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Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take?
A
\(\frac{3}{16}\)
B
\(\frac{7}{16}\)
C
\(\frac{9}{16}\)
D
\(\frac{13}{16}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket.
If the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)
Next, the second child takes \(\frac{3}{4}\) of the remainder
which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\)
= \(\frac{3}{4}\) x \(\frac{3}{4}\)
= \(\frac{9}{16}\)
the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\)
= \(\frac{12 - 9}{16}\)
= \(\frac{3}{16}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #31433)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?
A
\(\frac{1}{2}\)%
B
2\(\frac{1}{2}\)%
C
1.5%
D
25%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Interest I = \(\frac{PRT}{100}\)
∴ R = \(\frac{100 \times 1}{100 \times 5}\)
= \(\frac{100 \times 7.50}{500 \times 5}\)
= \(\frac{750}{500}\)
= \(\frac{3}{2}\)
= 1.5%
Source: WAEC / JAMB / NECO Classroom Archive (Record #31432)
Mathematics
UTME / JAMB 1990
Number and Numeration
Solution
A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pope is 10cm.Find the volume of metal used in making 3m of the pipe.
A
153\(\pi\)cm3
B
207\(\pi\)cm3
C
15 300\(\pi\)cm3
D
20 700\(\pi\)cm3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Volume of a cylinder = \pir\(^2\)h
First convert 3m to cm by multiplying by 100
Volume of External cylinder = \pi \times 13\(^2\) \times 300
Volume of Internal cylinder = \pi \times 10\(^2\) \times 300
Hence; Volume of External cylinder - Volume of Internal cylinder
Total volume (v) = \pi (169 - 100) \times 300
V = \pi \times 69 \times 300
V = 20700\picm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #31479)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Simplify 125\(^{\frac{-1}{3}}\) x 49\(^{\frac{-1}{2}}\) x 10\(^0\)
A
350
B
35
C
1/35
D
1/350
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
125\(^{\frac{-1}{3}}\) x 49\(^{\frac{-1}{2}}\) x 10\(^0\)
= 5\(^{-1}\) x 7\(^{-1}\) x 1
= \(\frac{1}{35}\)
Source: Myschool Past Questions Archive (Record #22599)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
If 3\(^{2x}\) = 27, what is x?
A
1
B
1.5
C
4.5
D
18
E
40.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3\(^{2x}\) = 27
3\(^{2x}\) = 3\(^3\)
2x = 3
x = 1.5
Source: Myschool Past Questions Archive (Record #22600)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Given that 1/3log10 P = 1, find the value of P
A
1/10
B
3
C
10
D
100
E
1000
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
1/3log10P = 1
log10P1/3 = log1010
P1/3 = 10 P = 1000
Source: Myschool Past Questions Archive (Record #22602)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Simplify \(\frac{\log \sqrt{8}}{\log 8}\)
A
1/3
B
1/2
C
1/3log√2
D
1/3log√8
E
1/2log√2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{\log \sqrt{8}}{\log 8}\)
= \(\frac{\log 8^{\frac{1}{2}}}{log 8}\)
= \(\frac{\frac{1}{2} \log 8}{\log 8}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #22603)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Evaluate using the logarithm table, log(0.65)2
A
1.6258
B
0.6272
C
0.6258
D
\(\overline{1}\).6258
E
1.6272
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log(0.65)\(^2\) = 2log(0.65) but log0.65 = \(\overline{1}\).8129
∴2 x \(\overline{1}\).8129 = \(\overline{1}\).6258
Source: Myschool Past Questions Archive (Record #22604)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
If log x = \(\bar{2}.3675\) and log y = 0.9750, what is the value of x + y? Correct to three significant figures
A
1.18
B
1.31
C
9.03
D
9.44
E
9.46
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
log x = \(\bar{2}.3675\) ; log y = 0.9750
\(x = 10^{\bar{2}.3675} = 0.02331 \)
\(y = 10^{0.9750} = 9.441 \)
\(x + y = 9.4641 \approxeq 9.46\)
Source: Myschool Past Questions Archive (Record #22605)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
While doing his physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error
A
1.17%
B
6.38%
C
7.44%
D
8.035%
E
9.00%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
%error = \(\frac{1.21 - 1.12}{1.21} \times 100%\)
= \(\frac{9}{121} \times 100%\)
= 7.44%
Source: Myschool Past Questions Archive (Record #22606)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Diagram
Solution
Find the values of x for which y = 5
Attached Figure / Diagram
A
-2.5, 2.0
B
-2.6, 2.1
C
-2.0, 1.5
D
-2.0, 2.0
E
0, 0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
from the graph, x = - 2.6 and 2.1
Source: Myschool Past Questions Archive (Record #22642)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
In a class of 80 students, every students had to study economics or geography, or both economics and geography, if 65 students studied economics and 50 studied geography, how many studied both subjects?
A
15
B
30
C
35
D
45
E
50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
∩(E∩G) = ∩(E) + ∩(G) - ∩(E∩G)
80 = 65 + 50 - ∩(F∩G)
∴∩(E∩G) = 115 - 80 = 35
Source: Myschool Past Questions Archive (Record #22646)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Factorize x\(^2\) + 4x - 192
A
(x-4) (x+48)
B
(x-48) (x+4)
C
(x-12) (x+16)
D
(x-12) (x-16)
E
(x+12) (x+16)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x\(^2\) + 4x - 192
x\(^2\) + 16x - 12x - 192
x(x + 16) - 12(x + 16)
(x + 16)(x - 12)
Source: Myschool Past Questions Archive (Record #22652)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Factorize 2e\(^2\) - 3e + 1
A
(2e-1) (e-1)
B
(e+1) (2e+1)
C
(2e+3) (e+2)
D
(2e-3) (e-1)
E
(e2-3(2e-1)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2e\(^2\) - 3e + 1
2e\(^2\) - 2e - e + 1
2e(e - 1) - 1(e - 1)
(2e - 1)(e - 1)
Source: Myschool Past Questions Archive (Record #22655)
Mathematics
WAEC / WASSCE 1990
Number and Numeration
Solution
Find the value of m which makes x\(^2\) + 8 + m a perfect square
A
2
B
4
C
8
D
12
E
16
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
x\(^2\) + 8 + m
To make it a perfect square, we add \((\frac{b}{2})^2\)
= \((\frac{8}{2})^2\)
= 16
Source: Myschool Past Questions Archive (Record #22660)