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Mathematics
UTME / JAMB 2007
Inequalities & Linear Programming
Solution
Solve the inequalities -3(x - 2) < -2(x + 3)
A
x > 12
B
x < 12
C
x > -12
D
x < - 12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
-3(x-3) -12/-1
x > 12
Source: Myschool Past Questions Archive (Record #9230)
Mathematics
UTME / JAMB 2007
Plane Geometry, Polygons & Circle Theorems
Solution
W ∝ L2 and W = 6 when L = 4. If L = √17 find W
A
67/8
B
65/8
C
63/8
D
61/8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
W ∝ L2
W = KL2
K = W/L2
K = 6/42
K = 6/16 = 3/8
W = 3/8 L2
W = 3/8(√17)2
W = 3/8 x 17
W = 51/8 = 63/8
Source: Myschool Past Questions Archive (Record #9231)
Mathematics
UTME / JAMB 2007
Binary Operations, Matrices & Determinants
Solution
A binary operation Δ is defined by aΔb = a + b + 1 for any numbers a and b. Find the inverse of the real number 7 under the operation Δ, if the identity element is -1
A
-7
B
-9
C
5
D
9
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a*e = a + e + 1 = a
implies e+ 1 = 0
∴ e = -1
7 * e = -1
∴ a + 7 + 1 = -1
a + 8 = -1
a+8 = -1
a = -1-8
a = -9
Source: Myschool Past Questions Archive (Record #9232)
Mathematics
UTME / JAMB 2007
Sequences & Series (AP & GP)
Solution
The nth term of the sequence \(\frac{3}{2}\), 3, 7, 16, 35, 74 ..... is
A
5 . 2n-2 - n
B
5 . 2n-2 - \(\frac{(n+1)}{2}\)
C
3 . 2n-2
D
\(\frac{3n}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3/2, 3, 7, 16, 35, 74, ....
Using the method of substitution
When n = 1, 5 . 2n-2 - 1 = 5 . 21-2 - 1
= 5 x 2-1 - 1
= 5 x 1/2 - 1
= 5/2 - 1 = 3/2
When n = 1, 5 . 2n-2 - n
= 5 . 22-2 - 2
= 5 x 20 - 2
= 5 x 1 – 2 = 3
When n = 3, 5 . 2n-2 - n
= 5 . 23-2 - 3
= 5 x 21 - 3
= 5 x 2 – 3
= 10 -3 = 7
When n = 4, 5 . 2n-2 - n
= 5 . 24-2 - 4
= 5 x 22 - 4
= 5 x 4 – 4
= 20 – 4 = 16
When n = 5, 5 . 2n-2 - n
= 5 . 25-2 - 5
= 5 x 23 - 5
= 5 x 8 – 5
= 40 – 5
= 35
When n = 6, 5 . 2n-2 - n
= 5 . 26-2 - 6
= 5 x 24 - 6
= 5 x 16 – 6
= 80 – 6 = 74
∴ 5 . 2n-2 - 1 = 3/2, 3, 7, 16, 35, 74
Source: Myschool Past Questions Archive (Record #9233)
Mathematics
UTME / JAMB 2007
Sequences & Series (AP & GP)
Solution
Find the sum to infinity of the series \(2+\frac{3}{2}+\frac{9}{8}+\frac{27}{32}+......\)
A
1
B
2
C
8
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
a = 2
r = \(\frac{3}{4}\)
S = \(\frac{a}{1-r}\)
S = \(\frac{2}{1-\frac{3}{4}}\)
= \(\frac{2}{\frac{1}{4}}\)
S = \(\frac{2}{1}\times \frac{4}{1}\)
= 8.
Source: Myschool Past Questions Archive (Record #9234)
Mathematics
UTME / JAMB 2007
Indices, Logarithms & Surds
Solution
Find y, if \(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\)
A
5
B
1
C
7
D
3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\sqrt{12}\) -\(\sqrt{147}\) + y\(\sqrt{3}\) = 0
\(\sqrt{4\times 3}\) - \(\sqrt{49\times 3}\) + y\(\sqrt{3}\) = 0
2\(\sqrt{3}\) - 7\(\sqrt{3}\) + y\(\sqrt{3}\) = 0
y\(\sqrt{3}\) = 7\(\sqrt{3}\) - 2\(\sqrt{3}\)
y = \(\frac{5\sqrt{3}}{\sqrt{3}}\)
y = 5
Source: Myschool Past Questions Archive (Record #9235)
Mathematics
UTME / JAMB 2007
Plane Geometry, Polygons & Circle Theorems
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
Fractions, Decimals, Percentages & Approximations
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
Indices, Logarithms & Surds
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
Plane Geometry, Polygons & Circle Theorems
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
Plane Geometry, Polygons & Circle Theorems
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
Fractions, Decimals, Percentages & Approximations
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
Sets, Logic & Venn Diagrams
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
Linear, Simultaneous & Quadratic Equations
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
Sets, Logic & Venn Diagrams
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)