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Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
Make Q the subject of formula when \(L=\frac{4}{3}M\sqrt{PQ}\)
A
\(\frac{9L^2}{16M^2P}\)
B
\(\frac{3L}{4M\sqrt{P}}\)
C
\(\frac{\sqrt{3L}}{4MP}\)
D
\(\frac{3L^2}{16M^2}P\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(L=\frac{4}{3}M\sqrt{PQ}\\
=\frac{3}{4M} \times L = \sqrt{PQ}\\
=\left(\frac{3L}{4M}\right)^2=(\sqrt{PQ})^2\\
=\frac{9L^2}{16M^2}=PQ\\
=Q=\frac{9L^2}{16M^2 P}\)
Source: Myschool Past Questions Archive (Record #9268)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
If 2x\(^2\) - kx - 12 is divisible by x-4, Find the value of k.
A
4
B
5
C
6
D
7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2x2 - kx - 12 is divisible by x-4
implies x is a factor ∴ x = 4
f(4) implies 2(4)2 - k(4) - 12 = 0
32 - 4k - 12 = 0
-4k + 20 = 0
-4k = -20
k = 5
Source: Myschool Past Questions Archive (Record #9269)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6.
A
30
B
21
C
16
D
12
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(x – 3) ∝ y2
X-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2 (6)2
X-3 = 1/2 x 36/1
X-3 = 18
X = 21
Source: Myschool Past Questions Archive (Record #9271)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
If p varies inversely as the square of q and p = 8 when q = 4, find q when p = 32
A
\(\pm\)16
B
\(\pm\)8
C
\(\pm\)4
D
\(\pm\)2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
p ∝ \(\frac{1}{q}\)
p = \(\frac{k}{q}\)
K = q\(^2\)p
= 4\(^2\)(8)
∴ p = \(\frac{128}{\text{q}}\)
32 = \(\frac{128}{\text{q}}\)
q\(^2\) = \(\frac{128}{32}\)
q\(^2\) = 4
q = \sqrt4 = \(\pm\) 2
Source: Myschool Past Questions Archive (Record #9272)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
A binary operation * is defined on the set of positive integers is such x*y = 2x-3y+2 for all positive integers x and y. The binary operation is?
A
commutative and close on the set of positive integers
B
neither commutative nor closed on the set of positive integers
C
commutative but not closed on the set of positive integers
D
not cummutative but closed on the set of positive integers
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
X * Y = 2X - 3Y + 2
2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer
Source: Myschool Past Questions Archive (Record #9276)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
A binary operation on the real set of numbers excluding -1 is such that for all m, n ∈ R, mΔn = m+n+mn. Find the identity element of the operation.
A
1
B
zero
C
-1/2
D
-1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
mΔn = m+n+mn
Let e be the identity element
∴mΔe = eΔm = m
m+e+me = m
e+me = m-m
e+me = 0
e(1+m) = 0
e = 0 / (1+m)
e = 0
Source: Myschool Past Questions Archive (Record #9277)
Mathematics
UTME / JAMB 2008
Number and Numeration
Diagram
Solution
In the diagram above ∠OPQ is?
Attached Figure / Diagram
A
90o
B
53o
C
36o
D
26o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a = a(base ∠s of Iss \Delta)
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53o
Source: Myschool Past Questions Archive (Record #9280)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters
[\pi = 22/7]
A
44,000 liters
B
4,400 liters
C
440 liters
D
44 liters
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
V = \pir2h
1m = 100cm
14cm = 1400cm
\(∴V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\
= 44, 000 liters\)
Source: Myschool Past Questions Archive (Record #9283)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
Evaluate \(\int_1 ^2(6x^2-2x)dx\)
A
16
B
13
C
12
D
11
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\int_1 ^2(6x^2-2x)\)dx = \(\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\)
= \(2x^3 - x^2)_1^2\)
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
Source: Myschool Past Questions Archive (Record #9291)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
On a pie chart there are six sectors of which four angles are 30^\circ, 45^\circ, 60^\circ, 90^\circ and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles.
A
15o
B
30o
C
45o
D
60o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
30 + 45 + 60 + 90 + 2x + x = 360^\circ
225 + 3x = 360
3x = 360 - 225
3x = 135
x = 45^\circ
Source: Myschool Past Questions Archive (Record #9293)
Mathematics
UTME / JAMB 2008
Number and Numeration
Diagram
Solution
The bar chart above shows the number of times the word "a, and , in, it, the ,to" appear in a paragraph in a book.
What is the ratio of the least frequent word to the most frequent word?
Attached Figure / Diagram
A
1/6
B
1/3
C
2/3
D
3/4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Ratio of least to most = 2:12
= 2/12
= 1/6
Source: Myschool Past Questions Archive (Record #9294)
Mathematics
UTME / JAMB 2008
Number and Numeration
Solution
Find the number of ways of selecting 6 out of 10 subjects for an examination
A
128
B
216
C
215
D
210
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(^{10}C_6 = \frac{10!}{(10-6)!6!}\)
= \(\frac{10!}{4!6!}\)
=\(\frac{10\times 9\times 8 \times 7 \times 6!}{4\times 3\times 2\times 1 \times 6!}\)
= 210.
Source: Myschool Past Questions Archive (Record #9300)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
A trader bought 100 tubers at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent.
A
3.6%
B
3.5%
C
3.4%
D
2.55
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Cost price, c.p = \(\frac{100}{5}\) x N350 = N7000
Selling price, s.p = \(\frac{100}{5}\) x N290 = N7250
%Gain = \(\frac{S.p - C.p}{C.p}\) x 100%
= \(\frac{7250 - 7000}{7000}\) x 100% = \(\frac{250 \times 100}{7000}\)
= 3.6% (approx.)
Source: WAEC / JAMB / NECO Classroom Archive (Record #36334)
Mathematics
NECO SSCE 2008
Number and Numeration
Solution
Given that x2 + y2 + k = 60 and x = \(\sqrt{10}\) when y = 4, find the value of k.
A
56
B
34
C
32
D
-34
E
-56
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x\(^2\) + y\(^2\) + k = 60
(\sqrt10)\(^2\) + (4)\(^2\) + k = 60
k + 10 + 16 = 60
k = 60 - 26
k = 34
Source: WAEC / JAMB / NECO Classroom Archive (Record #42529)
Mathematics
NECO SSCE 2008
Number and Numeration
Solution
Bello chooses a number randomly from 1 to 10. What is the probability that it is either odd or prime?
A
\(\frac{1}{10}\)
B
\(\frac{2}{5}\)
C
\(\frac{1}{2}\)
D
\(\frac{3}{5}\)
E
\(\frac{9}{10}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
the numbers from 1,2,3,4,5,6,7,8,9,10. n( total numbers) = 10
the odd numbers are 1, 3, 5, 7, 9 n( odd) = 5
the prime numbers are 2, 3, 5, 7 n( prime) = 4
but total favourable outcome = ( 1,2,3,5,7,9) = 6
Pro( odd or prime no) = \(\frac{6}{10}\) = \(\frac{3}{5}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #42655)