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Mathematics
WAEC / WASSCE 2007
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
Solution
A sector of a circle of radius 14cm containing an angle 60o is folded to form a cone. Calculate the radius of the base of the cone.
A
\(5\frac{1}{2}cm\)
B
\(4\frac{2}{3}cm\)
C
\(3\frac{1}{2}cm\)
D
\(2\frac{1}{3}cm\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(r=\frac{\theta \times l}{360^{\circ }}\\
r=?, \theta =60^{\circ }\), l = radius of the orginal sector of a circle = 14cm
\(r=\frac{60\times 14}{360}=\frac{7}{3}=2\frac{1}{3}cm\)
Source: Myschool Past Questions Archive (Record #26732)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
If y = (1 + x)2, find \(\frac{dy}{dx}\)
A
x - 1
B
2 + 2x
C
1 + 2x
D
2x - 1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If y = (1 + x)2, find \(\frac{dy}{dx}\)
y = (1 + x)2
\(\frac{dy}{dx}\) = 2(1 + x)
= 2 + 2x
Source: Myschool Past Questions Archive (Record #30081)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
The sum of the ages of Musa and Lawal is 28 years. After sharing a certain sum of money in the ratio of their ages, Musa gets N600 and Lawal N800. How old is Lawal?
A
14 years
B
20 years
C
12 years
D
16 years
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
M + L = 28,
M : L = 600 : 800
= 3 : 4
\(\frac{M}{L}\) = \(\frac{3}{4}\) \(\to\) M = \(\frac{3}{4}\)L
\(\frac{3}{4}\)L + L = 28
\(\frac{7L}{4}\) = 28
L = \(\frac{4 \times 28}{7}\)
= 16
Source: Myschool Past Questions Archive (Record #30393)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Evaluate(111two)\(^2\) and leave your answer in base 2.
A
111001two
B
110001two
C
101001two
D
10010two
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(111two)\(^2\) change to base 10
(111two)\(^2\) = 1 x 2\(^2\) + 1 x 2\(^1\) + 1 x 2\(^0\) = 4 + 2 + 1 = 7
(111two)\(^2\) = 7\(^2\) = 49 in base 10
convert 49 in base 10 to base 2
2
49
2
24 R 1
2
12 R 0
2
6 R 0
2
3 R 0
2
1 R 1
2
0 R 1
Therefore (111two)\(^2\) = 110001\(_2\)
Or solve by direct multiplication.
Source: Myschool Past Questions Archive (Record #36226)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Find the LCM of 2\(^3\) x 3 x 5\(^2\), 2 x 3\(^2\) x 5 and 2\(^3\) x 3\(^3\) x 5
A
22 x 33 x 52
B
23 x 33 x 5
C
22 x 32 x 52
D
23 x 33 x 52
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2\(^3\) x 3 x 5\(^2\)
2 x 3\(^2\) x 5
2\(^2\) x 3\(^3\) x 5
The L.C.M = 2\(^2\) x 3\(^3\) x 5\(^2\)
Source: Myschool Past Questions Archive (Record #36227)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
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\(\sqrt{15}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3 \(\sqrt{45} - 12\sqrt{5} + 16\sqrt{20}\)
= 3 x \(\sqrt{9 \times 5} - 12 \times \sqrt{5} + 16 \times \sqrt{4 \times 5}\)
= 3 x 3 x \(\sqrt{5} - 12 \times \sqrt{5} + 16 \times 2 \times \sqrt{5}\)
= 9\(\sqrt{5} - 2 \sqrt{5} + 32 \sqrt{5}\)
= 9\(\sqrt{5} + 32\sqrt{5} - 12\sqrt{5}\)
= 29\(\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #36233)