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Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
If x10 = 12145 find x
A
124
B
121
C
184
D
180
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x10 = 12145
= x10 = 1 x 53 + 2 x 52 + 1 * 51 + 4 x 50
= 1 x 125 + 2 x 25 + 1 x 5 + 4 x 1
= 125 + 50 + 5 + 4
= 184
Source: Myschool Past Questions Archive (Record #9236)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
Evaluate \(\frac{(0.5625)^2 - (0.4375)^2}{0.04}\) correct to three significant figures
A
3.11
B
3.13
C
0.313
D
3.12
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{(0.5625)^2) - (0.4375)^2}{0.04}\)
\(\frac{(0.5625 + 0.4375)(0.5625 - 0.4375)}{0.04}\)
\(\frac{1.000\times 0.125}{0.04}\)
= 3.125
= 3.13
Source: Myschool Past Questions Archive (Record #9237)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
Find the value of x for which 2(32x-1) = 162
A
5/2
B
3/2
C
2/5
D
1/2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2(32x-1) = 162
32x-1 = 162/2
32x-1 = 81
32x-1 = 32
2x - 1 = 4 (equating the indices)
2x = 5
5/2
x =
Source: Myschool Past Questions Archive (Record #9238)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
Simplify \(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\)
A
\(\frac{4}{5}\)
B
\(\frac{7}{10}\)
C
\(\frac{6}{6}\)
D
\(\frac{21}{6}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\\
=\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \times \frac{9}{4}\right)\\
=\frac{3}{5} \div \frac{6}{7}\\
=\frac{3}{5} \times \frac{7}{6}\\
=\frac{7}{10}\)
Source: Myschool Past Questions Archive (Record #9239)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
If log102 = x, express log1012.5 in terms of x
A
2(1 + x)
B
2 + 3x
C
2(1 - x)
D
2 - 3x
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log1012.5 = log10 121/2
= log1025/2
= log1025 - log102
= log1052 - log102
= 2log105 - log102
= 2log1010/2 - log102
= 2(1-x)- x
= 2 - 2x – x
= 2 – 3x
Source: Myschool Past Questions Archive (Record #9240)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
A man made a profit of 5% when he sold an article for N60,000.00. How much would he have sell the article to make a profit of 26%
A
N68,000
B
N72,000
C
N65,000
D
N70,000
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
5% profit = 100 + 5 = 105%
26% profit = 100 + 26 = 126%
∴ 105% → N60,000
1% → \(\frac{60000}{105}\)
126% = \(\frac{60000}{105}\) x \(\frac{126}{1}\)
= N72,000.
Source: Myschool Past Questions Archive (Record #9241)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
Given
P = {1, 3, 5, 7, 9, 11}
and Q = {2, 4, 6, 8, 10, 12}. Determine the relationship between P and Q
A
P∩Q = ∅
B
P ⊂ Q
C
Q⊂P
D
P = Q
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
P = {1, 3, 5, 7, 9, 11}
Q = {2, 4, 6, 8, 10, 12}
P∩Q = {1, 3, 5, 7, 9, 11}∩{2, 4, 6, 8, 10, 12}
= {} = ∅
Source: Myschool Past Questions Archive (Record #9242)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
Evaluate 101122 - 10122
A
1100002
B
1102
C
11000002
D
110002
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
101122 - 10122 = (1x23 + 0x22 + 1x21 + 1x20)2 - (1x22 + 0x21 + 1x22)2
(1x8 + 0x4 + 1x2 + 1x1) 2 - (1x4 + 0x2 + 1x1) 2)
= (8 + 0 + 2 + 1) 2 - (4 + 0 + 1) 2
= 112 - 52
= 16 x 6 = 96
9610 to base 2
2/96 = 48 R 0
2/48 = 24 R 0
2/24 = 12 R 0
2/12 = 6 R 0
2/6 = 3 R 0
2/3 = 1 R 1
2/1 = 0 R 1
11000002
Source: Myschool Past Questions Archive (Record #9243)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
If X = {all the perfect squares less than 40}
Y = {all the odd numbers fro, 1 to 15}. Find X ∩ Y.
A
{3, 9}
B
{9}
C
{9, 25}
D
{1, 9}
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
All the perfect squares < 40
X = {1, 4, 9, 16, 25, 36}
All the odd numbers from 1 to 15
Y = {1, 3, 5, 7, 9, 11, 13, 15}
X ∩ Y = {1, 9}
Source: Myschool Past Questions Archive (Record #9244)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
The volume of a hemispherical bowl is \(718\frac{2}{3}\). Find its radius .
A
4.0 cm
B
5.6 cm
C
7.0 cm
D
3.8 cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of bowl \(\frac{2}{3}\pi r^3\\
718\frac{2}{3}=\frac{2}{3}\pi r^3\\
\frac{2156}{3}=\frac{2}{3} \times \frac{22}{7} \times r^3
∴r^3 = \frac{2156 \times 3 \times 7}{3 \times 2 \times 22}\\
r^3 = 343\\
r = \sqrt[3]{343}\\
r= 7.0cm\)
Source: Myschool Past Questions Archive (Record #9248)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
What is the value of k if the mid-point of the line joining (1 - k, - 4) and (2, k + 1) is (-k , k)?
A
-3
B
-1
C
-4
D
-2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(1-k+2) / 2 = - k and -4 + k + 1 = k
3-k = -2k and -3 + k = 2k
K = -3 and k = -3
Source: Myschool Past Questions Archive (Record #9253)
Mathematics
UTME / JAMB 2007
Number and Numeration
Solution
The area of a square is 144 sqcm. Find the length of the diagonal.
A
13 cm
B
12√2 cm
C
12 cm
D
11√3 cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of a square = x * x
144 = x2
\sqrt144 = x
12 = x
But d2 = 122 + 122
= 144 + 144
= 288
d = \sqrt288
= \sqrt144 x 2
= 12\sqrt2
Source: Myschool Past Questions Archive (Record #9256)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
The volume of a cylinder is 1200cm3 and the area of its base is 150cm2. Find the height of the cylinder.
A
80.00cm
B
8.00cm
C
0.80cm
D
0.08cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Vol. of cylinder = \(\pi r^2h\) = 1200cm2
Area of base = \(\pi(r^2)\) = 150cm2
h = \(\frac{\text{volume of cylinder}}{\text{base area}} = \frac{1200}{150}\)
= 8.00cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #36295)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
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
Number and Numeration
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)