Question Library
Browse, filter, and study verified past examination questions with step-by-step mathematical reasoning.
Searching 18,000+ Questions...
Sifting topics, KaTeX formulas & verified solutions
Showing 1441–1455 of 2096 verified questions
Sort by:
Mathematics
WAEC / WASSCE 1997
Number and Numeration
Diagram
Solution
The table shows the scores of a group of students in a test. If the average score is 3.5, find the value of x
Attached Figure / Diagram
A
1
B
2
C
3
D
4
E
5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
1 + 8 + 15 + 24 + 12 + x/18 + x = 3.5
120 + 10x = 126 + 7x
3x = 6
x = 2
Source: Myschool Past Questions Archive (Record #23906)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Given that loga2 = 0.693 and loga3 = 1.097, find loga 13.5
A
1.404
B
1.790
C
2.598
D
2.790
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
loga 13.5 = loga \(\frac{27}{2}\)
= 3loga 3 - log2a
= 3 x 1.097 - 0.693
= 2.598
Source: Myschool Past Questions Archive (Record #30786)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
If \(8^{\frac{x}{2}} = (2^{\frac{3}{8}})(4^{\frac{3}{4}}\)), find x
A
\(\frac{3}{8}\)
B
\(\frac{3}{4}\)
C
\(\frac{4}{5}\)
D
\(\frac{5}{4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
8\({\frac{x}{2}}\) = \(2^{\frac{3}{8}})(4^{\frac{3}{4}}\))
applying the laws of indices.
(\(2^{3\times (\frac{x}{2})}) = (2^{\frac{3}{8}})(2^{2\times (\frac{3}{4})}\))
\(2^{\frac{3x}{2}} = (2^{\frac{3}{8}})(2^{(\frac{3}{2})}\))
\(\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}\)
\(\frac{3x}{2} = \frac{3 + 12}{8}\)
\(\frac{3x}{2} = \frac{15}{8}\)
24x = 30
x = \(\frac{30}{24} = \frac{5}{4}\)
Source: Myschool Past Questions Archive (Record #30790)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\)
A
\(\frac{19 + 4\sqrt{25}}{11}\)
B
\(\frac{19 + 4\sqrt{15}}{11}\)
C
\(\frac{19 + 2\sqrt{15}}{11}\)
D
\(\frac{19 + 2\sqrt{15}}{19}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - 2\sqrt{3})}\)
= \(\frac{57 + 12\sqrt{15}}{33}\)
=\(\frac{19 + 4\sqrt{15}}{11}\)
Source: Myschool Past Questions Archive (Record #30793)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years
A
6%
B
8%
C
10%
D
12%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
1 = \(\frac{PRT}{100}\)
1 = 1240 - 1000
= 240
R = \(\frac{240 \times 100}{100 \times 3}\)%
= 8%
Source: Myschool Past Questions Archive (Record #30795)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find X ∩( Y ∪ Z)
A
(p, o, u, r)
B
(s, p, d, r)
C
(s, p, n, e)
D
(n, d, u)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(Y \cup Z\) = \({s, e, n, o, u, p, r}\)
\(X \cap (Y \cup Z)\) = \({p, e, n}\)
Source: Myschool Past Questions Archive (Record #30797)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo?
A
0
B
9
C
11
D
20
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let the number of students that speak Hausa and Igbo be represented by H and I respectively.
n(H only) = 80 - 9 = 71.
n(I only) = 20 - 9 = 11.
n(neither H nor I) = 100 - (71 + 9 + 11)
= 100 - 91 = 9 students.
