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 601–615 of 2096 verified questions
Sort by:
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
(a) A boy had M Dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to \(\frac{1}{3}\) of M, find the value of M.
(b) A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, \(\frac{13}{30}\) by air and \(\frac{4}{15}\) by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) Amount shared = D(M - 15)
Sister's share = \(\frac{D(M - 15)}{2}\)
\(\implies \frac{D(M - 15)}{2} = \frac{1}{3}M\)
\(2M = 3(M - 15) \implies 3M - 2M = 45\)
\(M = 45.00\)
(b) (i)
(ii) (1) Total no interviewed = \(\frac{2}{5}x + \frac{4}{15}x + \frac{1}{6}x + 20 = x\)
\(\therefore 12x + 8x + 5x + 600 = 30x\) (Multiplying through with their LCM which is 30)
\(600 = 30x - 12x - 8x - 5x = 5x \implies 600 = 5x\)
\(x = \frac{600}{5} = 120\)
(2) Those that travelled by air only = \((\frac{13}{30} \times 120) - (\frac{4}{15} \times 120)\)
= \(52 - 32 = 20\)
Source: Myschool Past Questions Archive (Record #52690)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
(a)
In the diagram, ABCD is a rectangular garden (3n - 1)m long and (2n + 1)m wide. A wire mesh 135m long is used to mark its boundary and to divide it into 8 equal plots. Find the value of n.
(b) A cylinder with base radius 14 cm has the same volume as a cube of side 22 cm. Calculate the ratio of the total surface area of the cylinder to that of the cube. [Take \(\pi = \frac{22}{7}\)]
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \(3(3n - 1) + 5(2n + 1) = 135\)
\(9n - 3 + 10n + 5 = 135\)
\(19n + 2 = 135\)
\(19n = 135 - 2 = 133\)
\(n = \frac{133}{19} = 7\)
(b) Radius of a cylinder = 14 cm
side of a cube = 22 cm
\(\therefore \frac{22}{7} \times 14 \times 14 \times h = 22 \times 22 \times 22\)
\(44 \times 14 \times h = 22 \times 22 \times 22\)
\(h = \frac{22 \times 22 \times 22}{44 \times 14}\)
= \(\frac{121}{7} cm\)
TSA of a cylinder = \(2\pi r (r + h) = 2 \times \frac{22}{7} \times 14 (14 + \frac{121}{7})\)
= \(88(\frac{98 + 121}{7}) = \frac{88 \times 219}{7}\)
= \(\frac{19272}{7} cm^{2}\)
TSA of a cube = \(6s^{2}\)
= \(6 \times 22 \times 22\)
= \(2904 cm^{2}\)
Ratio = \(\frac{19272}{7} : 2904\)
= \(73 : 77\)
Source: Myschool Past Questions Archive (Record #52727)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
(a) In the diagram, /PQ/ = 6 cm, /QR/ = 13 cm, /RS/ = 5 cm and < RSQ is a right- angled triangle. Calculate, correct to one decimal place, /PS/.
(b) The diagram show a wooden structure in the form of a cone mounted on a hemispherical base. The vertical height of the cone is 24 cm and the base radius 7 cm. Calculate, correct to 3 significant figures, the surface area of the structure. [Take \(\pi = \frac{22}{7}\)].
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)
\(\cos R = \frac{5}{13} = 0.3846\)
\(R = \cos^{-1} (0.3846) = 67.38^\circ\)
\(/PS/^{2} = 5^{2} + 19^{2} - 2(5)(19)\cos 67.38\)
= \(25 + 361 - 190(0.3872)\)
= \(386 - 73.568\)
\(/PS/^{2} = 312.432\)
\(/PS/ = \sqrt{312.432}\)
= \(17.68 \approxeq 17.7 cm\)
(b) Slant height of a cone = \(l = \sqrt{7^{2} + 24^{2}}\)
\(\sqrt{49 + 576} = \sqrt{625}\)
= \(25 cm\)
C.S.A of a cone = \(\pi rl\)
= \(\frac{22}{7} \times 7 \times 25\)
= \(550 cm^{2}\)
Area of hemisphere = \(\frac{1}{2} \times 4\pi r^{2} = 2 \pi r^{2}\)
\(2 \times \frac{22}{7} \times 7 \times 7 = 308 cm^{2}\)
TSA of the structure = \(550 cm^{2} + 308 cm^{2} = 858 cm^{2}\)
Source: Myschool Past Questions Archive (Record #52734)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74^\circ. Find the distance of the boat from the base of the tree.
A
52 cm
B
43 cm
C
40 cm
D
15 cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\tan 16 = \frac{x}{150}\)
\(x = 150 \tan 16\)
= \(43 cm\)
Source: Myschool Past Questions Archive (Record #54915)
Mathematics
WAEC / WASSCE 2011
Number and Numeration
Solution
One of the factors of (mn - nq - n\(^2\) + mq) is (m - n). The other factor is?
