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Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is
A
21
B
42
C
63
D
18
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let f(p) = 6p3 - p2 - 47p + 30
Then by the remainder theorem,
(p - 3): f(3) = remainder R,
i.e. f(3) = 6(3)3 - (3)2 - 47(3) + 30 = R
162 - 9 - 141 + 30 = R
192 - 150 = R
R = 42
Source: Myschool Past Questions Archive (Record #27048)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\)
A
12\(\frac{8}{5}\)
B
15
C
10
D
28\(\frac{8}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
P \(\propto\) mu, p \(\propto \frac{1}{q}\)
p = muk ................ (1)
p = \(\frac{1}{q}k\).... (2)
Combining (1) and (2), we get
P = \(\frac{mu}{q}k\)
4 = \(\frac{m \times u}{1}k\)
giving k = \(\frac{4}{6} = \frac{2}{3}\)
So, P = \(\frac{mu}{q} \times \frac{2}{3} = \frac{2mu}{3q}\)
Hence, P = \(\frac{2 \times 6 \times 4}{3 \times \frac{8}{5}}\)
P = \(\frac{2 \times 6 \times 4 \times 5}{3 \times 8}\)
p = 10
Source: Myschool Past Questions Archive (Record #27049)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
If r varies inversely as the square root of s and t, how does s vary with r and t?
A
s varies inversely as r and t2
B
s varies inverely as r2 and t
C
s varies directly as r2 and t2
D
s varies directly as r and t
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(r \propto \frac{1}{\sqrt{s}}, r \propto \frac{1}{\sqrt{t}}\)
\(r \propto \frac{1}{\sqrt{s}}\) ..... (1)
\(r \propto \frac{1}{\sqrt{t}}\) ..... (2)
Combining (1) and (2), we get
\(r = \frac{k}{\sqrt{s} \times \sqrt{t}} = \frac{k}{\sqrt{st}}\)
This gives \(\sqrt{st} = \frac{k}{r}\)
By taking the square of both sides, we get
st = \(\frac{k^2}{r^2}\)
s = \(\frac{k^2}{r^{2}t}\)
Source: Myschool Past Questions Archive (Record #27050)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
Evaluate 3(x + 2) > 6(x + 3)
A
x < 4
B
x > -4
C
x < -4
D
x > 4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3(x + 2) > 6(x + 3)
3x + 6 > 6x + 18
3x - 6x > 18 - 6
-3x > 12
x < -4
Source: Myschool Past Questions Archive (Record #27051)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4)
A
24
B
16
C
14
D
26
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x * y = x + 2y (given)
3 * 4 = 3 + 2(4) = 11
Hence, 2 * (3 * 4) = 2 * 11
= 2 + 2(11)
= 2 + 22
= 24
Source: Myschool Past Questions Archive (Record #27055)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
If y = (2x + 2)\(^3\), find \(\frac{\delta y}{\delta x}\)
A
3(2x +2)2
B
6(2x +2)
C
3(2x +2)
D
6(2x +2)2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(y = (2x + 2)^{3}\)
\(\frac{\mathrm d y}{\mathrm d x} = 3(2x + 2)^{3 - 1} . 2\)
= \(6(2x + 2)^{2}\)
Source: Myschool Past Questions Archive (Record #27059)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
In how many ways can a student select 2 subjects from 5 subjects?
A
\(\frac{5!}{3!}\)
B
\(\frac{5!}{2!2!}\)
C
\(\frac{5!}{2!3!}\)
D
\(\frac{5!}{2!}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
A student can select 2 subjects from 5 subjects in;
5C3 ways, i.e. = \(\frac{5!}{2!(5 - 2)!}\)
= \(\frac{5!}{2!3!}\)
Source: Myschool Past Questions Archive (Record #27127)
Mathematics
UTME / JAMB 2013
Number and Numeration
Solution
In how many ways can 3 seats be occupied if 5 people are willing to sit?
A
60
B
20
C
5
D
120
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
5 people can take 3 places in;
5P3 ways, = \(\frac{5!}{(5 - 3)!}\) = \(\frac{5!}{2!}\)
= \(\frac{5 \times 4 \times 3 \times 2!}{2!}\)
= 5 x 4 x 3
= 60 ways
Source: Myschool Past Questions Archive (Record #27129)
Mathematics
UTME / JAMB 2013
Number and Numeration
Diagram
Solution
The graph above is correctly represented by
Attached Figure / Diagram
A
y = x2 - x - 2
B
y = x2 - 3x + 2
C
y = x2 - x - 1
D
y = x2 + x - 2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The graph crosses the x-axis at x = -1 and x = 2
Thus, x + 1 = 0 and x - 2 = 0
x\(^2\) - 2x + x - 2 = 0
x\(^2\) - x - 2 = 0
giving y = x\(^2\) - x - 2
Source: Myschool Past Questions Archive (Record #33151)
Mathematics
UTME / JAMB 2013
Number and Numeration
Diagram
Solution
In the diagram given, find the value of x.
Attached Figure / Diagram
A
30o
B
40o
C
45o
D
15o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram above, o
(base o - (15 + 15)o
= 180o - 30o = 150o
But x + 110o = 150o
(Sum of opp. interior o - 110o = 40o
Source: Myschool Past Questions Archive (Record #33152)
Mathematics
UTME / JAMB 2013
Number and Numeration
Diagram
Solution
The bar chart above shows the allotment of time(in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?
Attached Figure / Diagram
A
460mins
B
720mins
C
960mins
D
200mins
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
80 + 160 + 200 + 80 + 128 + 72 = 720minutes
Source: Myschool Past Questions Archive (Record #33154)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
If 9(2 - x) = 3, find x
A
1
B
\(\frac{3}{2}\)
C
2
D
\(\frac{5}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
9(2 - x) = 3
32(2 - x) = 3
2(2 - x) = 1
4 - 2x = 1
-2x = 1 - 4
-2x = -3
x = \(\frac{-3}{-2}\)
x = \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #36837)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
In what number base is the addition 465 + 24 + 225 = 1050?
A
ten
B
nine
C
eight
D
seven
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 #36838)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
Simplify \(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
A
9
B
4\(\frac{1}{2}\)
C
2
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
from numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)
= \(\frac{15}{8} \times \frac{12}{5}\)
= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)
from denominator \(6\frac{3}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \times \frac{4}{3}\)
= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)
\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36844)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
If Un = n(n2 + 1), evaluate U5 - U4
A
18
B
56
C
62
D
80
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Un = n(n2 + 1)
U5 = 5(2 + 1)
= 5(25 + 1)
= 5(26) = 130
U4 = 4(42 + 1) = 4(16 + 1)
= 4(17) = 68
U5 - U4 = 130 - 68
= 62
Source: Myschool Past Questions Archive (Record #36850)