Source: Myschool Past Questions Archive (Record #30798)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
If the function f(fx) = x3 + 2x2 + qx - 6 is divisible by x + 1, find q
A
-5
B
-2
C
2
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x + 1 = 0, x = -1; f(x) = x3 + 2x2 + qx - 6
0 = -1 + 2 - q - 6
q = -5
Source: Myschool Past Questions Archive (Record #30799)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Find the minimum value of X2 - 3x + 2 for all real values of x
A
-\(\frac{1}{4}\)
B
-\(\frac{1}{2}\)
C
\(\frac{1}{4}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
y = X2 - 3x + 2, \(\frac{dy}{dx}\) = 2x - 3
at turning pt, \(\frac{dy}{dx}\) = 0
∴ 2x - 3 = 0
∴ x = \(\frac{3}{2}\)
\(\frac{d^2y}{dx^2}\) = \(\frac{d}{dx}\)(\(\frac{d}{dx}\))
= 270
∴ ymin = 2\(\frac{3}{2}\) - 3\(\frac{3}{2}\) + 2
= \(\frac{9}{4}\) - \(\frac{9}{2}\) + 2
= -\(\frac{1}{4}\)
Source: Myschool Past Questions Archive (Record #30804)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
A
\(\frac{gv-t^2}{gt^2}\)
B
\(\frac{gt^2}{gv-t^2}\)
C
\(\frac{v}{\frac{1}{t^2} - \frac{1}{g}}\)
D
\(\frac{gv}{t^2 - g}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
t2 = \(\frac{v}{\frac{1}{f} + \frac{1}{g}}\)
= \(\frac{vfg}{ftg}\)
\(\frac{1}{f} + \frac{1}{g}\) = \(\frac{v}{t^2}\)
= (g + f)t2 = vfg
gt2 = vfg - ft2
gt2 = f(vg - t2)
f = \(\frac{gt^2}{gv-t^2}\)
Source: Myschool Past Questions Archive (Record #30807)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
What value of g will make the expression 4x2 - 18xy + g a perfect square?
A
9
B
\(\frac{9y^2}{4}\)
C
81y^2
D
\(\frac{18y^2}{4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4x2 - 18xy + g = g \(\to\) (\(\frac{18y}{4}\))2
= \(\frac{18y^2}{4}\)
Source: Myschool Past Questions Archive (Record #30808)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Find the value of k if \(\frac{5 + 2r}{(r + 1)(r - 2)}\) expressed in partial fraction is \(\frac{k}{r - 2}\) + \(\frac{L}{r + 1}\) where K and L are constants
A
3
B
2
C
1
D
-1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
5 + 2r = k(r + 1) + L(r - 2)
but r - 2 = 0 and r = 2
9 = 3k
k = 3
Source: Myschool Past Questions Archive (Record #30809)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Two binary operations \(\ast\) and \(\oplus\) are defines as m \(\ast\) n = mn - n - 1 and m \(\oplus\) n = mn + n - 2 for all real numbers m, n.
Find the value of 3 \(\oplus\) (4 \(\ast\) 5)
A
60
B
57
C
54
D
42
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
m \(\ast\) n = mn - n - 1, m \(\oplus\) n = mn + n - 2
3 \(\oplus\) (4 \(\ast\) 5) = 3 \(\oplus\) (4 x 5 - 5 - 1) = 3 \(\oplus\) 14
3 \(\oplus\) 14 = 3 x 14 + 14 - 2
= 54
Source: Myschool Past Questions Archive (Record #30818)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68
A
24
B
22
C
-12
D
-21
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x \(\ast\) y = x + y - xy
(x \(\ast\) 2) + (x \(\ast\) 3) = 68
= x + 2 - 2x + x + 3 - 3x = 68
-3x = 63
x = -21
Source: Myschool Past Questions Archive (Record #30819)
Mathematics
UTME / JAMB 1997
Number and Numeration
Solution
Each of the base angles of a isosceles triangle is 58^\circ and the verticles of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.
A
128o
B
16o
C
64o
D
58o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Base angle of the triangle = 58^\circ.
The third angle = 180^\circ - (58^\circ + 58^\circ)
= 64^\circ
Angle subtended at the centre = \(2 \times 64^\circ = 128^\circ\) (angle at the centre is twice the angle at the circumference).
Source: Myschool Past Questions Archive (Record #30822)