A
(n - q)
B
(q - n)
C
(n + q)
D
(q - m)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
mn - nq - n\(^2\) + mq
mn - n\(^2\) - nq + mq
(mn - n\(^2\)) (mq - nq)
n(m - n) + q(m - n)
= (n +q) (m - n)
Source: WAEC / JAMB / NECO Classroom Archive (Record #36639)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
If 2q35 = 778, find q
A
2
B
1
C
4
D
O
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2q35 = 778
2 x 52 + q x 51 + 3 x 50 = 7 x 81 + 7 x 80
2 x 25 + q x 5 + 3 x 1 = 7 x 8 + 7 x 1
50 + 5q + 3 = 56 + 7
5q = 63 - 53
q = \(\frac{10}{5}\)
q = 2
Source: Myschool Past Questions Archive (Record #27410)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
Simplify \(\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
A
\(5\frac{2}{3}\)
B
30
C
\(4\frac{1}{3}\)
D
50
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
\(\frac{\frac{11}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)
\(\frac{110}{54} \div \frac{66}{1620}\)
50
Source: Myschool Past Questions Archive (Record #27413)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
A man invested N5,000 for 9 months at 4%. What is the simple interest?
A
N150
B
N220
C
N130
D
N250
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
S.I. = \(\frac{P \times R \times T}{100}\)
If T = 9 months, it is equivalent to \(\frac{9}{12}\) years
S.I. = \(\frac{5000 \times 4 \times 9}{100 \times 12}\)
S.I. = N150
Source: Myschool Past Questions Archive (Record #27414)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
If the numbers M, N, Q are in the ratio 5:4:3, find the value of \(\frac{2N - Q}{M}\)
A
2
B
3
C
1
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
M:N:Q == 5:4:3
i.e M = 5, N = 4, Q = 3
Substituting values into equation, we have...
\(\frac{2N - Q}{M}\)
= \(\frac{2(4) - 3}{5}\)
= \(\frac{8 - 3}{5}\)
= \(\frac{5}{5}\)
= 1
Source: Myschool Past Questions Archive (Record #27416)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
Simplify \((\frac{16}{81})^{\frac{1}{4}} \div (\frac{9}{16})^{-\frac{1}{2}}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2}\)
C
\(\frac{8}{9}\)
D
\(\frac{1}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{9}{16})^{-\frac{1}{2}}\)
\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{16}{9})^{\frac{1}{2}}\)
\((\frac{2^4}{3^4})^{\frac{1}{4}} \div (\frac{4^2}{3^2})^{\frac{1}{2}}\)
\(\frac{2^{4 \times \frac{1}{4}}}{3^{4 \times \frac{1}{4}}} \div \frac{4^{2 \times \frac{1}{2}}}{3^{2 \times \frac{1}{2}}}\)
\(\frac{2}{3} \div \frac{4}{3}\)
\(\frac{2}{3} \times \frac{3}{4}\)
\(\frac{2}{4}\)
\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #27418)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
If log318 + log33 - log3x = 3, Find x.
A
1
B
2
C
o
D
3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3log33
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = log333
log3(\(\frac{18 \times 3}{X}\)) = log333
\(\frac{18 \times 3}{X}\) = 33
18 x 3 = 27 x X
x = \(\frac{18 \times 3}{27}\)
= 2
Source: Myschool Past Questions Archive (Record #29335)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
Rationalize \(\frac{2 - \sqrt5}{3 - \sqrt5}\)
A
\(\frac{1 - \sqrt5}{2}\)
B
\(\frac{1 - \sqrt5}{4}\)
C
\(\frac{ \sqrt5 - 1}{2}\)
D
\(\frac{1 + \sqrt5}{4}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)
\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)
= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)
= \(\frac{1 - \sqrt5}{4}\)
Source: Myschool Past Questions Archive (Record #29353)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
Simplify (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
A
\(\frac{7}{3}\)
B
\(\frac{5}{3}\)
C
\(\frac{5}{2}\)
D
\(\frac{3}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
= 2 - \(\frac {1}{3}\)
= \(\frac {16 - 1}{3}\)
= \(\frac{5}{3}\)
Source: Myschool Past Questions Archive (Record #29358)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
Raial has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms, how many choices does she have?
A
49
B
170
C
21
D
210
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The first poster has 7 ways to be arranges, the second poster can be arranged in 6 ways and the third poster in 5 ways.
= 7 x 6 x 5
= 210 ways
or \(\frac{7}{P_3}\) = \(\frac{7!}{(7 - 3)!}\) = \(\frac{7!}{4!}\)
= \(\frac{7 \times 6 \times 5 \times 4!}{4!}\)
= 210 ways
Source: Myschool Past Questions Archive (Record #29369)
Mathematics
UTME / JAMB 2011
Number and Numeration
Solution
Make R the subject of the formula if T = \(\frac {KR^2 + M}{3}\)
A
\(\sqrt\frac{3T - K}{M}\)
B
\(\sqrt\frac{3T - M}{K}\)
C
\(\sqrt\frac{3T + K}{M}\)
D
\(\sqrt\frac{3T - K}{M}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
T = \(\frac{KR^2 + M}{3}\)
3T = KR2 + M
KR2 = 3T - M
R2 = \(\frac{3T - M}{K}\)
R = \(\sqrt\frac{3T - M}{K}\)
Source: Myschool Past Questions Archive (Record #29375)