III
5x = 5 => x = 1
Substitute 1 for x in eqn I
1 + y = 2 => y = 1
Source: Myschool Past Questions Archive (Record #26728)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
If \(8^{x+1}=\frac{1}{4}\), find x
A
\(-\frac{5}{3}\)
B
-1
C
\(-\frac{1}{3}\)
D
\(\frac{1}{3}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(8^{x+1}=\frac{1}{4}\\
2^{3(x+1)}=2^{-2}\Rightarrow 3(x+1)=-2\Rightarrow 3x+3=-2\\
3x=-5\Rightarrow x = -\frac{5}{3}\)
Source: Myschool Past Questions Archive (Record #26729)
Mathematics
WAEC / WASSCE 2007
Fractions, Decimals, Percentages & Approximations
Solution
The area of a square field is 110.25m2. Find the cost of fencing it round at N75.00 per meter square
A
N1,575.00
B
N3,150.00
C
N4,734.30
D
N8,268.75
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
N75.00 x 110.25 = N8,268.75
Source: Myschool Past Questions Archive (Record #26730)